Even though information in the phase spectrum is critical to higher level tasks such as texture appearance judgments and can aid the discrimination of one texture from another, its relevance to a pre-attentive, low-level task such as texture segmentation remains unclear. The popular conception of an energy model of segmentation emphasizes global comparisons of lower order statistics, but other models have been based on different sets of statistics, some of which are higher order. Julesz (
1962) conjectured that texture segmentation mechanisms might operate on only a subset of available statistics, i.e., the relationship between the luminance values of any two pixels at a given distance from one another. This theory was later expanded to include relationships between triplets (Julesz, Gilbert, & Victor,
1978) and quadruplets (Julesz,
1981) of pixels. Graham, Sutter, and Venkatesan (
1993) demonstrated element arrangement patterns created with oriented Gabor patches that can be readily segmented along boundaries defined only by differences in the relative positions of the texture elements, implying a mechanism that is sensitive to phase information. To achieve human-like segmentation in natural scenes by a computer vision algorithm, Martin, Fowlkes, and Malik (
2004) and later Arbeláez, Maire, Fowlkes, and Malik (
2011) made use of higher order texture statistics along with other boundary cues. They classified each pixel of an image as belonging to one of a small collection of “textons” based on the responses of a range of co-localized oriented filters, followed by a second stage operator that compares the texton histograms on opposing sides of a putative boundary. Phase scrambling would remove the spatial co-localization of filter responses that define these textons, and so texton-based segmentation would be impossible. Thus, there is evidence suggesting that higher order statistics influence segmentation, but a systematic study is difficult because what constitutes a “higher order statistic” is unbounded and defined only by exclusion to consist of anything that is
not a lower order statistic. In this work, we use natural image photographs to sample higher order texture statistics that are likely to be critical to ecological vision and explore the relationship between these statistical regularities and human performance on a texture segmentation task.