Depth Scene Flow Estimation based on Variational Method using Thin-Plate Spline Regularization

Scene flow is a three-dimensional (3D) vector field with depth directional motion and optical flow and it can be applied to inter prediction in 3D video coding. The conventional method regularizes the scene flow so that it locally approaches a constant function, so there is the problem that it is difficult to handle spatial changes and motion boundaries. Regularizations called thin-plate spline or deformable model have been introduced in variational optical flow estimation because they find the solution locally as a linear function and may alleviate the problem. However, because the partial differential equation derived by thin-plate spline regularization includes the fourth-order partial differential, it is not easy to derive an analytical solution or solve it by a numerically stable iterative method in terms of numerical analysis. Previous researches have proposed a numerically stable iterative method that does not include thin plate spline regularization for scene flow estimation. Therefore, while making use of the framework of the previous researches, I derive a partial differential equation using thin plate spline regularization for scene flow estimation.