Computational Stereo: A Variational Method

Given a set of simultaneously acquired images of a scene, the stereo problem consists of reconstructing the three-dimensional shape of the objects in the scene. Traditionally, this problem has been tackled by separating the correspondence problem, i.e. that of establishing which points in the images are the projections in the retina of the same 3D point, and the reconstruction problem, i.e. that of reconstructing the 3D shapes from the correspondences. The approach described in this chapter does not separate the two problems. Given a set of objects (surfaces) in 3D space, we propose a function that measures the adequacy of these objects with the measured images. The problem is then to find a set of surfaces in the scene which maximize our function. This can be achieved by a variational approach. A level set implementation is described and results are given on synthetic and real images.