@inbook{3795, 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.}, author = {Edelsbrunner, Herbert and Morozov, Dmitriy and Patel, Amit}, booktitle = {Topological Data Analysis and Visualization: Theory, Algorithms and Applications}, pages = {27 -- 42}, publisher = {Springer}, title = {{The stability of the apparent contour of an orientable 2-manifold}}, doi = {10.1007/978-3-642-15014-2_3}, year = {2010}, }