Image Enhancement

In spite of the signicant advances made in biomedical imaging techniques over

the past few decades several practical factors often lead to the acquisition

of images with less than the desired levels of contrast visibility of detail

or overall quality In the preceding chapters we reviewed several practical

limitations considerations and tradeos that could lead to poor images

When the nature of the artifact that led to the poor quality of the image

is known such as noise as explained in Chapter we may design specic

methods to remove or reduce the artifact When the degradation is due to a

blur function deblurring and restoration techniques described in Chapter

may be applied to reverse the phenomenon In some applications of biomedical

imaging it becomes possible to include additional steps or modications in the

imaging procedure to improve image quality although at additional radiation

dose to the subject in the case of some Xray imaging procedures as we shall

see in the sections to follow

In several situations the understanding of the exact cause of the loss of

quality is limited or nonexistent and the investigator is forced to attempt to

improve or enhance the quality of the image on hand using several techniques

applied in an ad hoc manner In some applications a nonspecic improve

ment in the general appearance of the given image may suce Researchers

in the eld of image processing have developed a large repertoire of image en

hancement techniques that have been demonstrated to work well under certain

conditions with certain types of images Some of the enhancement techniques

indeed have an underlying philosophy or hypothesis as we shall see in the

following sections however the practical application of the techniques may

encounter diculties due to a mismatch between the applicable conditions or

assumptions and those that relate to the problem on hand

A few biomedical imaging situations and applications where enhancement

of the feature of interest would be desirable are

Microcalcications in mammograms

Lung nodules in chest Xray images

Vascular structure of the brain

Hairline fractures in the ribs

Some of the features listed above could be dicult to see in the given im

age due to their small size subtlety small dierences in characteristics with

respect to their surrounding structures or low contrast others could be ren

dered not readily visible due to superimposed structures in planar images

Enhancement of the contrast edges and general detail visibility in the im

ages without causing any distortion or artifacts would be desirable in the

applications mentioned above

In this chapter we shall explore a wide range of image enhancement tech

niques that can lead to improved contrast or visibility of certain image fea

tures such as edges or objects of specic characteristics In extending the

techniques to other applications it should be borne in mind that ad hoc

procedures borrowed from other areas may not lead to the best possible or

optimal results Regardless if the improvement so gained is substantial and

consistent as judged by the users and experts in the domain of application

one may have on hand a practically useful technique See the July and

May issues of the Proceedings of the IEEE for reviews and articles on

digital image processing including historically signicant images

Digital Subtraction Angiography

In digital subtraction angiography DSA an Xray contrast agent such as

an iodine compound is injected so as to increase the density attenuation co

ecient of the blood within a certain organ or system of interest A number

of Xray images are taken as the contrast agent spreads through the arterial

network and before the agent is dispersed via circulation throughout the body

An image taken before the injection of the agent is used as the mask or ref

erence image and subtracted from the live images obtained with the agent

in the system to obtain enhanced images of the arterial system of interest

Imaging systems that perform contrastenhanced Xray imaging without

subtraction in a motion or cine mode are known as cineangiography systems

Such systems are useful in studying circulation through the coronary system

to detect sclerosis narrowing or blockage of arteries due to the deposition of

cholesterol calcium and other substances

Figures a b and c show the mask live and the result of DSA

respectively illustrating the arterial structure in the brain of a subject

The arteries are barely visible in the live image Figure b in

spite of the contrast agent Subtraction of the skull and the other parts that

have remained unchanged between the mask and the live images has resulted

in greatly improved visualization of the arteries in the DSA image Figure

c The mathematical procedure involved may be expressed simply as

f f

f

or

fmn f

mn f

mn

where f

is the live image f

is the mask image and are weighting factors

if required and f is the result of DSA

The simple mathematical operation of subtraction on a pixelbypixel ba

sis has indeed a signicant application in medical imaging The technique

however is sensitive to motion which causes misalignment of the components

to be subtracted The DSA result in Figure c demonstrates motion

artifacts in the lowest quarter and around the periphery of the image Meth

ods to minimize motion artifact in DSA have been proposed by Meijering et

al Figure d shows the DSA result after correction of

motion artifacts Regardless of its simplicity DSA carries a certain risk of

allergic reaction infection and occasionally death due to the injection of the

contrast agent

Dualenergy and Energysubtraction Xray Imaging

Dierent materials have varying energydependent Xray attenuation coe

cients Xray measurements or images obtained at multiple energy levels also

known as energyselective imaging could be combined to derive information

about the distribution of specic materials in the object or body imaged

Weighted combinations of multipleenergy images may be obtained to display

softtissue and hardtissue details separately The disadvantages of dual

energy imaging exist in the need to subject the patient to two or more Xray

exposures at dierent energy or kV Furthermore due to the time lapse

between the exposures motion artifacts could arise in the resulting image

In a variation of the dualenergy method MacMahon describes

energysubtraction imaging using a dualplate CR system The Fuji FCR

ES Fujilm Medical Systems USA Stamford CT digital chest unit uses

two receptor plates instead of one The plates are separated by a copper lter

The rst plate acquires the fullspectrum Xray image in the usual manner

The copper lter passes only the highenergy components of the X rays on

to the second plate Because bones and calciumcontaining structures would

have preferentially absorbed the lowenergy components of the X rays and

because the highenergy components would have passed through lowdensity

tissues with little attenuation the transmitted highenergy components could

be expected to contain more information related to denser tissues than to

lighter tissues The two plates capture two dierent views derived from the

same Xray beam the patient is not subjected to two dierent imaging ex

posures but only one Weighted subtraction of the two images as in Equa

tion provides various results that can demonstrate soft tissues or bones

and calcied tissues in enhanced detail see Figures and

a b

c d

FIGURE

a Mask image of the head of a patient for DSA b Live image c DSA

image of the cerebral artery network d DSA image after correction of mo

tion artifacts Image data courtesy of EHW Meijering and MA Viergever

Image Sciences Institute University Medical Center Utrecht Utrecht The

Netherlands Reproduced with permission from EHW Meijering KJ

Zuiderveld and MA Viergever Image registration for digital subtraction

angiography International Journal of Computer Vision

c

Kluwer Academic Publishers

Energysubtraction imaging as above has been found to be useful in de

tecting fracture of the ribs in assessing the presence of calcication in lung

nodules which would indicate that they are benign and hence need not be

examined further or treated and in detecting calcied pleural plaques due

to prolonged exposure to asbestos The bonedetail image in Fig

ure a shows in enhanced detail a small calcied granuloma near the

lowerright corner of the image

FIGURE

Fullspectrum PA chest image CR of a patient See also Figure Im

age courtesy of H MacMahon University of Chicago Chicago IL Repro

duced with permission from H MacMahon Improvement in detection of

pulmonary nodules Digital image processing and computeraided diagnosis

RadioGraphics

c

RSNA

B i o m e d i c a l I m a g e A n a l y s i s

a b

FIGURE

a Bonedetail image and b softtissue detail image obtained by energy subtraction See also Figure Images courtesy

of H MacMahon University of Chicago Chicago IL Reproduced with permission from H MacMahon Improvement in

detection of pulmonary nodules Digital image processing and computeraided diagnosis RadioGraphics

c

RSNA

Temporal Subtraction

Temporal or timelapse subtraction of images could be useful in detecting

normal or pathological changes that have occurred over a period of time

MacMahon describes and illustrates the use of temporal subtraction in

the detection of lung nodules that could be dicult to see in planar chest im

ages due to superimposed structures DR and CR imaging facilitate temporal

subtraction

In temporal subtraction it is desired that normal anatomic structures are

suppressed and pathological changes are enhanced Registration of the images

is crucial in temporal subtraction misregistration could lead to artifacts sim

ilar to those due to motion in DSA Geometric transformation and warping

techniques are useful in matching landmark features that are not expected to

have changed in the interval between the two imaging sessions

Mazur et al describe image correlation and geometric transformation

techniques for the registration of radiographs for temporal subtraction

Grayscale Transforms

The graylevel histogram of an image gives a global impression of the presence

of dierent levels of density or intensity in the image over the dynamic range

available see Section for details and illustrations When the pixels in a

given image do not make full use of the available dynamic range the histogram

will indicate low levels of occurrences of certain graylevel values or ranges

The given image may also contain large areas representing objects with certain

specic ranges of gray level the histogram will then indicate large populations

of pixels occupying the corresponding graylevel ranges Based upon a study

of the histogram of an image we could design grayscale transforms or look

up tables LUTs that alter the overall appearance of the image and could

improve the visibility of selected details

Grayscale thresholding

When the gray levels of the objects of interest in an image are known or

can be determined from the histogram of the given image the image may be

thresholded to obtain a variety of images that can display selected features of

interest For example if it is known that the objects of interest in the image

have graylevel values greater than L

we could create an image for display

as

gmn

if fmn L

if fmn L

where fmn is the original image gmn is the thresholded image to be

displayed and the display range is The result is a bilevel or binary

image Thresholding may be considered to be a form of image enhancement in

the sense that the objects of interest are perceived better in the resulting im

age The same operation may also be considered to be a detection operation

see Section

If the values less than L

were to be considered as noise or features of no

interest and the gray levels within the objects of interest that are greater

than L

are of interest in the displayed image we could also dene the output

image as

gmn

if fmn L

fmn if fmn L

The resulting image will display the features of interest including their gray

level variations

Methods for the derivation of optimal thresholds are described in Sections

and

Example A CT slice image of a patient with neuroblastoma is shown

in Figure a A binarized version of the image with thresholding as in

Equation using L

HU is shown in part b of the gure As

expected the bony parts of the image appear in the result however the

calcied parts of the tumor which also have high density comparable to that

of bone appear in the result The result of thresholding the image as in

Equation with L

HU is shown in part c of the gure The

relative intensities of the hard bone and the calcied parts of the tumor are

evident in the result

Grayscale windowing

If a given image fmn has all of its pixel values in a narrow range of gray

levels or if certain details of particular interest within the image occupy a

narrow range of gray levels it would be desirable to stretch the range of

interest to the full range of display available In the absence of reason to

employ a nonlinear transformation a linear transformation as follows could

be used for this purpose

gmn

if fmn f

fmnf

f

f

if f

fmn f

if fmn f

where fmn is the original image gmn is the windowed image to be

displayed with its grayscale normalized to the range and f

f

is

the range of the original graylevel values to be displayed in the output after

a b

c d

FIGURE

a CT image of a patient with neuroblastoma The tumor which appears as a

large circular region on the lefthand side of the image includes calcied tissues that

