The stability of the apparent contour of an orientable 2-manifold

Abstract

The (apparent) contour of a smooth mapping from a 2-manifold to the plane, f: M → R2, is the set of critical values, that is, the image of the points at which the gradients of the two component functions are linearly dependent. Assuming M is compact and orientable and measuring difference with the erosion distance, we prove that the contour is stable.