Texture Boundary Classification Using Gabor Filters

Statistical and structural approaches abound for discriminating textures in images. Unfortunately, these approaches are not applicable in many circumstances. The human visual system, though, can discriminate textures robustly. One popular theory, supported by psychophysical and neurophysiological data, is that the visual system acts as an elaborate bank of filters, which interact to provide texture discrimination information [l]. This paradigm has motivated mathematically-baaed filtering models for texture discrimination 12-31. A class of functions often used within these models are the Gabor Elementary Functions (GEFs) [2]. Since the GEFs act as bandpass filters and are the only functions that achieve the lower bound of the space-bandwidth product, they can be designed to be highly selective in both the spatial and frequency domains. Unfortunately, while the filtering models have shown potential and some analytical work has been done to demonstrate the eficacy of GEFs, the relationship between textural diflerences and the filter configurati<on required to discriminate these diflerences is still unknown Define a Gabor filter as the operator G j ( i ( z , y ) ) = l i (z , y ) * h ( z , y ) l , where i ( x , y ) is an image, h ( z , y ) = g ( z , y ) exp[j2r(Uz + Vy)] is a 2-D GEF, * denotes convolution, g(z , y ) = (A) exp [ % I is a 2-D Gaussian, (z, y) represent spatial-domain coordinates, and (U, V ) represent a particular 2-D spatial frequency [a]. Bovik et al. have shown that textures differing significantly in frequency content exhibit differences in their respective amplitude envelopes Gf this can be used for texture discrimination [a]. We show analytically, based on mathematical texture imodels, that the Gabor-filter output Gj exhibits specific types of discontinuities at the boundaries of adjacent textures. A step change in Gj occurs between textures of differing loctal spatial-frequency content. A ridge or valley can occur in Gj between textures that appear identical, but are out of phase with each other. More complex textures can exhibit a combination of these discontinuities in Gj or show a step change in average local statistical variation. These results can be used to define appropriate configurations of Gabor filters for texture segmentation. Experimental results verify these findings.