ABSTRACT
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