A Priori and A Posteriori Error Estimates in Recovery of 3D Scenes by Factorization Algorithms

摘要

Many various algorithms for recovering three-dimensional scenes from a set of digital images have currently been developed. For certain scenes and shooting conditions, some algorithms give nice results, whereas others produce unacceptable results. In this paper, for a group of algorithms based on the matrix factorization, criteria are derived that make it possible, (a) by known statistical characteristics of the scene and shooting conditions, to predict whether a given algorithm can be used in the given case and, if it can, to determine the expected accuracy, (b) when recovering an unknown scene, to compute not only the desired results but also their accuracy (authenticity). A modification of the algorithm based on the adaptive selection of the approximation is suggested. Experimental verification of the criteria and estimates obtained showed their high efficiency and reliability.