Abstract

This work proposes a novel framework for optimization in the constrained diffeomorphism space for deformable surface registration. First the diffeomorphism space is modeled as a special complex functional space on the source surface, the Beltrami coeffificient space. The physically plausible constraints, in terms of feature landmarks and deformation types, defifine subspaces in the Beltrami coeffificient space. Then the harmonic energy of the registration is minimized in the constrained subspaces. The minimization is achieved by alternating two steps: 1) optimization - diffuse the Beltrami coeffificient, and 2) projection - fifirst deform the conformal structure by the current Beltrami coeffificient and then compose with a harmonic map from the deformed conformal structure to the target. The registration result is diffeomorphic, satisfifies the physical landmark and deformation constraints, and minimizes the conformality distortion. Experiments on human facial surfaces demonstrate the effifi- ciency and effificacy of the proposed registration framework.