Optical Flow for Motion Images with Large Displacement by Functional Expansion

One of the representative methods of optical flow is a gradient method which estimates the movement of an object based on the differential of image brightness. However, the method is ineffective for large displacement of the object and many improved methods have been proposed to copy with such limitations. One of these improved techniques is the multigrid processing, which is used in many optical flow algorithms. As an alternative novel technique we have been proposing an orthogonal functional expansion method, where whole displacements are expanded from low frequency terms. This method is expected to be applicable to flow estimation with large displacement and deformation including expansion and contraction, which are difficult to cope with by conventional optical flow methods. In the orthogonal functional expansion method, the apparent displacement field is calculated iteratively by a projection method which utilizes derivatives of the invariant constraint equations of brightness constancy. One feature of this method is that differentiation of the input image is not necessary, thereby reducing sensitivity to noise. In this paper, we apply our method to several real images in which the objects undergo large displacement and/or deformation including expansion. We demonstrate the effectiveness of the orthogonal functional expansion method by comparing with conventional methods including our optimally scaled multigrid optical flow algorithm.