Analytical results on error sensitivity of motion estimation from two views

摘要

Fundamental instabilities have been observed in the performance of the majority of the algorithms for three dimensional motion estimation from two views. Many geometric and intuitive interpretations have been offered to explain the error sensitivity of the estimated parameters. In this contribution, the importance of the form of the error norm to be minimized with respect to the motion parameters is addressed. The error norms used by the existing algorithms are described in a unifying notation, and a geometric interpretation of them is given. Then, for the continuous case of pure translational motion it is proved that the minimization of the objective function leading to an eigenvector solution suffers from a crucial instability. The analyticity of the results allows the examination of error sensitivity in terms of the translation direction, the viewing angle and the distance of the moving object from the camera. A norm possessing a reasonable geometric interpretation in the image plane is proposed to eliminate the effects of the instability mentioned above. Due to the high nonlinearity of this norm it has not been possible to prove explicitly its stabilizing role. It is shown by analytical means that a simplification of this norm — leading to a closed form solution — has undesirable properties.