In the conventional gradient method of optical flow the movement of an object is estimated by a bottom-up algorithm starting from local processing. However, the method cannot be applied to the large displacement of the object. Many methods have been proposed to cope with this limitation. As one such method, we have proposed an optimally scaled multigrid optical flow algorithm in which the expanding flow scale between consecutive multigrid levels is optimized. We have also proposed an orthogonal functional expansion method as a novel optical flow method. The orthogonal functional expansion method is a top-down method where the total image displacements are expanded from a low-frequency term to that of a high-frequency term. This method is expected to be applicable to the flow estimation with large displacements and deformation with expansion or shrinkage, which are difficult for conventional optical flow methods to cope with. Here, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives with regard to the invariant constraint of the brightness integral value. In this paper, we apply our proposed method to several real images in which the objects are displaced largely through rotation or deformed with expansion. We demonstrate the effectiveness of the proposed orthogonal functional expansion method by comparing it with conventional methods including an optimally scaled multigrid optical flow algorithm proposed by us.
