Fast global SA(2,R) shape registration based on invertible invariant descriptor

Abstract

Here, we intend to introduce a fast and non-rigid global registration for simple planar closed curves relatively to the planar Special Affine group SA(2,R). In previous work, Ghorbel (1998) has been introduced a complete and stable set of invariant for simple closed planar curves which is invariant jointly under its original parametrization and special planar affine transformations. Such property allows us a robust reconstruction of the considered object up to a special affine transformation. In this paper, several numerical difficulties of the computation of the proposed reconstruction are considered. The robustness of this inverse problem with respect to noise and reasonable deformations of non-rigid shape is demonstrated experimentally. The proposed new registration is based, on the one hand, on the shift theorem relating to the group SA(2,R) and, on the other hand, on the invertibility of the set of invariant. Since this shift theorem allows the extraction of a pose parameters exciting between reference and target objects. The low algorithmic complexity is due to the fact that the computation of the inverse descriptors are based essentially on the Fast Fourier Transformation (FFT) algorithm. Experiments are conducted on different known datasets such as MPEG-7, MCD, Kimia-99, Kimia216, ETH-80 and Swedish leaf datasets. Promising results on the sense of shape retrieval and shape recognition rates will also be demonstrated.