Un-Biased Linear Algorithm for Recovering Three-Dimensional Motion from optical Flow

Norio TAGAWA  Takashi TORIU  Toshio ENDOH  

IEICE TRANSACTIONS on Information and Systems   Vol.E76-D   No.10   pp.1263-1275
Publication Date: 1993/10/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: PAPER
Category: Image Processing, Computer Graphics and Pattern Recognition
image processing,  computer vision,  motion analysis,  structure from motion,  optical flow,  

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This paper describes a noise resistant algorithm for recovering the three-dimensional motion of a rigid object from optical flow. First, it is shown that in the absence of noise three-demensional motion can be obtained exactly by a linear algorithm except in the special case in which the surface of the object is on a general quadratic surface passing through the viewpoint, and the normal vector of the surface at the viewpoint is perpendicular to the translation velocity vector. In the presence of noise, an evaluation function is introduced based on the least squares method. It is shown, however, that the solution which minimizes the evaluation function is not always optimal due to statistical bias. To deal with this problem, a method to eliminate the statistical bias in the evaluation function is proposed for zero mean white noise. Once the statistical bias is eliminated, the solution of the linear algorithm coincides with the correct solution by means of expectation. In this linear algorithm, only the eigenvector corresponding to the zero eigenvalue of a 33 matrix is necessary to find the translational velocity. Once the translational velocity is obtained, the rotational velocity can be computed directly. This method is also shown to be noise resistant by computer simulation.