Towards a criterion for evaluating the quality of 3D reconstructions

Even though numerous algorithms exist for estimating the structure of a scene from its video, the solutions obtained are often of unacceptable quality. To overcome some of the deficiencies, many application systems rely on processing more information 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 information processed by the algorithm. Can we define 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? This paper proposes 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 (or equivalently the conditional differential entropy) between a scene and its reconstructions and its effectiveness is shown through simulations.