Shape registration using characteristic functions

This study presents a fast algorithm for the registration of shapes implicitly represented by their characteristic functions. The algorithm proposed here aims to recover the registration parameters (scaling, rotation and translation) by minimising a dissimilarity term between the two shapes. The proposed algorithm is based on phase correlation and statistical shape moments to compute the registration parameters individually. The registration method proposed here is applied to various registration problems, to address issues such as the registration of shapes with various topologies and registration of complex shapes containing various numbers of sub-shapes. The method proposed here is characterised with a better accuracy, a higher convergence speed, robustness at the presence of excessive noise and a better performance for registration over large databases of shapes, in comparison with other state-of-the-art shape registration techniques in the literature.