appear as bright regions The HU range of has been linearly mapped

to the display range of see also Figures and Image courtesy of

Alberta Childrens Hospital Calgary b The image in a thresholded at the level

of HU as in Equation Values above HU appear as white and values

below this threshold appear as black c The image in a thresholded at the level

of HU as in Equation Values above HU appear at their original level

and values below this threshold appear as black d The HU range of has

been linearly mapped to the display range of as in Equation Pixels

corresponding to tissues lighter than water appear as black Pixels greater than

HU are saturated at the maximum gray level of

stretching to the full range Note that the range in the result needs to

be mapped to the display range available such as which is achieved

by simply multiplying the normalized values by Details pixels below

the lower limit f

will be eliminated rendered black and those above the

upper limit f

will be saturated rendered white in the resulting image The

details within the range f

f

will be displayed with increased contrast and

latitude utilizing the full range of display available

Example A CT slice image of a patient with neuroblastoma is shown

in Figure a This image displays the range of HU linearly

mapped to the display range of as given by Equation The full

range of HU values in the image is HU Part d of the gure

shows another display of the same original data but with mapping of the

range HU to as given by Equation In this result pixels

corresponding to tissues lighter than water appear as black pixels greater

than HU are saturated at the maximum gray level of Graylevel

thresholding and mapping are commonly used for detailed interpretation of

CT images

Example Figure a shows a part of the chest Xray image in Fig

ure b downsampled to pixels The histogram of the image is

shown in Figure a observe the large number of pixels with the gray level

zero Figure b shows two linear grayscale transformations LUTs that

map the range dashdot line and solid line to the range

the results of application of the two LUTs to the image in Figure a

are shown in Figures b and c respectively The image in Figure

b shows the details in and around the heart with enhanced visibility how

ever large portions of the original image have been saturated The image in

Figure c provides an improved visualization of a larger range of tissues

than the image in b regardless the details with normalized gray levels less

than and greater than have been lost

Example Figure a shows an image of a myocyte Figure a

shows the normalized histogram of the image Most of the pixels in the image

have gray levels within the limited range of the remainder of the

available range is not used eectively

Figure b shows the image in a after the normalized graylevel range

of was stretched to the full range of by the linear transformation

in Equation The details within the myocyte are visible with enhanced

clarity in the transformed image The corresponding histogram in Figure

b shows that the image now occupies the full range of gray scale available

however several gray levels within the range are unoccupied as indicated by

the white stripes in the histogram

Gamma correction

Figure shows the HD curves of two devices The slope of the curve is

known as An imaging system with a large could lead to an image with

a b

c

FIGURE

a Part of a chest Xray image The histogram of the image is shown in

Figure a b Image in a enhanced by linear mapping of the range

to c Image in a enhanced by linear mapping of the range

to See Figure b for plots of the LUTs

a

b

FIGURE

a Normalized histogram of the chest Xray image in Figure a entropy

bits b Linear densitywindowing transformations that map the ranges

to dashdot line and to solid line

a b

FIGURE

a Image of a myocyte as acquired originally b Image in a enhanced by

linear mapping of the normalized range to See Figure for

the histograms of the images

high contrast however the image may not utilize the full range of the available

gray scale On the other hand a system with a small could result in an

image with wide latitude but poor contrast Gamma correction is a nonlinear

transformation process by which we may alter the transition from one gray

level to the next and change the contrast and latitude of gray scale in the

image The transformation may be expressed as

gmn fmn

where fmn is the given image with its gray scale normalized to the range

and gmn is the transformed image Note Lindley provides a

dierent denition as

gmn exp

lnffmng

which would be equivalent to the operation given by Equation if the gray

levels were not normalized that is the gray levels were to remain in a range

such as Grayscale windowing as in Equation could also be

incorporated into Equation

Example Figure a shows a part of a chest Xray image Figure

illustrates three transforms with and Parts b and c of

Figure show the results of gamma correction with and

respectively The two results demonstrate enhanced visibility of details in the

darker and lighter grayscale regions with reference to the original image

a

b

FIGURE

Normalized histograms of a the image in Figure a entropy bits

and b the image in Figure b entropy bits

a b

c

FIGURE

a Part of a chest Xray image b Image in a enhanced with

c Image in a enhanced with See Figure for plots of the

gammacorrection transforms LUTs

FIGURE

Gammacorrection transforms with solid line dotted line

and dashdot line

Histogram Transformation

As we saw in Section the histogram of an image may be normalized and

interpreted as a PDF Then based upon certain principles of information

theory we reach the property that maximal information is conveyed when

the PDF of a process is uniform that is the corresponding image has all

possible gray levels with equal probability of occurrence see Section

Based upon this property the technique of histogram equalization has been

proposed as a method to enhance the appearance of an image Other

techniques have also been proposed to map the histogram of the given image

into a dierent desired type of histogram with the expectation that the

transformed image so obtained will bear an enhanced appearance Although

the methods often do not yield useful results in biomedical applications and

although the underlying assumptions may not be applicable in many practical

situations histogrambased methods for image enhancement are popular The

following sections provide the details and results of a few such methods

Histogram equalization

Consider an image fmn of size M N pixels with gray levels l

L Let the histogram of the image be represented by P

f

l as dened in

Equation Let us normalize the gray levels by dividing by the maximum

level available or permitted as r

l

L

such that r Let p

f

r be

the normalized histogram or PDF as given by Equation

If we were to apply a transformation s T r to the random variable r

the PDF of the new variable s is given by

p

g

s p

f

r

dr

ds

rT

s

where g refers to the resulting image gmn with the normalized gray levels

s Consider the transformation

s T r

Z

r

p

f

w dw r

This is the cumulative probability distribution function of r T r has the

following important and desired properties

T r is singlevalued and monotonically increasing over the interval

r This is necessary to maintain the blacktowhite transition order

between the original and processed images

T r for r This is required in order to maintain the

same range of values in the input and output images

It follows that

ds

dr

p

f

r Then we have

p

g

s

p

f

r

p

f

r

rT

s

s

Thus T r equalizes the histogram of the given image that is the histogram

or PDF of the resulting image gmn is uniform As we saw in Section

a uniform PDF has maximal entropy

Discrete version of histogram equalization For a digital image fmn

with a total of P MN pixels and L gray levels r

k

k L

r

k

occurring n

k

times respectively the PDF may be approximated by

the histogram

p

f

r

k

n

k

P

k L

The histogramequalizing transformation is approximated by

s

k

T r

k

k

X

i

p

f

r

i

k

X

i

n

i

P

k L

Note that this transformation may yield values of s

k

that may not equal the

available quantized gray levels The values will have to be quantized and

hence the output image may only have an approximately uniform histogram

In practical applications the resulting values in the range have to

be scaled to the display range such as Histogram equalization is

usually implemented via an LUT that lists the related s

k

r

k

pairs as given

by Equation It should be noted that a quantized histogramequalizing

transformation is likely to contain several segments of manytoone graylevel

transformation this renders the transformation nonunique and irreversible

Example Figure a shows a image of a girl in a snow cave

the high reectivity of the snow has caused the details inside the cave to have

poor visibility Part b of the same gure shows the result after histogram

equalization the histograms of the original and equalized images are shown

in Figure Although the result of equalization shows some of the features

of the girl within the cave better than the original several details remain dark

and unclear

The histogram of the equalized image in Figure b indicates that

while a large number of gray levels have higher probabilities of occurrence

than their corresponding levels in the original see Figure a several gray

levels are unoccupied in the enhanced image observe the white stripes in the

histogram which indicate zero probability of occurrence of the corresponding

gray levels The equalizing transform LUT shown in Figure indicates

that there are several manytoone graylevel mappings note the presence of

several horizontal segments in the LUT It should also be observed that the

original image has a wellspread histogram with an entropy of bits due

to the absence of several gray levels in the equalized image its entropy of

bits turns out to be lower than that of the original

Figure c shows the result of linear stretching or windowing of the

range in the original image in Figure a to the full range of

The result shows the details of the girl and the inside of the cave more clearly

than the original or the equalized version however the highintensity details

outside the cave have been washed out

Figure d shows the result of enhancing the original image in Fig

ure a with Although the details inside the cave are not as

clearly seen as in Figure c the result has maintained the details at all

gray levels

a b

c d

FIGURE

a Image of a girl in a snow cave pixels b Result of histogram

equalization c Result of linear mapping windowing of the range

to d Result of gamma correction with Image courtesy of

WM Morrow

Example Figure a shows a part of a chest Xray image part b

of the same gure shows the corresponding histogramequalized image Al

a

b

FIGURE

Normalized histograms of a the image in Figure a entropy bits

and b the image in Figure b entropy bits See also Figure

FIGURE

Histogramequalizing transform LUT for the image in Figure a see

Figure for the histograms of the original and equalized images

though some parts of the image demonstrate improved visibility of features

it should be observed that the lowdensity tissues in the lower righthand por

tion of the image have been reduced to poor levels of visibility The histogram

of the equalized image is shown in Figure a the equalizing transform

is shown in part b of the same gure It is seen that several gray levels

are unoccupied in the equalized image for this reason the entropy of the

enhanced image was reduced to bits from the value of bits for the

original image

Example Figure b shows the histogramequalized version of the

myocyte image in Figure a The corresponding equalizing transform

shown in Figure b indicates a sharp transition from the darker gray

levels to the brighter gray levels The rapid transition has caused the output

to have high contrast over a small eective dynamic range and has rendered

the result useless The entropies of the original and enhanced images are

bits and bits respectively

Histogram specication

A major limitation of histogram equalization is that it can provide only one

output image which may not be satisfactory in many cases The user has

a b

FIGURE

a Part of a chest Xray image The histogram of the image is shown in

Figure a b Image in a enhanced by histogram equalization The

histogram of the image is shown in Figure a See Figure b for a

plot of the LUT

no control over the procedure or the result In a related procedure known

as histogram specication a series of histogramequalization steps is used to

obtain an image with a histogram that is expected to be close to a prespecied

histogram Then by specifying several histograms it is possible to obtain a

range of enhanced images from which one or more may be selected for further

analysis or use

Suppose that the desired or specied normalized histogram is p

d

t with

the desired image being represented as d having the normalized gray levels

t L Now the given image f with the PDF p

f

r may be

histogramequalized by the transformation

s T

r

Z

r

p

f

w dw r

