IEEE Transactions on Pattern Analysis and Machine Intelligence
Image and Vision Computing
Statistical Methods and Models for Video-Based Tracking, Modeling, and Recognition
Foundations and Trends in Signal Processing
An algorithm of determining the plane based on monocular vision and laser loop
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
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The present state-of-the-art in computing the error statistics in three-dimensional (3-D) reconstruction from video concentrates on estimating the error covariance. A different source of error which has not received much attention is the fact that the reconstruction estimates are often significantly statistically biased. In this paper, we derive a precise expression for the bias in the depth estimate, based on the continuous (differentiable) version of structure from motion (SfM). Many SfM algorithms, or certain portions of them, can be posed in a linear least-squares (LS) framework Ax=b. Examples include initialization procedures for bundle adjustment or algorithms that alternately estimate depth and camera motion. It is a well-known fact that the LS estimate is biased if the system matrix A is noisy. In SfM, the matrix A contains point correspondences, which are always difficult to obtain precisely; thus, it is expected that the structure and motion estimates in such a formulation of the problem would be biased. Existing results on the minimum achievable variance of the SfM estimator are extended by deriving a generalized Cramer-Rao lower bound. A detailed analysis of the effect of various camera motion parameters on the bias is presented. We conclude by presenting the effect of bias compensation on reconstructing 3-D face models from rendered images.