Diffeomorphic Registration of 3D Surfaces with Point and Curve Landmarks

Abstract

This paper proposes a novel method to compute the diffeomorphic registration of 3D surfaces with point and curve feature landmarks. First the surfaces are mapped to the canonical domain by a curve constrained harmonic map, where the landmark curves are straightened to line segments and their positions and inclining angles are determined intrinsically by the surface geometry and its curve landmarks. Then, the canonical domains are registered by aligning the corresponding point and straight line segments using the dynamic quasiconformal map (DQCM), which introduces the combinatorial diagonal switches to the quasiconformal optimization such that the resultant map is diffeomorphic. The end points of the source curve landmarks are mapped to their corresponding points on the target surface, while the interior points of the source curves can slide on the corresponding target curves, which provides more freedom for the surface registration than the point-based registration methods. Experiments on the real surfaces with point and curve landmarks demonstrate the efficiency, efficacy and robustness of the proposed method.

Keywords

Surface registration / Harmonic map / Dynamic quasiconformal map / Feature landmarks

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Funding

China Natural Science Foundation(61202146)