VARIATIONAL-PRINCIPLES, SURFACE EVOLUTION, PDES, LEVEL SET METHODS, AND THE STEREO PROBLEM

We present a novel geometric approach for solving the stereo problem f or an arbitrary number of images (greater than or equal to 2). It is b ased upon the definition of a variational principle that must be satis fied by the surfaces of the objects in the scene and their images, The Euler-Lagrange equations that are deduced from the variational princi ple provide a set of partial differential equations (PDE's) that are u sed to deform an initial set of surfaces which then move toward the ob jects to he detected, The level set implementation of these PDE's pote ntially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topolo gy during the deformations, i.e., to deal with multiple objects, Resul ts of an implementation of our theory also dealing with occlusion and vilility are presented on sydnthetic and real images.