as we saw in Section to obtain the image g with the normalized gray

levels s We may also derive a histogramequalizing transform for the desired

but as yet unavailable image as

q T

t

Z

t

p

d

w dw t

Observe that in order to derive a histogramequalizing transform we need

only the PDF of the image the image itself is not needed Let us call the

hypothetical image so obtained as e having the gray levels q The inverse

a

b

FIGURE

a Normalized histogram of the histogramequalized chest Xray image in

Figure b entropy bits b The histogramequalizing transfor

mation LUT See Figure a for the histogram of the original image

a b

FIGURE

a Image of a myocyte The histogram of the image is shown in Figure

a b Image in a enhanced by histogram equalization The histogram of

the image is shown in Figure a See Figure b for a plot of the

LUT

of the transform above which we may express as t T

q will map the

gray levels q back to t

Now p

g

s and p

e

q are both uniform PDFs and hence are identical func

tions The desired PDF may therefore be obtained by applying the transform

T

to s that is t T

s It is assumed here that T

s exists and is

a singlevalued unique transform Based on the above the procedure for

histogram specication is as follows

Specify the desired histogram and derive the equivalent PDF p

d

t

Derive the histogramequalizing transform q T

t

Derive the histogramequalizing transform s T

r from the PDF

p

f

r of the given image f

Apply the inverse of the transform T

to the PDF obtained in the previ

ous step and obtain t T

s This step may be directly implemented

as t T

T

r

Apply the transform as above to the given image f the result provides

the desired image d with the specied PDF p

d

t

Although the procedure given above can theoretically lead us to an image

having the specied histogram the method faces limitations in practice Dif

culty arises in the very rst step of specifying a meaningful histogram or

a

b

FIGURE

a Normalized histogram of the histogramequalized myocyte image in Fig

ure b b The histogramequalizing transformation LUT See Figure

a for the histogram of the original image

PDF several trials may be required before a usable image is obtained More

importantly in a practical implementation with discrete gray levels it will be

dicult if not impossible to derive the inverse transform T

The possi

ble existence of manytoone mapping segments in the histogramequalizing

transform T

as we saw in the examples in Section may render inversion

impossible Appropriate specication of the desired PDF could facilitate the

design of an LUT to approximately represent T

The LUTs corresponding

to T

and T

may be combined into one LUT that may be applied to the

given image f to obtain the desired image d in a single step Note that the

image obtained as above may have a histogram that only approximates the

one specied

Limitations of global operations

Global operators such as grayscale and histogram transforms provide simple

mechanisms to manipulate the appearance of images Some knowledge about

the range of gray levels of the features of interest can assist in the design of

linear or nonlinear LUTs for the enhancement of selected features in a given

image Although histogram equalization can lead to useful results in some

situations it is quite common to result in poor images Even if we keep aside

the limitations related to nonunique transforms a global approach to image

enhancement ignores the nonstationary nature of images and hence could

lead to poor results The results of histogram equalization of the chest X

ray and myocyte images in Figures and demonstrate the limitations

of global transforms Given the wide range of details of interest in medical

images such as the hard tissues bone and soft tissues lung in a chest X

ray image it is desirable to design local and adaptive transforms for eective

image enhancement

Localarea histogram equalization

Global histogram equalization tends to result in images where features hav

ing gray levels with low probabilities of occurrence in the original image are

merged upon quantization of the equalizing transform and hence are lost in

the enhanced image Ketchum attempted to address this problem by

suggesting the application of histogram equalization on a local basis In local

area histogram equalization LAHE the histogram of the pixels within a D

sliding rectangular window centered at the current pixel being processed is

equalized and the resulting transform is applied only to the central pixel the

process is repeated for every pixel in the image The window provides the

local context for the pixel being processed The method is computationally

expensive because a new transform needs to be computed for every pixel

Pizer et al Leszczynski and Shalev and Rehm and Dallas

proposed variations of LAHE and extended the method to the enhancement

of medical images In one of the variations of LAHE the histogramequalizing

transforms are computed not for every pixel but only for a number of nonover

lapping rectangular blocks spanning the image The pixels at the center of

each block are processed using the corresponding transform Pixels that are

not at the centers of the blocks are processed using interpolated versions of

the transforms corresponding to the four neighboring center pixels The suc

cess of LAHE depends upon the appropriate choice of the size of the sliding

window in relation to the sizes of the objects present in the image and of the

corresponding background areas

Example The images in Figures c and d show the results of

application of the LAHE method to the image in part a of the gure using

windows of size and pixels respectively The result of

global histogram equalization is shown in part b of the gure for comparison

Although the results of LAHE provide improved visualization of some of the

details within the snow cave the method has led to graylevel inversion in

a few regions black patches in white snow areas this eect is due to the

spreading of the gray levels in a small region over the full range of

which is not applicable to all local areas in a given image The overall quality

of the results of LAHE has been downgraded by this eect

Adaptiveneighborhood histogram equalization

A limitation of LAHE lies in the use of rectangular windows although such

a window provides the local context of the pixel being processed there is

no apparent justication to the choice of the rectangular shape for the mov

ing window Furthermore the success of the method depends signicantly

upon proper choice of the size of the window the use of a xed window of a

prespecied size over an entire image has no particular reasoning

Paranjape et al proposed an adaptiveneighborhood approach to his

togram equalization As we saw in Section the adaptiveneighborhood

image processing paradigm is based upon the identication of variableshape

variablesize neighborhoods for each pixel by region growing Because the

regiongrowing procedure used for adaptiveneighborhood image processing

leads to a relatively uniform region with graylevel variations limited to that

permitted by the specied threshold the local histogram of such a region will

tend to span a limited range of gray levels Equalizing such a histogram and

permitting the occurrence of the entire range of gray levels in any and every

local context is inappropriate In order to provide an increased context to

histogram equalization Paranjape et al included in the local area not only

the foreground region grown but also a background composed of a ribbon

of pixels molded to the foreground see Figure The extent of the local

context provided depends upon the tolerance specied for region growing the

width of the background ribbon of pixels and the nature of graylevel vari

ability present in the given image The method adapts to local details present

in the given image regions of dierent size and shape are grown for each pixel

a b

c d

e f

FIGURE

a Image of a girl in a snow cave pixels b Result of global histogram

equalization Results of LAHE with c a window and d a

window Results of adaptiveneighborhood histogram equalization with e growth

tolerance and background width pixels and f growth tolerance and back

ground width pixels Reproduced with permission from RB Paranjape WM

Morrow and RM Rangayyan Adaptiveneighborhood histogram equalization for

image enhancement CVGIP Graphical Models and Image Processing

c

Academic Press

After obtaining the histogram of the local region the equalizing transform

is derived and applied only to the seed pixel from where the process was

started The same value is applied to all redundant seed pixels in the region

that is to the pixels that have the same graylevel value as the seed for which

the same region would have been grown using a simple tolerance

In an extension of adaptiveneighborhood histogram equalization to color

images proposed by Ciuc et al instead of equalizing the local histogram

an adaptive histogram stretching operation is applied to the local histograms

The enhancement operation is applied only to the intensity of the image

undesired changes to the color balance hue are prevented by this method

Example Figure shows a simple test image with square objects of dif

ferent gray levels as well as its enhanced versions using global localarea and

adaptiveneighborhood histogram equalization The limitations of global his

togram equalization are apparent in the fact that the brighter inner square on

the righthand side of the image remains almost invisible The result of LAHE

permits improved visualization of the inner squares however the artifacts due

to blockwise processing are obvious and disturbing Adaptiveneighborhood

histogram equalization has provided the best result with enhanced visibility

of the inner squares and without any artifacts

FIGURE

a A test image and its enhanced versions by b global or fullframe his

togram equalization c LAHE and d adaptiveneighborhood histogram

equalization Image courtesy of RB Paranjape

Example The images in Figures e and f show the results of ap

plication of the adaptiveneighborhood histogram equalization method to the

image in part a of the gure The two images were obtained using growth

tolerance values of and and background width of and pixels The

larger tolerance and larger background width provide for larger areas of the

local context to be included in the local histogram The result of global his

togram equalization is shown in part b of the gure for comparison The

results of adaptiveneighborhood histogram equalization provide improved vi

sualization of details and image features both inside and outside the snow

cave Furthermore the result with the larger growth tolerance and back

ground ribbon width is relatively free of the graylevel inversion black patches

in otherwise white areas present in the results of LAHE shown in parts c

and d of the same gure

Convolution Mask Operators

Filtering images using convolution masks is a popular approach Several

such masks have been proposed and are in practical use for image enhance

ment Equation demonstrates the use of a simple mask to represent

the local mean lter We shall explore a few other convolution masks

for image enhancement in the following sections

Unsharp masking

When an image is blurred by some unknown phenomenon we could assume

that each pixel in the original image contributes in an additive manner a

certain fraction of its value to the neighboring pixels Then each pixel is

composed of its own true value plus fractional components of its neighbors

The spreading of the value of a pixel into its neighborhood may be viewed as

the development of a local fog or blurred background

In an established photographic technique known as unsharp masking the

given degraded image in its negative form is rst blurred and a positive

transparency is created from the result The original negative and the positive

are held together and a positive print is made of the combination The

procedure leads to the subtraction of the local blur or fog component and

hence to an improved and sharper image

A popular convolution mask that mimics unsharp masking is given by

Observe that the net sum of the values in the mask equals unity therefore

there is no net change in the local average intensity

The operation above may be generalized to permit the use of other local

window sizes and shapes as

f

e

mn gmn

g

mn gmn

This expression indicates that the pixel at the location mn in the enhanced

image f

e

mn is given as a weighted combination of the corresponding pixel

gmn in the given degraded image and the dierence between the pixel

and the local mean

g

mn The expression is equivalent to the mask in

Equation with and the local mean being computed as the average

of the eight neighbors of the pixel being processed Note that because the

mask possesses symmetry about both the x and y axes reversal has no eect

and hence is not required in performing convolution

The relative weighting between the pixel being processed and the local

dierence could be modied depending upon the nature of the image and the

desired eect leading to various values at the central location in the mask

given in Equation Equivalently dierent values of could be used in

