Surface growing from stereo images

We present a new theoretical result for the problem of surface reconstruction from stereo images. For a given initial seed point, i.e. for a pair of corresponding points in the left and right image, the proposed algorithm grows the surface without directly computing the point correspondences. The method assumes the Lambertian surface reflectance model. Our approach is based on a surface normal calculation from the left and right image gradients. Knowing the surface normal, the algorithm grows the surface in the directions defined by the tangent plane. The algorithm is independent of the camera model, and requires placement of an initial seed point for each surface to be reconstructed. Technical problems associated with errors in the image gradient estimates and camera calibration are discussed and a solution is suggested. In addition to this algorithm, we present a theoretical result that permits one to track surfaces deforming in time, which is often encountered in medical applications (e.g. brain surface deforms during the surgery). These methods of surface reconstruction and deformable surface tracking are applied to the particular problem of brain shift, commonly recognized as one of the main source of errors in surgical navigation systems used in neurosurgery. We also suggest a way to overcome problems associated with brain surface specularities caused by fluids on the brain surface and lights in the operating room. We conclude with experimental results on real brain images and show that the surface reconstruction algorithm is robust to the position of the initial seed point.