An Efficient Way to Estimate the Focus of Expansion

Detecting independent motion from a single camera is a difficult task in computer vision. It is because the captured image sequences are the combinations of the objects' movements and the camera's ego-motion. One major branch is to find the focus of expansion (FOE) instead as the goal. This is ideal for the situation commonly seen in UAV's camera system. In this case, the translation is dominant in camera's motion while the rotation is relatively small. To separate the ego motion and scene structure, many researchers used the directional flow as the theoretic basis and extracted its properties related to FOE. In this paper, we formulate finding FOE as an optimizing problem. The position of FOE has the minimal standard deviation for the directional flow in all directions, which is also subjected to the introduced constraint. The experiments show the proposed methods out-perform the previous method.