Abstract
Although it is commonly assumed that there are stable image features that relate directly to parts of a surface, this question is subtle because it involves an ill-posed inverse problem. In particular, what does one mean by a `stable feature of the image' or a `part of the surface'? What does one mean by a `stable relationship'? We adopt the concept of critical contours and the Morse Smale (MS) complex to answer these questions. The MS complex (similar to a generalized segmentation) considers topological properties of the image gradient to construct a qualitative representation of the image. We use this to analyze global and topological properties of the image and to relate them to parts of the surface rigorously. We have shown previously (arxiv.org/abs/1705.07329) that critical contours, particular curves in the MS complex, are remarkably stable in the image as the lighting changes. We now study the 3D surface shape properties that relate 1-to-1 with the segmentation regions. We explore the important case where the critical contours define a complete segmentation. This can happen in two ways. First, all the critical contours can join the boundary. Then one can generically conclude that the segmented surface regions are either ridges or monotonic. Second, when critical contours form closed cycles in the MS complex, one can generically conclude that the interior surface regions are bumps or valleys. Thus, these regions of the image relate directly to Morse properties of the surface. Strong independence properties among the different segmentation regions follow from the MS segmentation. Specifically, the model predicts that some segmented regions can be perceptually bistable, with convex/concave switches occurring within an otherwise stable surround. Novel examples of such effects support the model experimentally.
Meeting abstract presented at VSS 2018