TOPOGRAPHICAL PROPERTIES OF GENERIC IMAGES

摘要

Topographical curves in images are defined by certain extremality conditions involving the gradient of the greyvalue function. Curves extracted by some edge operators and watersheds studied in geography are both examples of such topographical curves. In the first part of this article we list the possible geometrical features of certain topographical curves-such as intersection points, singular points, endpoints, curvature extrema and inflections-for generic images and for generic 1-parameter families of, linearly or non-linearly, diffused images (intuitively, generic phenomena arise with probability 1). In a second experimental part the same topographical curves are computed in discrete images and in Gaussian blurred families of images. It turns out that the geometrical features of the smooth classification also figure in these discrete approximations. The consequences of these results for edge-linking algorithms are briefly discussed. [References: 25]