Tracing crease curves by solving a system of differential equations

Different kinds of digital images can be modelled as the sampling of a continuous surface, being described and analyzed through the extraction of geometric features from the underlying surface. Among them, ridges and valleys or, generically, creases, have deserved special interest. The computer vision community has been relying on different crease definitions, some of them equivalent. Although they are quite valuable in a number of applications, they usually do not correspond to the real creases of a topographic relief. These definitions give rise either to algorithms that label pixels as crease points, and then focus on the problem of grouping them into curves, or to operators whose outcome is a creaseness image. We draw our attention to the real crease definition for a landscape, due to Rudolf Rothe, which is based on the convergence of slopelines. They are computed by numerically solving a system of differential equations. Afterwards, we extract Rothe creases which are parts of slopelines where others converge, avoiding in such a way any pixel-grouping step. At the same time we compute a creaseness image according to this definition.