Shape registration in implicit spaces using information theory and free form deformations
Résumé
We present a novel, variational and statistical approach for shape registration. Shapes of interest are implicitly embedded in a higher- dimensional space of distance transforms. In this implicit embedding space, registration is formulated in a hierarchical manner: the Mutual Information criterion supports various transformation models and is optimized to perform global registration; then, a B- spline- based Incremental Free Form Deformations ( IFFD) model is used to minimize a Sum- of- Squared- Differences ( SSD) measure and further recover a dense local nonrigid registration field. The key advantage of such framework is twofold: 1) it naturally deals with shapes of arbitrary dimension ( 2D, 3D, or higher) and arbitrary topology ( multiple parts, closed/ open) and 2) it preserves shape topology during local deformation and produces local registration fields that are smooth, continuous, and establish one- to- one correspondences. Its invariance to initial conditions is evaluated through empirical validation, and various hard 2D/ 3D geometric shape registration examples are used to show its robustness to noise, severe occlusion, and missing parts. We demonstrate the power of the proposed framework using two applications: one for statistical modeling of anatomical structures, another for 3D face scan registration and expression tracking. We also compare the performance of our algorithm with that of several other well- known shape registration algorithms.