Physics-Based Modeling of Nonrigid Objects for Vision and Graphics (Dissertation)

This thesis develops a physics-ba,sed framework for 3D slia,pe and nonrigid motion modeling for computer vision and computer gra,phics. In computer vision it addresses the problems of complex 3D sha,pe representa.tion, shape reconstruction, quantitative model extraction froin biomedical data for ana.lysis a,nd visualizabion, shape estimatio11, and motion tracliing. In computer grapllics it delllo~lst,rates the generative power of our framework to synthesize collstra,ilied sha.pes, llollrigicl object motions and object interactions for the purposes of computer animation. Our framework is based on the use of a new class of dynamically deforniable primitives which allow the combination of globa,l and 1oca.l deformations. It incorporates physical constraints to colnpose articulated ~noclels from deforlnable primitives and provides force-based techniques for fitt,ing such models to spa.rse, noise-corrupted 2D and 3D visua.1 data. The framework 1ea.d~ to shape and nonrigid motion estilnators that exploit dynamically deforma.ble models to track lnoving 3D objects froin time-varying 011serva.tions. We develop models with global deformation para.meters which represent the salient shape fea.tures of natural parts, and loca,l deforma.tjon pa,ra.meters which capture sha.pe details. In the context of conlputer gra.phics, these nlodels represent the physics-based marriage of the pa.rameterized a,nd free-form inodeling paradigms. An important benefit of their global/local descriptive power in the context of computer vision is that it can potentially satisfy the often conflicting requirements of shape reconstruction and shape recognition. The Lagrange equations of motion that govern our models, augmented by constraints, make them responsive to externally applied forces derived from input data or applied by the user. This system of differential equations is discretized using finite element methods and simulated through time using standard numerical techniques. We employ these equations to formulate a shape and nonrigid motion estimator. The estimator is a continuous extended Kalman filter that recursively transforms the discrepancy between the sensory data, and the estimated inodel state into generalized forces. These adjust the translational, rotational, and deformational degrees of freedom such that the model evolves in a coilsistent fashion with the noisy data. We demonstrate the int,eractive time performance of our techniclues in a series of experiments in computer vision, graphics, and visualization. Dedicated to my parents Nikolas and Ada