Equation Because the local dierence in Equation is a measure of

the local gradient and because gradients are associated with edges combining

the given image with its local gradient could be expected to lead to edge

enhancement or highfrequency emphasis

Example Figure a shows a test image of a clock part b of the

same gure shows the result of unsharp masking using the mask in

Equation It is evident that the details in the image such as the numerals

have been sharpened by the operation However it is also seen that the high

frequency emphasis property of the lter has led to increased noise in the

image

Figures a a a and a show the image of a myocyte

a part of a chest Xray image an MR image of a knee and the Shapes test

image the results of enhancement obtained by the unsharp masking operator

are shown in parts b of the same gures The chest image in particular has

been enhanced well by the operation details of the lungs in the dark region in

the lowerright quadrant of the image are seen better in the enhanced image

than in the original

An important point to observe from the result of enhancement of the Shapes

test image is that the unsharp masking lter performs edge enhancement Fur

thermore strong edges will have a clearly perceptible overshoot and under

shoot this could be considered to be a form of ringing artifact The images

in Figure illustrate the artifact in an enlarged format Although the ar

tifact is not as strongly evident in the other test images the eect is indeed

present Radiologists often do not prefer edge enhancement possibly for this

reason

Note that the unsharp masking operation could lead to negative pixel values

in the enhanced image the user has to decide how to handle this aspect

when displaying the result The illustrations in this section were prepared

by linearly mapping selected ranges of the results to the display range of

as stated in the gure captions compression of the larger dynamic

range in the enhanced image to a smaller display range could mute the eect

of enhancement to some extent

Subtracting Laplacian

Under certain conditions a degraded image g may be modeled as being the

result of a diusion process that spreads intensity values over space as a

function of time according to the partial dierential equation

g

t

r

g

where t represents time is a constant and

r

g

g

x

g

y

In the initial state at t we have gx y fx y the original image

At some time instant t the degraded image gx y is observed

The degraded image may be expressed in a Taylor series as

gx y gx y

g

t

x y

g

t

x y

Ignoring the quadratic and higherorder terms letting gx y fx y

and using the diusion model in Equation we get

f

e

g r

g

where f

e

represents an approximation to f Thus we have an enhanced

image obtained as a weighted subtraction of the given image and its Laplacian

gradient

A discrete implementation of the Laplacian is given by the convolution

mask

a b

c d

FIGURE

a Clock test image b Result of unsharp masking display range

out of c Laplacian gradient of the image display range

out of d Result of the subtracting Laplacian display range

out of

a b

c d

FIGURE

a Image of a myocyte the range from the minimum to the maximum of the

image has been linearly mapped to the display range b Result of

unsharp masking display range out of c Laplacian

gradient of the image display range out of d Result

of the subtracting Laplacian display range out of

a b

c d

FIGURE

a Part of a chest Xray image b Result of unsharp masking display range

out of c Laplacian gradient of the image display

range out of d Result of the subtracting Laplacian

display range out of

a b

c d

FIGURE

a MR image of a knee b Result of unsharp masking display range

out of c Laplacian gradient of the image display

range out of d Result of the subtracting Laplacian

display range out of

a b

c d

FIGURE

a Shapes test image b Result of unsharp masking display range

out of See also Figure c Laplacian gradi

ent of the image display range out of d Result of the

subtracting Laplacian display range out of

a b

FIGURE

Enlarged views of a part of a the Shapes test image and b the result

of unsharp masking see also Figure a and b Observe the edge

enhancement artifact

see also Equation and the associated discussion Observe that the net

weight of the coecients in the Laplacian mask is zero therefore the mask

performs a dierentiation operation that will lead to the loss of intensity

information that is the result in an area of any uniform brightness value will

be zero

Letting the weighting factor in Equation we get the following

mask known as the subtracting Laplacian

Because the net weight of the mask is equal to unity the mask retains the

local average intensity in the image

Comparing Equations and we see that they have a similar struc

ture the main dierence being in the number of the neighboring pixels used

in computing the local gradient or dierence For this reason the unsharp

masking lter is referred to as the generalized subtracting Laplacian by some

authors On the same note the subtracting Laplacian is also an unsharp mask

ing lter For the same reasons as in the case of the unsharp masking lter

the subtracting Laplacian also leads to edge enhancement or highfrequency

emphasis see also Equation and the associated discussion

Example Part c of Figure shows the Laplacian of the test image

in part a of the same gure The Laplacian shows large values positive or

negative at the strong edges that are present in the image Part d of the

gure shows the result of the subtracting Laplacian which demonstrates the

edgeenhancing property of the lter

Figures c c c and c show the Laplacian of the

corresponding images in parts a of the same gures Parts d of the g

ures show the results of the subtracting Laplacian operator The subtracting

Laplacian has provided higher levels of sharpening than the unsharp masking

lter in most cases the result is also noisier in the case of the Clock test

image

Observe that the Laplacian does not maintain the intensity information

present in the image whereas the subtracting Laplacian does maintain this

information the former results in a depiction of the edges gradient present

in the image whereas the latter provides a sharper image As in the case

of unsharp masking the subtracting Laplacian could lead to negative pixel

values in the enhanced image the user has to decide how to handle this aspect

when displaying the result The illustrations in this section were prepared by

linearly mapping selected ranges of the results to the display range of

as stated in the gure captions compression of the larger dynamic range

in the enhanced image to a smaller display range could mute the eect of

enhancement to some extent and also alter the intensity values of parts of

the image

Similar to the artifact introduced by the unsharpmasking operator as illus

trated in Figure the subtracting Laplacian could also introduce disturb

ing overshoot and undershoot artifacts around edges see Figure d This

characteristic of the operator is illustrated using a D signal in Figure

Such artifacts could aect the quality and acceptance of images enhanced

using the subtracting Laplacian

Limitations of xed operators

Fixed operators such as the unsharpmasking and subtractingLaplacian l

ters apply the same mathematical operation at every location over the entire

space of the given image The coecients and the size of such lters do not

vary and hence the lters cannot adapt to changes in the nature of the im

age from one location to another For these reasons xed operators may

encounter limited success in enhancing large images with complex and space

variant features In medical images we encounter a wide latitude of details

for example in a chest Xray image we see softtissue patterns in the lungs

and hardtissue structures such as ribs Similar changes in density may be of

concern in one anatomical region or structure but not in another The spatial

scale of the details of diagnostic interest could also vary signicantly from one

part of an image to another for example from ne blood vessels or bronchial

tubes to large bones such as the ribs in chest Xray images Operators with

xed coecients and xed spatial scope of eect cannot take these factors into

FIGURE

Top to bottom a rectangular pulse signal smoothed with a Gaussian blur

function the rst derivative of the signal the second derivative of the signal

and the result of a lter equivalent to the subtracting Laplacian The deriva

tives are shown with enlarged amplitude scales as compared to the original

and ltered signals

consideration Adaptive lters and operators are often desirable to address

these concerns

Highfrequency Emphasis

Highpass lters are useful in detecting edges under the assumption that high

frequency Fourier spectral components are associated with edges and large

changes in the image This property follows from the eect of dierentiation

of an image on its Fourier transform as expressed by Equation

The ideal highpass lter The ideal highpass lter is dened in the D

Fourier space as

Hu v

ifDu v D

otherwise

where Du v

p

u

v

is the distance of the frequency component at u v

from the DC point u v with the spectrum being centered such that

the DC component is at its center see Figures and D

is

the cuto frequency below which all components of the Fourier transform of

the given image are set to zero Figure a shows the ideal highpass lter

function Figure shows the prole of the lter

The Butterworth highpass lter As we saw in the case of lowpass

lters in Section prevention of the ringing artifacts encountered with

the ideal lter requires that the transition from the stopband to the passband

be smooth The Butterworth lter response is monotonic in the passband as

well as in the stopband See Rangayyan for details and illustrations of

the D Butterworth lter

In D the Butterworth highpass lter is dened as

Hu v

p

h

D

Duv

i

n

where n is the order of the lter Du v

p

u

v

and D

is the half

power D radial cuto frequency the scale factor in the denominator leads to

the gain of the lter being

p

at Du v D

The lters transition from

the stopband to the passband becomes steeper as the order n is increased

Figure b illustrates the magnitude gain of the Butterworth highpass

lter with the normalized cuto D

and order n Figure shows

the prole of the lter

Because the gain of a highpass lter is zero at DC the intensity information

is removed by the lter This leads to a result that depicts only the edges

present in the image Furthermore the result will have positive and negative

a b

FIGURE

a The magnitude transfer function of an ideal highpass lter The cuto

frequencyD

is times the maximum frequency b The magnitude transfer

function of a Butterworth highpass lter with normalized cuto D

and

order n The u v point is at the center Black represents a gain

of zero and white represents a gain of unity See also Figure

values If the enhancement rather than the extraction of edges is desired

it is necessary to maintain the intensity information This eect could be

achieved by using a highemphasis lter dened simply as a highpass lter

plus a constant in the u v space The Butterworth highemphasis lter may

be specied as

Hu v

p

h

D

Duv

i

n

which is similar to the Butterworth highpass lter in Equation except for

the addition of the factors

and

The highemphasis lter has a nonzero gain at DC Highfrequency com

ponents are emphasized with respect to the lowfrequency components in

the image however the lowfrequency components are not removed entirely

Figure shows the prole of the Butterworth highemphasis lter with

D

and n

Examples Figure a shows a test image of a clock part b of the

same gure shows the result of the ideal highpass lter Although the edges

in the image have been extracted by the lter the strong presence of ringing

artifacts diminishes the value of the result Part c of the gure shows the

result of the Butterworth highpass lter where the edges are seen without the

ringing artifact The result of the Butterworth highemphasis lter shown in

FIGURE

Proles of the magnitude transfer functions of an ideal highpass lter solid

line a Butterworth highpass lter dashdot line normalized cuto D

and order n and a Butterworth highemphasis lter dashed line See

also Figure

part d of the gure demonstrates edge enhancement however the relative

intensities of the objects have been altered

Figures a a a and a show the image of a my

ocyte a part of a chest Xray image an MR image of a knee and the Shapes

test image respectively The results of the ideal highpass lter Butterworth

highpass lter and Butterworth highemphasis lter are shown in parts b

c and d respectively of the same gures The distinction between edge

enhancement and edge extraction is demonstrated by the examples

Homomorphic Filtering for Enhancement

We have studied several linear lters designed to separate images that were

added together The question asked has been given gx y fx yx y

how could one extract fx y only Given that the Fourier transform is linear

we know that the Fourier transforms of the images as above are also combined

in an additive manner Gu v F u v u v Therefore a linear lter

