Using moments to acquire the motion parameters of a deformable object without correspondences

In the topic of motion analysis in image understanding, we usually need to find the motion of a particular object. However, frequently the correspondence problem, which is well known to be difficult, must first be solved. If the correspondence problem can be avoided in motion analysis, it will greatly reduce the difficulty of solving motion parameters. Using the concept of object normalization described in this paper, we can determine the motion parameters without solving the correspondence problem. The object of interest is not necessarily assumed rigid here. It can undergo a uniformly, linearly deformable motion (affine transformation), including translation, rotation and skewing. Under the assumption of this motion model, a closed-form solution of the desired motion parameters can be obtained efficiently by our proposed method. In some special cases where the closedform solution cannot be determined uniquely, a modified method is also developed to solve them. A theoretical error analysis is presented to show for what kinds of object it IS inherently hard to acquire motion parameters.