Direct recovering of Nth order surface structure using unified optical flow field

Abstract

There are two different approaches for estimation of structure and/or motion of objects from image sequences in the computer vision community today. One is the optical flow approach, and the other is the feature correspondence approach. There are many difficulties and limitations encountered with the feature correspondence method, while the optical flow method requires a substantial amount of extra calculations if the optical flow is to be computed as an intermediate step. Direct methods have been developed, that use the optical flow approach, but avoid computing the full optical flow field as an intermediate step for recovering structure and motion. The unified optical flow field (UOFF) theory was recently established. It is an extension of the optical flow formulations to the temporal-spatial domain. In this paper, a direct method is developed to reconstruct the curved surface structure characterized by an N-degree polynomial equation based on the UOFF. It is a direct method since it also directly recovers surface structure, without computing the quantities in the UOFF. However, it is different from the direct method in that it is based on the theoretical framework of the unified spatial-and-temporal optical field instead of the optical flow field determined. Hence, the structure is recovered from a given pair of stereo images instead of from a monocular image sequence. Two computer simulations: a sphere which is a second-order surface and an unbounded α-shaped surface which is a third-order one are presented. The fairly good results demonstrate the effectiveness of our direct method using the UOFF. Some numerical consideration and error analysis are also included. Compared with the existing techniques of the direct method where only the first-order surface can be recovered, the new method has made significant progress in the recovery of curved structure.