An efficient fuzzy algorithm for aligning shapes under affine transformations

A fuzzy algorithm for aligning object shapes under affine transformations is proposed in this paper. The algorithm, with the name of fuzzy alignment algorithm (FAA), extends Marques' algorithm to affine transformations. It can efficiently estimate the point correspondence and the relevant affine transformational parameters between the feature points of the object shape and the reference shape. In this algorithm, the fuzzy point-correspondence degrees are used to describe an uncertainty point assignment, then both the parameters of the affine transformation and the fuzzy correspondence degrees are iteratively calculated by minimizing a constrained fuzzy objective function. To prevent FAA from sinking into local minimum when the shapes are greatly deformed, an initialization method based on affine invariants is designed. Comparing to the eigenvector method, the effectiveness and robustness of the proposed algorithm is investigated with a sensitivity study based on randomly generated points. At last, good performance of FAA is illustrated with several experiments on aligning digits and object shapes.