will facilitate the separation of F u v and u v with the assumption that

they have signicant portions of their energies in dierent frequency bands

Suppose now that we are presented with an image that contains the product

of two images such as gx y fx y sx y From the multiplication or

convolution property of the Fourier transform we have Gu v F u v

Su v where represents D convolution in the frequency domain How

would we be able to separate fx y from sx y

Furthermore suppose we have gx y hx y fx y where stands

for D convolution as in the case of the passage of the original image fx y

through an LSI system or lter with the impulse response hx y The Fourier

transforms of the signals are related as Gu v Hu vF u v How could

we attempt to separate fx y and hx y

Generalized linear ltering

Given that linear lters are well established and understood it is attractive

to consider extending their application to images that have been combined by

operations other than addition especially by multiplication and convolution

as indicated in the preceding paragraphs An interesting possibility to achieve

this is via conversion of the operation combining the images into addition by

one or more transforms Under the assumption that the transformed images

occupy dierent portions of the transform space linear lters may be applied

to separate them The inverses of the transforms used initially would then

take us back to the original space of the images This approach was proposed

in a series of papers by Bogert et al and Oppenheim et al see

a b

c d

FIGURE

a Clock test image Result of b the ideal highpass lter display range

out of c the Butterworth highpass lter display range

out of and d the Butterworth highemphasis lter dis

play range out of

a b

c d

FIGURE

a Image of a myocyte the range from the minimum to the maximum of the

image has been linearly mapped to the display range Result of b the

ideal highpass lter display range out of c the Butter

worth highpass lter display range out of and d the

Butterworth highemphasis lter display range out of

a b

c d

FIGURE

a Part of a chest Xray image Result of b the ideal highpass lter display

range out of c the Butterworth highpass lter display

range out of and d the Butterworth highemphasis lter

display range out of

a b

c d

FIGURE

a MR image of a knee Result of b the ideal highpass lter display range

out of c the Butterworth highpass lter display range

out of and d the Butterworth highemphasis lter

display range out of

a b

c d

FIGURE

a Shapes test image Result of b the ideal highpass lter display range

out of c the Butterworth highpass lter display

range out of and d the Butterworth highemphasis

lter display range out of

also Childers et al and Rangayyan for details and illustrations of

application to biomedical signals Because the procedure extends the applica

tion of linear lters to multiplied and convolved images it has been referred

to as generalized linear ltering Furthermore as the operations can be repre

sented by algebraically linear transformations between the input and output

vector spaces they have been called homomorphic systems

As a simple illustration of a homomorphic system for multiplied images

consider again the image

gx y fx y sx y

Given the goal of converting the multiplication operation to addition it is

evident that a simple logarithmic transformation is appropriate

loggx y logfx y sx y logfx y logsx y

fx y sx y x y The logarithms of the two images are now

combined in an additive manner Taking the Fourier transform we get

G

l

u v F

l

u v S

l

u v

where the subscript l indicates that the Fourier transform has been applied

to a logtransformed version of the image

Assuming that the logarithmic transformation has not aected the sepa

rability of the Fourier components of the two images fx y and sx y a

linear lter lowpass highpass etc may now be applied to G

l

u v to sep

arate them An inverse Fourier transform will yield the ltered image in the

space domain An exponential operation will complete the reversal procedure

This procedure was proposed by Stockham for image processing in the

context of a visual model

Figure illustrates the operations involved in a multiplicative homo

morphic system or lter The symbol at the input or output of each block

indicates the operation that combines the image components at the corre

sponding step A system of this nature is useful in image enhancement where

an image may be treated as the product of an illumination function and a

transmittance or reectance function The homomorphic lter facilitates the

separation of the illumination function and correction for nonuniform lighting

The method has been used to achieve simultaneous dynamic range compres

sion and contrast enhancement

The extension of homomorphic ltering to separate convolved signals is

described in Section

Example The test image in Figure a shows a girl inside a snow

cave The intensity of illumination of the scene diers signicantly between

the outside and the inside of the snowcave Although there is high contrast

between the outside and the inside of the snowcave there is poor contrast of

the details within the snowcave Because the image possesses a large dynamic

FIGURE

Homomorphic ltering for enhancement of images combined by multiplication

range linear stretching of the graylevel range of the full image is not viable

However a part of the range may be stretched to the full range as illustrated

in Figure

Figure b shows the result of logarithmic transformation of the image

in part a of the gure Although the girl is now visible the image is not

sharp The image was ltered using a Butterworth highemphasis lter as

illustrated in Figure within the context of the homomorphic system

shown in Figure The lter was specied as in Equation with

D

and n The result shown in Figure

c demonstrates reduced dynamic range in terms of the dierence in

illumination between the inside and the outside of the snowcave but increased

contrast and sharpness of the details within the snowcave Application of the

Butterworth highemphasis lter without the homomorphic system resulted

in the image in Figure d which does not present the same level of

enhancement as seen in Figure c

Example A part of a mammogram containing calcications is shown in

Figure a The multiplicative model of an illuminated scene does not ap

ply to Xray imaging however the image has nonuniform brightness density

that aects the visibility of details in the darker regions and could benet

from homomorphic enhancement Figure b shows the result of logarith

mic transformation of the image in part a of the gure the result of ltering

using a Butterworth highemphasis lter is shown in part c The log op

eration has improved the visibility of the calcications in the dark region in

the uppercentral part of the image arranged along an almostvertical linear

pattern application of the Butterworth highemphasis lter illustrated in

Figure has further sharpened these features The result Figure c

a b

c d

FIGURE

a Test image of a girl in a snowcave Result of b log transformation c ho

momorphic ltering including a Butterworth highemphasis lter and d the

Butterworth highemphasis lter only The test image in this illustration is

of size pixels and is slightly dierent from that in Figures

and regardless comparison of the results indicates the advantages of

homomorphic ltering The Butterworth highemphasis lter used is shown

in Figure Image courtesy of WM Morrow

FIGURE

Prole of the highemphasis Butterworth lter used to enhance highfrequency

components along with homomorphic ltering as illustrated in Figures

and

however does not depict the distinction between highdensity tissues bright

areas and lowdensity tissues dark areas

The result of application of the Butterworth highemphasis lter without

the homomorphic system is shown in Figure d This operation has also

resulted in improved depiction of the calcications in the dark regions albeit

not to the same extent as within the context of the homomorphic procedure

Yoon et al extended the application of homomorphic highemphasis

ltering to the wavelet domain for contrast enhancement of mammograms

Adaptive Contrast Enhancement

Diagnostic features in medical images such as mammograms vary widely

in size and shape Classical image enhancement techniques cannot adapt

to the varying characteristics of such features The application of a global

transform or a xed operator to an entire image often yields poor results in

at least some parts of the given image It is therefore necessary to design

methods that can adapt the operation performed or the pixel collection used

to derive measures to the local details present in the image The following

section provides the details of an adaptiveneighborhood approach to contrast

enhancement of images

Adaptiveneighborhood contrast enhancement

Morrow et al proposed an adaptiveneighborhood contrast enhance

ment technique for application to mammograms As we saw in Section in

adaptiveneighborhood or regionbased image processing an adaptive neigh

borhood is dened about each pixel in the image the extent of which is

dependent on the characteristics of the image feature in which the pixel being

processed is situated This neighborhood of similar pixels is called an adaptive

neighborhood or region

Note that in image segmentation groups of pixels are found that have some

property in common such as similar gray level and are used to dene disjoint

image regions called segments Regionbased processing may be performed by

initially segmenting the given image and then processing each segment in turn

Alternatively for regionbased processing we may dene possibly overlapping

regions for each pixel and process each of the regions independently

Regions if properly dened should correspond to image features Then

features in the image are processed as whole units rather than pixels be

ing processed using arbitrary groups of neighboring pixels for example

masks Regionbased processing could also be designated as pixelindependent

a b

c d

FIGURE

a Original image of a part of mammogram with malignant calcications

Result of b log transformation c homomorphic ltering including a But

terworth highemphasis lter and d the Butterworth highemphasis lter

only See also Figures and

processing featurebased processing adaptiveneighborhood

processing or objectoriented processing

The fundamental step in adaptiveneighborhood image processing is den

ing the extent of regions in the image Overlapping regions are used in this

application because disjoint segmentation of an image with subsequent en

hancement of the segments would result in noticeable edge artifacts and an

inferior enhanced image

Seed ll region growing Morrow et al used a regiongrowing

technique based on a simple graphical seedll algorithm also known as pixel

aggregation In this method regions consist of spatially connected pix

els that fall within a specied graylevel deviation from the starting or seed

pixel For highresolution digitized mammograms connectivity was found

by visual comparison to be adequate to allow accurate region growing al

though small features were better matched with connected regions The

use of connectivity for region growing requires longer computing time than

connectivity

The owchart in Figure illustrates the regiongrowing algorithm The

algorithm starts with the pixel being processed called the seed pixel or simply

the seed The seed is placed in an initially empty queue that holds pixels to

be evaluated for inclusion in or exclusion from the region being grown The

main loop is then entered If the queue is empty the program exits the loop

otherwise the rst pixel is taken from the queue This pixel is called the

current pixel if its gray level value is within the specied deviation from the

seed it is labeled as a foreground pixel The immediate neighbors either

connected or connected as specied of the current pixel could possibly

qualify to be foreground pixels and are added to the queue if they are not

already in the queue from being connected to previously checked pixels If

the current pixel is outside the permitted graylevel range it is marked as

a background pixel and a border pixel of the region has been reached A

region may have a number of internal borders in addition to the encompassing

external border Thus the background may consist of more than one set of

pixels with each such set being disconnected from the others After all of the

current pixels neighbors have been checked control is directed back to the

start of the loop to check the next pixel in the queue

The nal step in growing a region around the seed is completing the back

ground This is done by starting with the existing background points as

found during foreground region growing The neighbors of this set of pixels

are examined to see if they belong to either the foreground or background If

not they are set to be the next layer of the background The new layer is then

used to grow another layer and so on until the specied background width is

achieved The regiongrowing procedure as described above does have ine

ciencies in that a given pixel may be checked more than once for placement in

