A Generic Deformation Model for Dense Non-rigid Surface Registration: A Higher-Order MRF-Based Approach

Abstract

We propose a novel approach for dense non-rigid 3D surface registration, which brings together Riemannian geometry and graphical models. To this end, we first introduce a generic deformation model, called Canonical Distortion Coefficients (CDCs), by characterizing the deformation of every point on a surface using the distortions along its two principle directions. This model subsumes the deformation groups commonly used in surface registration such as isometry and conformality, and is able to handle more complex deformations. We also derive its discrete counterpart which can be computed very efficiently in a closed form. Based on these, we introduce a higher-order Markov Random Field (MRF) model which seamlessly integrates our deformation model and a geometry/texture similarity metric. Then we jointly establish the optimal correspondences for all the points via maximum a posteriori (MAP) inference. Moreover, we develop a parallel optimization algorithm to efficiently perform the inference for the proposed higher-order MRF model. The resulting registration algorithm outperforms state-of-the-art methods in both dense non-rigid 3D surface registration and tracking.

On Mean Pose and Variability of 3D Deformable Models

“…isometric deformations [21,8,22,23]. Such properties relate to local rigidities, for instance in [31,32] local surface distorsions are constrained, however they are usually known priors. While efficient to register or match surfaces, intrinsic surface properties are not necessarily sufficient to track complex shapes such as human bodies.…”

Discrete Visual Perception

“…Such a formulation was extended in [10] to track evolving/deforming surfaces and was endowed with a powerful local shape similarity metric that was the Mobius transform. This idea was further extended in [11] towards handling non-rigid shapes through a discrete minimum distortion principle that was modular under various classes of deformations. More recently, such a higher order model was seamlessly integrated with a generic deformation model, called Canonical Distortion Coefficients (CDCs), that characterizes the deformation of every point on a surface using the distortions along its two principle directions leading to an efficient inference paradigm that can easily handle different types of geometry/texture similarity metrics.…”

Non-Rigid Registration of Visual Objects

“…Triangular surfaces can be registered by either using the vertices of the meshes only, by applying any point set registration approach [5,6,41] to them. Another way is to utilize the structure information of triangles as well [37,64,65]. Modeling the deformation is done similarly to the previous cases by using interpolating splines or element-wise (vertices or faces) correspondences.…”

“…A similar approach based on the MRF model has been presented in [65]. The singleton potentials are modeled as differences between extracted local features and the higher order potentials defined as constraints on the deformation using a novel model called Canonical Distortion Coefficient (CDC).…”