Chapter 3

Image Representation

Wolfgang Birkfellner

3.1 Pixels and Voxels

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,

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