Shape Reconstruction from Contours Using Isotopic Deformation

A method for shape reconstruction from contours using isotopic deformation is presented. The proposed method considers the case where one contour encloses the other contour when they are projected in a common plane, as is the case for terrain contour maps. Unlike many other methods which generate piecewise linear interpolation, the proposed method smoothly interpolates between two contours located in parallel planes. The algorithm runs in O(nk+n log n) time, where n is the total number of vertices in two contours and k is an integer variable less than n which indicates how convoluted the contours are (the larger, the more convoluted). The running time of the algorithm is shown to be worst-case optimal for the class of task defined. The reconstructed shape is free of self-intersections and it can incorporate given feature correspondences. The method is extended to handle bifurcations and is shown to cope easily with some cases which are problematic for some other algorithms. The method proposed is suitable for terrain modeling, since reconstructed shapes generated by the method do not have overhangs. Experimental results are included to illustrate the feasibility of the approach.