An Eecient and Provably Correct Algorithm for the Multiscale Estimation of Image Contours by Means of Polygonal Lines

A large portion of image contours is characterized by local properties such as sharp variations of the image intensity across the contour. However, the integration of local image descriptors estimated by using these local properties into curvilinear descriptors is a dii-cult problem from a theoretical perspective because of the combinatorially large number of possible curvilinear descriptors. An approach, based on the notion of compressibility of a graph, is proposed to deal with this issue. A linear-time multiscale algorithm is proposed which provably recovers contours with an upper bound on the approximation error. In the noise-free limit case, all contours are recovered with probability one. 1 Figure 1: Curve-based representations of image contours computed by the proposed approach (middle) and by more traditional methods (right). The edge representation on the right has been computed by using the Canny's algorithm implementation of the Matlab's image processing toolbox.