What Statistics Determine Segmentation of Orientation-Defined Textures?

Abstract

Beck suggested that texture segmentation is based upon differences in the first-order statistics of stimulus features such as orientation, size, and contrast. However, this theory does not indicate how these differences might be quantified, or what properties of the statistics might be used. Some alternative models postulate that texture segmentation is determined by the responses of spatial-frequency channels, where the channels contain both a linear filtering mechanism and various nonlinearities. Such models do a good job of predicting human performance, but do not give us much insight into what textures will segment, since the comparison carried out by the model is often obscured by the details of the filtering, nonlinearity, and image-based decision processes. It is suggested here that, for orientation-defined textures (eg in which each ‘texel’ has a single orientation), segmentation is well-described by something like the ‘significance’ of the differences between (1) the mean orientations, and (2) the angular variances of the two textures. The ‘significance’ of the difference in means takes into account the variability in the texture, so that two homogeneous textures with means differing by 30° may easily segment, while two heterogeneous textures with the same difference in mean may not. Furthermore, it is shown that these statistics may be computed in a biologically plausible way, which greatly resembles the typical filter-based approaches to texture segmentation. Thus the connection between statistical theories of texture segmentation and spatial-frequency channel models becomes more transparent.