Complexity, Confusion, and Perceptual Grouping. Part II: Mapping Complexity

Intermediate-level vision is central to form perception, and we outline an approach to intermediate-level segmentation based on complexity analysis. In this second of a pair of papers, we continue the focus on edge-element grouping, and the motivating example of an edge element inferred from an unknown image. Is this local edge part of a long curve, or part of a texture? If the former, which is the next element along the curve? If the latter, is the texture like a well-combed hair pattern, in which nearby elements are oriented similarly, or more chaotic, as in a spaghetti pattern? In the previous paper we showed how these questions raise issues of complexity and dimensionality, and how context in both position and orientation are important. We now propose a measure based on tangential and normal complexities, and illustrate its computation. Tangential complexity is related to extension; normal complexity to density. Taken together they define four canonical classes of tangent distributions: those arising from curves, from texture flows, from turbulent textures, and from isolated “dust”. Examples are included.