Surface matching for image-derived geometries with a projection-based separation of rigid body modes

Overview & Synopsis

The large diffeomorphic deformation metric mapping (LDDMM) framework offers numerous techniques for analyzing shapes and images. Surface matching computes a non-rigid, smooth, and invertible mapping that registers one surface to another. The computed deformation may contain rigid body motion, which frequently does not represent meaningful shape differences but is due to external factors like imaging modalities, such as the object's positioning during image acquisition. We present a simple extension to the LDDMM framework's surface matching that uniquely decomposes the computed deformation into rigid body modes (RBM) and RBM-free motion by introducing a suitable projection. This enables a focused analysis of each component individually and additionally helps to preserve the surface discretization quality. Three sets of examples illustrate our approach. A small-scale example demonstrates the proposed method's effects, followed by an example using a single pair of heart geometries, and finally an example involving a cohort of 98 heart shapes.