Dense Depth Map Reconstruction: A Minimization and Regularization Approach which Preserves Discontinuities

We present a variational approach to dense stereo reconstruction which combines powerful tools such as regularization and multi-scale processing to estimate directly depth from a number of stereo images, while preserving depth discontinuities. The problem is set as a regularization and minimization of a nonquadratic functional. The Tikhonov quadratic regularization term usually used to recover smooth solution is replaced by a function of the gradient depth specifically derived to allow depth discontinuities formation in the solution. Conditions to be fulfilled by this specific regularizing term to preserve discontinuities are also presented. To solve this problem in the discrete case, a PDE-based explicit scheme for moving iteratively towards the solution has been developed. This approach presents the additional advantages of not introducing any intermediate representation such as disparity or rectified images: depth is computed directly from the grey-level images and we can also deal with any number (greater than two) of cameras. Promising experimental results illustrate the capabilities of this approach.