Global Methods for Image Motion Analysis
2:00 p.m., Friday, October 2, 1992
12th floor conference room
Processing motion information is an important problem in building automated vision systems. A moving sensor can obtain knowledge about the environmental layout, its own motion, and motion of objects in the scene by processing the temporal information in the imagery. We provide algorithms that can determine self-motion (or egomotion) by observing a sequence of images produced by a moving sensor in a rigid, stationary environment. The algorithms make use of optical flow information extracted from the sequence, and unlike most alternative methods, are global and robust to inaccuracies in the flow data.
Two algorithms are presented. Both algorithms assume that the first stage of visual motion analysis, the computation of an image vector flow field that describes the instantaneous motion of individual points, has been solved.
The first algorithm, the flow circulation algorithm, determines the rotational parameters using the curl of the flow field, which under many conditions is approximately a linear function. The coefficients of the linear function, which may be determined by simple regression, are the desired rotational parameters. Circulation values, defined to be contour integrals of the vector field on the image plane, may be used in place of curl values, resulting in robustness. The second algorithm determines the translational parameters of the motion. The inner product of the image vector flow field and a certain circular vector field gives rise to a scalar function that is of a particular quadratic polynomial form when the center of the circlular field is chosen appropriately. This correct choice of the center is related to the translational parameters and can be found by projecting the inner product function onto suitable subspaces determined by the quadratic polynomial form. Three different methods, of increasing complexity and accuracy, are developed. A fourth, fast but approximate method is also presented.
The algorithms are described, analyzed and experimental results are shown. The thesis contains mathematical observations that provide insight into the problem of motion analysis, and experimental observations that demonstrate the applicability of the algorithms.