The Stability of the Apparent Contour of an Orientable 2Manifold
Proceedings of the Workshop on Topological Methods in Data Analysis and Visualization, 2009. 

TopoInViz

Abstract
The (apparent) contour of a smooth mapping from a 2manifold to the plane, f: M → R^{2} , 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.