Surface matching method separates shape shifts from rigid motions
Surface matching for image-derived geometries with a projection-based separation of rigid body modes
Computational Engineering, Finance, and Science
Summary
When comparing shapes from images, sometimes the shapes appear different because of how they were positioned or moved, not because their actual forms changed. The authors improve an existing mathematical method so it can tell the difference between true shape changes and simple movements like rotation or sliding. This helps in focusing analysis on meaningful shape differences and keeps the shape details clear. They show how this works using examples with heart shapes from medical images.
What this means in practice
- •For medical image analysts: Improve heart shape comparison by separating meaningful shape changes from patient positioning differences in image registrations.
- •For computer vision engineers: Enhance shape registration algorithms by decomposing deformations into rigid and non-rigid parts for clearer shape difference analysis.
Authors
Ludwig Wagmüller, Christian Bilas, Markus Gitterle, Michael Wibmer, Michael W. Gee
Abstract
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.