the queue More complicated algorithms may be used to grow regions along

line segments and thereby partially eliminate this ineciency Prelimi

nary testing of a scanline based algorithm showed minimal improvement with

FIGURE

Procedure for region growing for adaptiveneighborhood contrast enhance

ment of mammograms Reproduced with permission from WM Morrow

RB Paranjape RM Rangayyan and JEL Desautels Regionbased con

trast enhancement of mammograms IEEE Transactions on Medical Imaging

c

IEEE

mammogram images because the type of regions grown in mammograms are

usually complex

The adaptiveneighborhood contrast enhancement procedure may be stated

in algorithmic form as follows

The rst pixel or the next unprocessed pixel in the image is taken as

the seed pixel

The immediate neighbors connected pixels of the seed are checked

for inclusion in the region Each neighbor pixel is checked to see if its

graylevel value is within the specied deviation from the seed pixels

graylevel value The growth tolerance or deviation is specied as

fmn seed

seed

where fmn is the graylevel value of the neighbor pixel being checked

for inclusion and the threshold

If a neighbor pixels graylevel value is within the specied deviation it

is added to a queue of foreground pixels that will make up the region

being grown A pixel is added to the queue only if it has not already

been included while processing another connected pixel

A pixel fmn is taken from the start of the foreground queue This be

comes the current pixel whose connected neighbors are checked against

the seeds graylevel according to the tolerance specied as in Steps

and above

If a neighbor pixels graylevel value is outside the specied graylevel

tolerance range it is marked as a background pixel A background

pixel indicates that the border of the region has been reached at that

position However if a neighbor pixels graylevel value is within the

specied deviation it is added to the foreground

Once all the current pixels neighbors have been checked the program

goes back to Step to check the connected neighbor pixels of the next

pixel in the foreground queue

Steps are repeated until region growing stops that is no more

pixels can be added to the foreground region

The borders of the foreground region marked as background pixels

are expanded in all directions by a prespecied number of pixels three

pixels in the work of Morrow et al to obtain a background region

that is molded to the shape of the foreground region The foreground

and background regions together form the adaptive neighborhood of

the seed pixel that was used to start the regiongrowing procedure See

Figure for an example of region growing with an image

The contrast of the region is computed as per Equation and en

hanced as desired see Figure The graylevel value of the seed

pixel is modied as per Equation All pixels in the foreground

region having the same graylevel value as the seed referred to as the

redundant seed pixels are also modied to the same value as for the

seed pixel

Steps are executed until all the pixels in the image have been

processed

It should be noted that each pixel in the connected foreground that has the

same gray level as the seed will lead to the same foreground and background

These pixels are called the regions redundant seed pixels Considerable com

putation may be saved by using this redundancy and obviating the repeated

growing of the same regions Furthermore the same nal transformation

that is applied to the regions seed pixel is also applicable to the regions re

dundant seed pixels In highresolution mammogram images redundant seed

pixels were seen to account for over of the pixels in a given image this

large percentage is partially due to the dark background in the image o the

projection of the breast and due to the relatively smooth variations in gray

levels in mammograms The number of redundant seeds is also dependent

upon the growth tolerance used for region growing

Parameters for region growing The crucial parameter in controlling

seedll region growing is the criterion used to decide whether a pixel is to

be included or excluded in the region This criterion is dened by the growth

tolerance The growth tolerance indicates the deviation positive or nega

tive about the seed pixels gray level that is allowed within the foreground

region For example with a growth tolerance of any pixel with a gray

value between and times the seed pixels value which also satises

the spatialconnectivity criterion is included in the region The reason for

using this type of growth tolerance is found from a closer examination of the

denition of contrast Seedll region growing results in regions having con

trast greater in magnitude than a certain minimum contrast C

min

It is

desired that this minimum contrast be independent of a regions gray level

so that the results of enhancement will be independent of a multiplicative

transformation of the image A region with the minimum positive contrast

C

min

will have a mean foreground value of f and a mean background value of

f Using Equation the minimum contrast C

min

is

C

min

f f

f f

The contrast C

min

is thus independent of the foreground gray level or the

background gray level and depends only upon the regiongrowing tolerance

parameter Webers ratio of for a justnoticeable feature suggests that

the growth tolerance should be about in order to grow regions that are

barely noticeable prior to enhancement and are subsequently enhanced to

a contrast above the Weber ratio A lower bound on may be established

empirically or depending upon the class of images being enhanced through

an analysis of the noise present in the images

Contrast enhancement Equation denes a regions contrast as a

function of the mean gray levels of the foreground f and background b The

contrast of a region may be increased by changing f or b Rearranging Equa

tion and replacing C with an increased contrast C

e

gives

f

e

b

C

e

C

e

where f

e

is the new foreground value Only the seed pixel and the redundant

seed pixels in the foreground are modied to the value f

e

The remaining

pixels in the foreground obtain new values when they in turn act as seed

pixels and are used to grow dierent regions If all the pixels in the foreground

were replaced by f

e

the output image would depend on the order in which

regions are grown furthermore the graylevel variations and details within

each region would be lost and the resulting image would be a collection of

uniform regions The new contrast C

e

for the region may be calculated using

an analytic function of C or an empirically determined

relationship between C

e

and C Morrow et al proposed an empirical

relationship between C

e

and C as shown in Figure which was designed

to boost the perceptibility of regions with lowtomoderate contrast in the

range while not aecting highcontrast regions

Example Contrast enhancement of a cluster of calcications

Figure a shows a part of a mammogram with a cluster of calcications

Some of the calcications are linearly distributed suggesting that they are

intraductal Cancer was suspected because of the irregular shape and size of

the individual constituents of the calcication cluster although hyperdense

tissue could not be clearly seen in this area of the image A biopsy was

subsequently performed on the patient which conrmed the presence of an

invasive intraductal carcinoma

Figure b shows the same part of the image as in a after adaptive

neighborhood contrast enhancement was applied to the entire mammogram

The curve shown in Figure was used as the contrast transformation curve

the growth tolerance was and a background width of three pixels was used

Increased contrast is apparent in the enhanced image and subtle details are

visible at higher contrast Observe the presence of sharper edges between

features the contrast of the calcications has been greatly increased in the

processed image The closedloop feature immediately below the cluster of

calcications is possibly the crosssectional projection of a mammary duct

If this interpretation is correct the distorted geometry dierent from the

normally circular crosssection could be indicative of intraductal malignancy

This feature is not readily apparent in the original image

FIGURE

An empirical relationship between the contrast C of an adaptive neighborhood

and the increased contrast C

e

for enhancement of mammograms C

e

C

for C

In order to compare the results of the adaptiveneighborhood contrast en

hancement method with those of other techniques a simple nonlinear rescaling

or gammacorrection procedure was applied with the output being dened

as gmn f

mn without normalization of the gray scale The result

was linearly scaled to the display range of and is shown in Figure

c Contrast in the area of the calcication cluster was increased at the cost

of decreased contrast in the darker areas of the image Although the enhance

ment is not as good as with adaptiveneighborhood contrast enhancement

the advantage of this method is its simplicity

The unsharp masking lter was applied to the complete mammogram

from which the image in Figure a was obtained The corresponding

portion of the resulting image is shown in Figure d The contrast

and sharpness of the calcication cluster was increased although not to the

same degree as in the image generated using adaptiveneighborhood contrast

enhancement The overall appearance of the image was altered signicantly

from that of the original image

Global histogram equalization of the full mammogram led to complete

washout of the region with the calcications The result shown in Figure

indicates the unsuitability of global techniques for the enhancement of mam

mograms

The enhancement shown in the above case has limited practical value be

cause the characteristics of the calcication cluster in the original image are

sucient to lead the radiologist to recommend biopsy However if mammary

ducts and other anatomical features become more clearly visible in the en

hanced image as suggested above the extent and degree of disease could

be judged more accurately and the biopsy method and location determined

accordingly

Example Contrast enhancement of dense masses Figure

a shows a portion of a mammogram in the lowerright quadrant of which

a dense mass with diuse edges and a spiculated appearance is present The

probable presence of calcications was suggested after examination of the

lm through a hand lens Figure b shows the corresponding part of

the mammogram after adaptiveneighborhood contrast enhancement The

internal details of the mass are more readily seen in the enhanced image the

bright irregular details were suspected to be calcications Also of interest is

the appearance of the dense mass to the left of the spiculated mass The mass

has smooth margins and a generally benign appearance After enhancement

bright irregularly shaped features are apparent in this mass and may possibly

be calcications associated with malignancy as well

Example Contrast enhancement of a benign mass Figure

a shows a part of a mammogram with a histologically veried benign cyst

The brighter regions at the center of the cyst do not demonstrate any irregular

outline they were interpreted to be the result of superimposition of crossing

linear supporting tissues The corresponding portion from the enhanced im

age is shown in Figure b Few changes are apparent as compared with

the original image although contrast enhancement was perceived over the

entire image Enhancement did not aect the appearance or the assessment

of the benign cyst

Objective Assessment of Contrast Enhancement

The improvement in images after enhancement is often dicult to measure

or assess A processed image can be said to be an enhanced version of the

original image if it allows the observer to perceive better the desired infor

mation in the image With mammograms the improvement in perception is

dicult to quantify The use of statistical measures of graylevel distribution

as measures of local contrast enhancement for example variance or entropy

is not particularly meaningful for mammographic images

Morrow et al proposed a new approach to assess image enhancement

through the contrast histogram The contrast histogram represents the distri

bution of contrast of all possible regions present in the image If we measure

the contrast of all regions in the image as obtained by the regiongrowing

procedure described in Section prior to enhancement and subsequent

a b

c d

FIGURE

a Part of a mammogram with a cluster of calcications true size mm

Results of enhancement by b adaptiveneighborhood contrast enhancement

c gamma correction and d unsharp masking See also Figures and

Reproduced with permission from WM Morrow RB Paranjape RM

Rangayyan and JEL Desautels Regionbased contrast enhancement of

mammograms IEEE Transactions on Medical Imaging

c

IEEE

FIGURE

Result of enhancement of the image in Figure a by global histogram

equalization applied to the entire image See also Figures and

Reproduced with permission from WM Morrow RB Paranjape RM

Rangayyan and JEL Desautels Regionbased contrast enhancement of

mammograms IEEE Transactions on Medical Imaging

c

IEEE

a b

FIGURE

a Part of a mammogram with dense masses true size mm b Re

