Texture Segmentation using 2-D Gabor Elementary Functions

Many texture-segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint spacehpatial-frequency representation. Although these schemes show promise, and although some analytical work work has been done, the relationship between texture differences and the filter configurations required to distinguish them remain largely unknown. This paper examines the issue of designing individual filters. Using a 2-D texture model, we show analytically that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries; the analysis is based on Gabor elementary functions, but it is the bandpass nature of the filter that is essential. Depending on the type of texture difference, these discontinuities form one of four characteristic signatures: a step, ridge, valley, or a step change in average local output variation. Accompanying experimental evidence indicates that these signatures are useful for segmenting an image. The analysis indicates those texture characteristics that are responsible for each signature type. Detailed criteria are provided for designing filters that can produce quality output signatures. We also illustrate occasions when asymmetric filters are beneficial, an issue not previously addressed.