Depth Map Estimation with Consistent Normals from Stereo Images

The total variation regularization of non-convex data terms in continuous variational models can be convexified by the so called functional lifting, which may be considered as a continuous counterpart of Ishikawa’s method for multi-label discrete variational problems. We solve the resulting convex continuous variational problem by the augmented Lagrangian method. Application of this method to the dense depth map estimation allows us to obtain a consistent normal field to the depth surface as a byproduct. We illustrate the method with numerical examples of the depth map estimation for rectified stereo image pairs.