An efficient fuzzy algorithm for aligning shapes under affine transformation

A fuzzy algorithm for aligning object shapes under affine transformations i s proposed in this paper. The algorithm, with the name of fuzzy alignment a lgorithm (FAA), extends Marques' algorithm to affine transformations. It ca n efficiently estimate the point correspondence and tile relevant affine tr ansformational parameters between the feature points of the object shape an d the reference shape, In this algorithm, the fuzzy point-correspondence de grees are used to describe an uncertainty point assignment, then both the p arameters of the affine transformation and the fuzzy correspondence degrees are iteratively calculated by minimizing a constrained fuzzy objective fun ction. To prevent FAA from sinking into local minimum when the shapes are g reatly deformed, an initialization method based on affine invariants is des igned. Comparing to the eigenvector method, the effectiveness and robustnes s of the proposed algorithm is investigated with a sensitivity study based on randomly generated points. At last, good performance of FAA is illustrat ed with several experiments on aligning digits and object shapes. (C) 2001 Pattern Recognition Society. Published by Elsevier Science Ltd. all rights reserved.