How Folds Cut a Scene

We consider the interactions between edges and intensity distributions in semi-open image neighborhoods surrounding them. Locally this amounts to a kind of figure-ground problem, and we analyze the case of smooth figures occluding arbitrary backgrounds. Techniques from differential topology permit a classiffication into what we call folds (the side of an edge from a smooth object) and cuts (the background). Intuitively, cuts arise when an arbitrary scene is “cut” from view by an occluder. The condition takes the form of transversality between an edge tangent map and a shading flow field, and examples are included.