title: Shape registration in implicit spaces using information theory and free form deformations.
abstract: 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.
authors.affiliation: Center for Computational Biomedicine Imaging and Modeling, Division of Computer and Information Sciences, Rutgers University, New Brunswick, NJ 08854-8019, USA. xiaolei@cs.rutgers.edu
authors.forename: Xiaolei
authors.initials: X
authors.lastname: Huang
authors.forename: Nikos
authors.initials: N
authors.lastname: Paragios
authors.forename: Dimitris N
authors.initials: DN
authors.lastname: Metaxas
mesh_terms: D000465:Algorithms; D001185:Artificial Intelligence; D004548:Elasticity; D005145:Face / Q000033:anatomy & histology*; D006801:Humans; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D016247:Information Storage and Retrieval / Q000379:methods; D007257:Information Theory; D010363:Pattern Recognition, Automated / Q000379:methods*