sult of enhancement by adaptiveneighborhood contrast enhancement Repro

duced with permission fromWM Morrow RB Paranjape RM Rangayyan

and JEL Desautels Regionbased contrast enhancement of mammograms

IEEE Transactions on Medical Imaging

c

IEEE

a b

FIGURE

a Part of a mammogram with a benign cyst true size mm b Re

sult of enhancement by adaptiveneighborhood contrast enhancement Repro

duced with permission fromWM Morrow RB Paranjape RM Rangayyan

and JEL Desautels Regionbased contrast enhancement of mammograms

IEEE Transactions on Medical Imaging

c

IEEE

to enhancement the contrast histogram of the enhanced image should contain

more counts of regions at higher contrast levels than the contrast histogram

of the original image Various enhancement methods can be quantitatively

compared by measuring the properties of their respective contrast histograms

The spread of a contrast histogram may be quantied by taking the second

moment about the zerocontrast level For a distribution of contrast values c

i

quantized so that there are N bins over the range the second moment

M

is

M

N

X

i

c

i

pc

i

where pc

i

is the normalized number of occurrences of seed pixels including

redundant seed pixels that lead to the growth of a region with contrast c

i

A lowcontrast image that is an image with a narrow contrast histogram

will have a low value for M

an image with high contrast will have a broader

contrast histogram and hence a greater value of M

For the purpose described above image contrast needs to be recomputed

after the entire image has been enhanced because the relative contrast be

tween adjacent regions is dependent upon the changes made to each of the

regions In order to measure the contrast in an image after enhancement

region growing using the same parameters as in the enhancement procedure

is performed on the output enhanced image and a contrast histogram is gen

erated

In general the nal contrast values in the output image of adaptiveneigh

borhood contrast enhancement will not match the contrast values specied by

the contrast transformation in Equation This is because Equation is

applied pixelbypixel to the input image and the adaptive neighborhood for

each pixel will vary Only if all the pixels in an object have exactly the same

graylevel value will they all have exactly the same adaptive neighborhood

and be transformed in exactly the same way Thus the contrast enhance

ment curve is useful for identifying the ranges in which contrast enhancement

is desired but cannot specify the nal contrast of the regions The contrast

of each region grown in the image is dependent on the value specied by the

initial region contrast and the transformation curve as well as the transfor

mation applied to adjacent regions

Figure shows the contrast histograms of the complete mammograms

corresponding to the images in Figure The contrast distribution is

plotted on a logarithmic scale in order to emphasize the small numbers of

occurrence of features at high contrast values The wider distribution and

greater occurrence of regions at high contrast values in the histogram of the

adaptiveneighborhood enhanced image show that it has higher contrast The

histograms of the results of gamma correction and unsharp masking also show

some increase in the counts for larger contrast values than that of the original

but not to the same extent as the result of adaptiveneighborhood contrast

enhancement The values of M

for the four histograms in Figure are

and

The contrast histogram

and its statistics provide objective means for the analysis of image enhance

ment

Application Contrast Enhancement of Mammo

grams

The accurate diagnosis of breast cancer depends upon the quality of the mam

mograms obtained in particular the accuracy of diagnosis depends upon the

visibility of small lowcontrast objects within the breast image Unfortu

nately the contrast between malignant tissue and normal tissue is often so

low that the detection of malignant tissue becomes dicult Hence the fun

damental enhancement needed in mammography is an increase in contrast

especially for dense breasts

Dronkers and Zwaag suggested the use of reversal lm rather than

negative lm for the implementation of a form of photographic contrast en

hancement for mammograms They found that the image quality produced

a

Figure b

c

d

FIGURE

Contrast histograms of the full mammograms corresponding to the images in Fig

ure a Original M

b adaptiveneighborhood contrast

enhancement M

c gamma correction M

and

d unsharp masking M

Reproduced with permission from WM

Morrow RB Paranjape RM Rangayyan and JEL Desautels Regionbased

contrast enhancement of mammograms IEEE Transactions on Medical Imaging

c

IEEE

was equal to that of conventional techniques without the need for special

mammographic equipment A photographic unsharpmasking technique for

mammographic images was proposed by McSweeney et al This pro

cedure includes two steps rst a blurred image is produced by copying the

original mammogram through a sheet of glass or clear plastic that diuses

the light then by using subtraction print lm the nal image is formed by

subtracting the blurred image from the original mammogram Although the

photographic technique improved the visualization of mammograms it was

not widely adopted possibly due to the variability in the image reproduction

procedure

Askins et al investigated autoradiographic enhancement of mammo

grams by using thiourea labeled with

S Mammograms underexposed as

much as tenfold could be autoradiographically intensied so that the enhanced

image was comparable to a normally exposed lm The limitations to rou

tine use of autoradiographic techniques include cost processing time and the

disposal of radioactive solutions

Digital image enhancement techniques have been used in radiography for

more than three decades See Bankman for a section including dis

cussions on several enhancement techniques Ram stated that images

considered unsatisfactory for medical analysis may be rendered usable through

various enhancement techniques and further indicated that the application of

such techniques in a clinical situation may reduce the radiation dose by about

Rogowska et al applied digital unsharp masking and local contrast

stretching to chest radiographs and reported that the quality of images was

improved Chan et al investigated unsharpmask ltering for digital

mammography according to their receiver operating characteristics ROC

studies unsharp masking could improve the detectability of calcications on

digital mammograms However this method also increased noise and caused

some artifacts

Algorithms based on adaptiveneighborhood image processing to enhance

mammographic contrast were rst reported on by Gordon and Rangayyan

Rangayyan and Nguyen dened a tolerancebased method for

growing foreground regions that could have arbitrary shapes rather than

square shapes Morrow et al further developed this approach with

a new denition of background regions Dhawan et al investigated

the benets of various contrast transfer functions including

p

C ln C

e

C

and tanhC where C is the original contrast but used square

adaptive neighborhoods They found that while a suitable contrast function

was important to bring out the features of interest in mammograms it was

dicult to select such a function Later Dhawan and Le Royer pro

posed a tunable contrast enhancement function for improved enhancement of

mammographic features

Emphasis has recently been directed toward image enhancement based upon

the characteristics of the human visual system leading to innovative

methods using nonlinear lters scalespace lters multiresolution lters and

wavelet transforms Attention has been paid to designing algorithms to en

hance the contrast and visibility of diagnostic features while maintaining con

trol on noise enhancement Laine et al presented a method for nonlinear

contrast enhancement based on multiresolution representation and the use of

dyadic wavelets A software package named MUSICA MUltiScale Im

age Contrast Amplication has been produced by AgfaGevaert Belikova

et al discussed various optimal lters for the enhancement of mammo

grams Qu et al used wavelet techniques for enhancement and evaluated

the results using breast phantom images Tahoces et al presented a mul

tistage spatial ltering procedure for nonlinear contrast enhancement of chest

and breast images Qian et al reported on treestructured nonlinear

lters based on median lters and an edge detector Chen et al pro

posed a regional contrast enhancement technique based on unsharp masking

and adaptive density shifting

The various mammogram enhancement algorithms that have been reported

in the literature may be sorted into three categories algorithms based on

conventional image processing methods adaptive

algorithms based on the principles of human visual perception

and multiresolution enhancement algorithms

In order to evaluate the diagnostic utility of an

enhancement algorithm an ROC study has to be conducted however few of

the abovementioned methods have been tested with

ROC procedures see Sections and for details on ROC analysis

Clinical evaluation of contrast enhancement

In order to examine the dierences in radiological diagnoses that could re

sult from adaptiveneighborhood enhancement of mammograms eight test

cases from the teaching library of the Foothills Hospital Calgary Alberta

Canada were studied in the work of Morrow et al For each of the

cases the pathology was known due to biopsy or other followup procedures

For each case a single mammographic lm that presented the abnormality

was digitized using an Eikonix scanner Eikonix Inc Bedford MA to

by about pixels with bit grayscale resolution The size of

the digitized image diered from lm to lm depending upon the the size

of the actual image in the mammogram The eective pixel size was about

mm mm Films were illuminated by a Plannar light

box Gordon Instruments Orchard Park NY Although the light box was

designed to have a uniform light intensity distribution it was necessary to

correct for nonuniformities in illumination After correction pixel gray levels

were determined to be accurate to bits with a dynamic range of approxi

mately OD

The images were enhanced using the adaptiveneighborhood contrast en

hancement method For all images the tolerance for region growing was set

at the width of the background was set to three pixels and the enhance

ment curve used was that presented in Figure The original and processed

images were downsampled by a factor of two for processing and display for

interpretation on a MegaScan monitor Advanced Video Products Inc

Littleton MA Although the memory buer of the MegaScan system was of

size bits the display buer was limited to

bits with panning and zooming facilities The monitor displayed images at

noninterlaced frames per second

In each case the original digitized mammogram was rst presented on the

MegaScan monitor The image occupied about cm on the screen

An experienced radiologist while viewing the digitized original described the

architectural abnormalities that were observed Subsequently the enhanced

image was added to the display While observing both the enhanced mam

mogram and the original mammogram together the radiologist described any

new details or features that became apparent

Case was that of a yearold patient with a history of diuse nodu

larity in both breasts The MLO view of the left breast was digitized for

assessment The unenhanced mammogram revealed two separate nodular

lesions one with welldened boundaries with some indication of lobular

calcium the other smaller with poorly dened borders some spiculation

but no microcalcications The unenhanced mammogram suggested that the

smaller lesion was most likely associated with carcinoma however there was

some doubt about the origins of the larger lesion An examination of the

enhanced mammogram revealed denite calcium deposits in the larger lesion

and some indication of microcalcications in the smaller lesion The enhanced

image suggested carcinoma as the origin of both lesions more strongly than

the unenhanced mammogram The biopsy report for both areas indicated in

traductal inltrating carcinoma conrming the diagnosis from the enhanced

mammogram

Case was that of a yearold patient The digitized original mam

mogram was the CC view of the left breast The unenhanced mammogram

contained two lesions The lesion in the lowerouter part of the breast had

irregular edges and coarse calcications whereas the other lesion appeared to

be a cyst Examination of the unenhanced mammogram suggested that both

lesions were benign Examination of the enhanced mammogram revealed no

additional details that would suggest a change in the original diagnosis The

appearance of the lesions was not much dierent from that seen in the un

enhanced mammogram however the details in the internal architecture of

the breast appeared clearer adding further weight to the diagnosis of benign

lesions Excision biopsies carried out at both sites conrmed this diagnosis

Case was that of a yearold patient for whom the MLO view of the

left breast was digitized The original digitized mammogram revealed multiple

