Visual Modeling

The goal of visual modeling research is to develop mathematical models and associated algorithms for the analysis and synthesis of visual information. Image analysis and synthesis characterize the domains of computer vision and computer graphics, respectively. For nearly three decades, the vision and graphics fields have been developing almost entirely independently—this despite the fact that, at least conceptually, the two disciplines are bound in a mutually converse relationship. Graphics, the direct problem, involves the synthesis of images from object models, whereas vision, the inverse problem, involves the analysis of images to infer object models. Visual modeling takes a unified approach to vision and graphics via modeling that exploits computational physics. In addition to geometry, physics-based modeling employs forces, torques, internal strain energies, and other physical quantities to control the creation and evolution of models. Mathematically, the approach prescribes systems of dynamic (ordinary and partial) differential equations to govern model behavior. These equations of motion may be simulated using standard numerical techniques. The equations unify the representation of shape and motion, making the modeling primitives responsive to simulated physical environments, physical constraints, user interactions, and all sorts of input data sets. Significant effort has gone into the development of deformable models, a powerful class of physics-based modeling primitives inspired by the behavior of natural materials. Deformable models move rigidly or deform in response to applied forces in accordance with the principles of continuum mechanics [1], In applications to computer vision, deformable models may be used to infer image disparity and flow fields or infer the shapes and motions of objects from their images [2, 3]. In this context, external forces that impose constraints derived from image data are applied to the models. The forces actively shape and move models to achieve maximal consistency with imaged objects of interest and to maintain the consistency over time. The following list surveys various deformable models and some important vision problems to which they have been applied: