Designing Gabor filters for texture segmentation
Dennis F. Dunn · 1992
Many texture-segmentation schemes use an elaborate bank of filters to decompose a textured image into a joint space/spatial-frequency representation. While these schemes show promise and some analytical work has been done, the relationship between texture differences and the filter configurations required to discriminate them remains largely unknown. This thesis examines the issue of designing individual filters. Analysis based on mathematically defined texture models shows that applying a properly configured bandpass filter to a textured image produces distinct output discontinuities at texture boundaries. Depending on the type of texture difference and the filter parameters, these discontinuities form one of four characteristic signatures: a step, valley, ridge, or a step change in average local output variation. Accompanying experimental evidence indicates that these signatures are useful for segmenting an image. Initially, a simple 1-D texture model is used to derive the step and valley signatures. This model leads to a simple analytical development providing helpful insight. The 1-D model, however, has certain limitations. For example, the existence of the ridge signature cannot be shown using this model. Consequently, a more general 2-D model is also presented, leading to a more complex but informative analysis. In particular, the 2-D analysis indicates those texture characteristics that are responsible for each signature type and leads to detailed filter design criteria. Even the 2-D analysis, though, makes certain simplifying assumptions that lead to inaccuracies in designing filters for nonhomogeneous textures. To overcome this difficulty, an algorithm was developed that determines the best filter parameters for an arbitrary texture pair. The algorithm effectively performs an exhaustive (but efficient) search of the filter parameter space to determine the filter producing the highest quality signature. Signal detection theory is used to provide a measure of signature quality. Although the analyses presented in this study are based on filters derived from Gabor elementary functions, it is the bandpass nature of the filter that is essential; thus, the results apply to bandpass filters in general.