Numerically stable estimation of scene flow independent of brightness and regularizer weights

In video images, apparent motions can be computed using optical flow estimation. However, estimation of the depth directional velocity is difficult using only a single viewpoint. Scene flows (SF) are three-dimensional (3D) vector fields with apparent motion and a depth directional velocity field, which are computed from stereo video. The 3D motion of objects and a camera can be estimated using SF, thus it is used for obstacle detection and self-localization. SF estimation methods require the numerical computation of nonlinear equations to prevent over-smoothing due to the regularization of SF. Since the numerical stability depends on the image and regularizer weights, it is impossible to determine appropriate values for the weights. Thus, we propose a method that is independent of the images and weights, which simplifies previous methods and derives the numerical stability conditions, thereby facilitating the estimation of suitable weights. We also evaluated the performance of the proposed method.