Deformable Registration of Organic Shapes via Surface Intrinsic Integrals: Application to Outer Ear Surfaces

Abstract

We propose a method for the deformable registration of organic surfaces. Meaningful correspondences between a source surface and a target surface are established by means of a rich surface descriptor that incorporates three categories of features: (1) local and regional geometry; (2) surface anatomy; and (3) global shape information. First, surface intrinsic, geodesic distance integrals, are exploited to constrain the global geodesic layout. Consequently, the resulting transformation ensures topological consistency. Local geometric features are then introduced to enforce local conformity of various regions. To this end, the extrema of appropriate curvatures – the extrema of mean curvature, minima of Gauss and minimum principal curvature, and the maxima of maximum principal curvature – are considered. Regional features are introduced through curvature integrals over various scales. On top of this, explicit anatomical priors are included, thereby resulting in anatomically more consistent registration. The source surface is deformed to the target by minimizing the energy of matching the source features to the target features under a Gaussian propagation model. We validate the proposed method with application to the outer ear surfaces.