ABSTRACT
In digital image processing, every image is represented by numerical values associated with positions in a regular grid. A single position is usually referenced as picture element, or pixel, and the associated numerical value usually gives a gray value or a color. In medical image processing, we often deal with three-dimensional image elements. Here, the aforementioned numerical value is associated with a point in 3D space, and these positions are called volume elements or voxels. Therefore, an image can be regarded as a discrete mathematical function mapping a position in two-or three dimensional space to a number. Formally speaking, the image is represented as
I(x, y) = ρ (3.1)
A
for 2D images, and I(x, y, z) = ρ (3.2)
for 3D volume images, where x, y, and z are spatial coordinates, and ρ is the gray value.1
The special case of color images will be discussed soon in Section 3.2. In short, one can imagine the 2D image something similar to a map, where the altitude of a mountain range is translated to different colors or shades of gray. Figure 3.1 shows a single CT slice of the lower abdomen with an enlarged area – the single pixels can be clearly identified.
