Shape reconstruction on a varying mesh

A central class of image understanding problems is concerned with reconstructing a shape from an incomplete data set, such as fitting a surface to (partially) given contours. A new theory for solving such problems is presented. Unlike the current heuristic methods, the method used starts from fundamental principles that should be followed by any reconstruction method, regardless of its mathematical or physical implementation. A mathematical procedure which conforms to these principles is presented. One major advantage of the method is the ability to handle shapes containing both smooth and sharp parts without using thresholds. A sharp variation, such as a corner, requires a high-resolution mesh for adequate representation, while slowly varying sections can be represented with sparser mesh points. Unlike current methods, this procedure fits the surface on a varying mesh. The mesh is constructed automatically to be more dense at parts of the image that have more rapid variation. Analytical examples are given in simple cases, followed by numerical experiments