Abstract

Even though numerous algorithms exist for estimating the 3D structure of a scene from its video, the solutions obtained are often of unacceptable quality. To overcome some of the de ciencies, many application systems rely on processing more data than necessary with the hope that the redundancy will help improve the quality. This raises the question about how the accuracy of the solution is related to the amount of data processed by the algorithm. Can we de ne the accuracy of the solution precisely enough that we automatically recognize situations where the quality of the data is so bad that even a large number of additional observations will not yield the desired solution? Previous eorts to answer this question have used statistical measures like second order moments. They are useful if the estimate of the structure is unbiased and the higher order statistical eects are negligible, which is often not the case. This paper proposes an alternative criterion to evaluate a 3D reconstruction in an algorithm-independent manner. It introduces an information-theoretic criterion for evaluating the quality of a 3D reconstruction in terms of the statistics of the observed parameters (i.e. the image correspondences). The accuracy of the reconstruction is judged by considering the change in mutual information (termed as the incremental mutual information) between a scene and its reconstructions. An example of 3D reconstruction from a video sequence using optical ow equations and known noise distribution is considered and it is shown how the mutual information can be computed from rst principles in terms of the parameters of the input video sequence. We present simulations on both synthetic and real data to demonstrate the eectiveness of the proposed criterion.

Citations