Variational principles, surface evolution, PDEs, level set methods, and the stereo problem

We present a novel geometric approach for solving the stereo problem for an arbitrary number of images (= or >2). It is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images. The Euler-Lagrange equations that are deduced from the variational principle provide a set of partial differential equations (PDE's) that are used to deform an initial set of surfaces which then move toward the objects to be detected. The level set implementation of these PDE's potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations, i.e., to deal with multiple objects. Results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images.