Temporal Regularisation Of Optical Flow

It is well known that the recovery of 3D structure and motion from apparent velocities in the 2D image plane (Optical Flow) is an ill-posed problem. That is, the solution of the structure from motion problem is non-unique, and also small perturbations in the data lead to large changes in the solution. This paper gives the background to this problem, and a structure from motion algorithm is presented which operates on a sequence of images. The Optical Flow of an initial pair of images is computed, and a structure from motion inter-pretation made using the so-called "8-point" algorithm. This solution then forms the starting point for a predictor-corrector scheme based on a quasi-Newton method which continues the solution on in time for an arbitrary number of images. The de-tails of the method are discussed, and the role of Temporal Regularisation considered. The accuracy and stability of the method are investigated, and it is shown that errors do not accumulate with time. The ability of the technique to follow the solution through singular points is examined. Some exam-ple results using synthetic data are presented, and possible practical applications are briefly discussed.

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