A level-set approach for stereo

In this paper, an original approach to deal with the important problem of stereovision using a weakly calibrated pair of images is presented. Given two different views of some 3D objects, and a virtual 3D plan set by an external operator, the method we propose allows to recover the 2D projections, in the two images, of the 3D planar curves corresponding to the intersection of the virtual plan with the different objects in the scene. To this end, an arbitrary curve is first initialized in one of the two images. This curve, and its associated homographic curve in the second image are then designed to move under the influence of internal and external image dependent forces while minimizing an energy functional. Following the work on geodesic active contours by Caselles et al(2,3) and Malladi et al,(9,8) we then transform the problem of minimizing this functional into a problem of geodesic computation in a Riemannian space, according to a new metric. The Euler-Lagrange equation of this new functional is derived and its associated PDE is then solved using the level set formulation scheme of Osher and Sethian(10) by viewing it as a front propagating with internal and external image correlation dependent speed. The curves to be matched are therefore modelized as geodesic active contours evolving toward the minimum of the designed functional. Using this level set based approach, complex curves can be matched and topological changes for the evolving curves are naturally managed. The final result is also relatively independent of the curve initialization. Promising experimental results have been obtained on real images and some of these results will be illustrated in the experimental section of this paper.