Project Description:
We
address the problem of registering two surfaces, of which a natural
bijection between them does not exist. More precisely, only a partial
subset of the source domain is assumed to be in correspondence with a
subset of the target domain. We call such a problem an {\it
inconsistent surface registration} problem. This problem is challenging
as the corresponding regions on each surfaces and a meaningful
bijection between them have to be simultaneously determined. In this
paper, we propose a variational model to solve the inconsistent surface
registration problem by minimizing mapping distortions. Mapping
distortions are described by the Beltrami coefficient as well as the
differential of the mapping. Registration is then guided by feature
landmarks and/or intensities, such as curvatures, defined on each
surfaces. The key idea of the approach is to control angle and scale
distortions via quasiconformal theory as well as minimizing landmark
and/or intensity mismatch. A splitting method is proposed to
iteratively search for the optimal corresponding regions as well as the
optimal bijection between them. Bijectivity of the mapping is easily
enforced by a thresholding of the Beltrami coefficient. We test the
proposed method on both synthetic and real examples. Experimental
results demonstrate the efficacy of our proposed model.
Publication: