A fast and robust affine-invariant method for shape registration under partial occlusion

The acquisition of the planar images of the same object may be considerably different due to viewpoint dependencies, which influences the shape extraction, hence possibly making the curves partially visible and often accompanied by perspective distortions. In this paper, we propose a new contour alignment system relating to the special affine transformations that contain rotations and stretches, useful for describing planar contours which move in three-dimensional space and which are far enough away from the camera. The registration system that we suggest here includes a first optimization step relating to the dataset concerned. It consists in optimizing the number of correspondence points N between the curves to be registered. This is achieved by minimizing the conditioning of the correspondence matrix which is obtained by matching the re-sampling points by the equi-affine length of the two curves. This correspondence matrix is calculated for all the pairs of curves of the dataset by varying N. After extracting the optimal value of N, the estimation of the special affine transformation between a given couple of curves is realized by the pseudo-inverse of the correspondence matrix in the \(N_{0}\) resolution. This approach allows both providing the best accuracy and stabilizing the results of registration. We evaluate and compare our algorithm with other existing methods under different shape variations including noise, missing parts, and articulated deformations. The experiments are conducted on several known datasets.