Next: Segmentation Up: Texture Models Previous: Random Fields

## Statistical Models

The aforementioned models are currently the most popular for describing textures. In addition, there are a number of other models for analyzing textures, and while they might not be as popular as the above models, they are by no means useless. They are briefly described below.

Co-occurrence matrices, also called Spatial Grey Level Dependence Matrices, attempt to capture texture using a sparse representation. Each matrix in the set corresponds to an offset (e.g. 2 pixels down and 1 pixel to the left). The entry in row i and column j of each matrix is the number of pixels in the image of grey level i that have a neighbor of grey level j in the direction of the offset. From these matrices a number of statistical quantities can be measured, such as mean, variance, entropy, energy, contrast, and correlation.

The auto-correlation measure in statistics determines how a function varies with itself as it is displaced from the origin. When applied to images, auto-correlation can be used as a measure of the coarseness of textures in different directions.

The Discrete Fourier Transform and the Discrete Cosine Transform are two examples of a general class of mathematical techniques called orthogonal transforms. This set includes some of the filters mentioned in conjunction with image pyramids, such as the Haar transform. In general, a set of orthogonal basis functions is generated, and then each function is convolved with the image to yield a set of numbers at each point.

Textures have also been discriminated on the basis of how many edges fall within a unit area, or how many relative extrema fall within a unit area. A relative extremum in an image is simply a pixel whose grey-level value is higher (or lower) than those of all its immediate neighbors.

Fractals are sometimes used for texture analysis and segmentation because, like texture, fractals have inherent scales attached to them. Rather than guessing at a scale at which the analysis should proceed, a fractal analysis can yield the fractal dimension of a texture, which should indicate the scale.

Next: Segmentation Up: Texture Models Previous: Random Fields

Mark A. Ruzon
Fri Sep 5 16:40:07 PDT 1997