benign cysts as well as a spiculated mass in the upperouter quadrant of the

breast There was some evidence of calcium but it was dicult to conrm

the same by visual inspection A dense nodule was present adjacent to the

spiculated mass Examination of the enhanced mammogram revealed that the

spiculated mass did contain microcalcications The dense nodule appeared to

be connected to the spiculated mass suggesting a further advanced carcinoma

than that suspected from the unenhanced mammogram Biopsy reports were

available only for the spiculated region and indicated lobular carcinoma No

further information was available to verify the modied diagnosis from the

enhanced mammogram

Case was that of a yearold patient whose mammograms indicated

dense breasts The image of the right breast indicated an area of uniform

density The CC view of the right breast was digitized and enhanced The

digitized original mammogram indicated a cluster of microcalcications all

of approximately uniform density centrally located above the nipple The

enhanced mammogram indicated a similar nding with a larger number of

microcalcications visible and some irregularity in the density of the calci

cations Both the original and the enhanced mammograms suggested a similar

diagnosis of intraductal carcinoma Biopsy of the suspected area conrmed

this diagnosis

Case was that of a yearold patient with a history of a benign mass

in the right breast A digitized mammogram of the CC view of the right

breast was examined The unenhanced mammogram clearly showed numer

ous microcalcications that were roughly linear in distribution with some

variation in density The original mammogram clearly suggested intraductal

carcinoma The enhanced mammogram showed a greater number of calci

cations indicating a lesion of larger extent The variation in the density of

the calcications was more evident Biopsy indicated an inltrating ductal

carcinoma

Case was that of a yearold patient whose right CC view was digitized

The original mammogram indicated a poorly dened mass with some spicu

lations The lesion was irregular in shape and contained some calcium The

unenhanced mammogram suggested intraductal carcinoma The enhanced

mammogram provided stronger evidence of carcinoma with poor margins of

the lesion a greater number of microcalcications and inhomogeneity in the

density of the calcications Biopsy conrmed the presence of the carcinoma

Case involved the same patient as in Case however the mammo

gram was taken one year after that described in Case The digitized

mammogram was the CC view of the right breast The unenhanced view

showed signicant architectural distortion due to segmental mastectomy The

unenhanced mammogram showed an area extending past the scarred region

of fairly uniform density with irregular boundaries The unenhanced mammo

gram along with the patients history suggested the possibility of cancer and

biopsy was recommended The enhanced mammogram suggested a similar

nding with added evidence of some small microcalcications in the uni

form area Biopsy of the region showed that the mass was in fact a benign

hematoma

Case was that of an yearold patient the MLO view of the left breast

was digitized In the unenhanced mammogram a dense region was observed

with some spiculations The mammogram suggested the possibility of carci

noma and biopsy was recommended The enhanced mammogram showed the

same detail as the unenhanced mammogram with the additional nding of

some microcalcications this added to the suspicion of cancer The biopsy of

the region indicated intraductal invasive carcinoma with lymphnode metas

tasis present

In each of the eight cases described above the overall contrast in the en

hanced mammogram was signicantly improved This allowed the radiologist

to comment that much better overall anatomical detail was apparent in

the enhanced mammograms and that overall detail internal architecture

is improved in the enhanced mammograms In all cases the radiological

diagnosis was conrmed by biopsy In seven of the eight cases the enhanced

mammogram added further weight to the diagnosis made from the original

mammogram and the diagnosis was conrmed by biopsy In one case the

enhanced mammogram as well as the unenhanced mammogram suggested

the possibility of carcinoma however the biopsy report indicated a benign

condition This case was however complicated by the fact that the patients

history inuenced the radiologist signicantly While it is not possible to make

a quantitative assessment of the dierences in diagnoses from the qualitative

comparison as above it appeared that a clearer indication of the patients

condition was obtained by examination of the enhanced mammogram

The adaptiveneighborhood contrast enhancement method was used in a

preference study comparing the performance of enhancement algorithms by

Sivaramakrishna et al The other methods used in the study were

adaptive unsharp masking contrastlimited adaptive histogram equalization

and waveletbased enhancement The methods were applied to mammograms

of cases including each of benign and malignant masses and each

of benign and malignant microcalcications The four enhanced images and

the original image of each case were displayed randomly across three high

resolution monitors Four expert mammographers ranked the images from

best to worst In a majority of the cases with microcalcications the

adaptiveneighborhood contrast enhancement algorithm provided the most

preferred images In the set of images with masses the unenhanced images

were preferred in most of the cases

See Sections and for discussions on statistical analysis

of the clinical outcome with enhanced mammograms

Remarks

Quite often an image acquired in a reallife application does not have the

desired level of quality in terms of contrast sharpness of detail or the visibility

of the features of interest We explored several techniques in this chapter that

could assist in improving the quality of a given image The class of lters

based upon mathematical morphology has not been

dealt with in this chapter

An understanding of the exact phenomenon that caused the poor quality

of the image at the outset could assist in the design of an appropriate tech

nique to address the problem However in the absence of such information

one could investigate the suitability of existing and established models of

degradation as well as the associated enhancement techniques to improve the

quality of the image on hand It may be desirable to obtain several enhanced

versions using a variety of approaches the most suitable image may then be

selected from the collection of the processed images for further analysis In

situations as above there is no single or optimal solution to the problem

Several enhanced versions of the given image may also be analyzed simulta

neously however this approach could demand excessive time and resources

and may not be feasible in a largescale screening application

Given the subjective nature of image quality and in spite of the several

methods we studied in Chapter to characterize image quality and infor

mation content the issue of image enhancement is nonspecic and elusive

Regardless if a poorquality image can be enhanced to the satisfaction of

the user and if the enhanced image leads to improved analysis and more

accurate or condent diagnosis in the biomedical context an important

achievement could result

The topic of image restoration image quality improvement when the

exact cause of degradation is known and can be represented mathematically

is investigated in Chapter

Study Questions and Problems

Note Some of the questions may require background preparation with other sources

on the basics of signals and systems as well as digital signal and image processing

such as Lathi Oppenheim et al Oppenheim and Schafer Gonzalez and

Woods Pratt Jain Hall and Rosenfeld and Kak

Selected data les related to some of the problems and exercises are available at

the site

wwwenelucalgarycaPeopleRangaenel

A poorly exposed image was found to have gray levels limited to the range

Derive a linear transform to stretch this range to the display range

of

Give the display values for the original gray levels of and

Explain the dierences between the Laplacian and subtracting Laplacian op

erators in the spatial and frequency domains

Compute by hand the result of linear convolution of the following two images

and

Explain the dierences between the mean and median lters

Would you be able to compare the lters in the Fourier domain Why not

Derive the frequency response of the unsharp masking lter and explain

its characteristics

An image has a uniform PDF normalized graylevel histogram over the range

A novice researcher derives the transform to perform histogram equal

ization

Derive an analytical representation of the transform Explain its eects on

the image in terms of the modication of gray levels and the histogram

An image has a uniform PDF normalized graylevel histogram over the range

with the probability being zero outside this interval within the avail

able range of Derive an analytical representation of the transform to

perform histogram equalization Explain its eects on the image in terms of

the modication of gray levels and the histogram

Give an algorithmic representation of the method to linearly map a selected

range of graylevel values x

x

to the range y

y

in an image of sizeMN

Values below x

are to be mapped to y

and values above x

mapped to y

Use pseudocode format and show all the necessary programming steps and

details

An image with an available graylevel range of at bitspixel has

the following pixel values

Derive the transformation and lookup table for enhancement of the image by

histogram equalization Clearly show all of the steps involved and give the

pixel values in the enhanced image using the available graylevel range of

bitspixel

Draw the histograms of the original image and the enhanced image Explain

the dierences between them as caused by histogram equalization

Write the expression for the convolution of an N N digital image with an

M M digital image or lter function with M N

Using pseudocode format show all of the necessary programming steps and

details related to the implementation of convolution as above

Explain how you handle the size and data at the edges of the resulting image

Prepare a image with zero pixel values Add a square of size pixels

with the value at the center of the image Apply

a the subtracting Laplacian operator

and

b the Laplacian operator

to the image Examine the pixel values inside and around the edges of the

square in the resulting images Give reasons for the eects you nd

Apply

a the subtracting Laplacian operator

and

b the Laplacian operator

to the image in Equation Give reasons for the eects you nd

Derive the MTF of the unsharp masking operator

Explain its characteristics

An image is processed by applying the subtracting Laplacian mask and then

by applying the mean lter mask

What is the impulse response of the complete system

What is the MTF of the complete system

Explain the eect of each operator

Derive the MTF of the subtracting Laplacian operator and explain its

characteristics

What causes ringing artifact in frequencydomain ltering

How do you prevent the artifact

Discuss the dierences between highpass ltering and highfrequency emphasis

ltering in the frequency domain in terms of their

a transfer functions and

b eects on image features

List the steps of computation required in order to perform lowpass ltering

of an image in the frequency domain by using the Fourier transform

Laboratory Exercises and Projects

Select two underexposed images or images with bright and dark regions such

that the details in some parts are not clearly visible from your collection Ap

ply histogram equalization gamma adjustment and linear graylevel mapping

transforms to the images

Compare the results in terms of the enhancement of the visibility of details

saturation or loss of details at the high or low ends of the gray scale and

overall visual quality

Plot the histograms of the resulting images and compare them with the his

tograms of the original images Comment upon the dierences

Select two images from your collection with one containing relatively sharp

and welldened edges and the other containing smooth features

Apply the unsharp masking lter the Laplacian operator and the subtracting

Laplacian lter to the images Study the results in terms of edge enhancement

Create noisy versions of the images by adding Gaussian noise Apply the

enhancement methods as above to the noisy images Study the results in

terms of edge enhancement and the eect of noise

Select two images from your collection with one containing relatively sharp

and welldened edges and the other containing smooth features

Apply the ideal highpass lter the Butterworth highpass lter and the But

terworth highemphasis lter to the images Use at least two dierent cuto

frequencies Study the results in terms of edge enhancement or edge extrac

tion

Create noisy versions of the images by adding Gaussian noise Apply the lters

as above to the noisy images Study the results in terms of edge enhancement

or extraction and the eect of noise