Nonrigid Motion Analysis Based on Dynamic Refinement of Finite Element Models

ÐIn this paper, we propose new algorithms for accurate nonrigid motion tracking. Given an initial model representing general knowledge of the object, a set of sparse correspondences, and incomplete or missing information about geometry or material properties, we can recover dense motion vectors using finite element models. The method is based on the iterative analysis of the differences between the actual and predicted behavior. Large differences indicate that an object's properties are not captured properly by the model describing it. Feedback from the images during the motion allows the refinement of the model by minimizing the error between the expected and true position of the object's points. These errors are due to flaws in the model parameter estimation such as geometry and material properties. Unknown parameters are recovered using an iterative descent search for the best nonlinear finite element model that approximates nonrigid motion of the given object. During this search process, we not only estimate material properties, but also infer dense point correspondences from our initial set of sparse correspondences. Thus, during tracking, the model is refined which, in turn, improves tracking quality. As a result, we obtain a more precise description of nonrigid motion. Experimental results demonstrate the success of the proposed algorithm. The method was applied to man-made elastic materials and human skin to recover unknown elasticity, to complex 3D objects to find details of their geometry, and to a hand motion analysis application. Our work demonstrates the possibility of accurate quantitative analysis of nonrigid motion in range image sequences with objects consisting of multiple materials and 3D volumes. Index TermsÐPhysically-based vision, deformable models, nonrigid motion analysis, biomedical applications, finite element analysis.