%0 Journal Article
%J Image Processing, IEEE Transactions on
%D 2005
%T Statistical bias in 3-D reconstruction from a monocular video
%A Roy-Chowdhury, A.K.
%A Chellapa, Rama
%K 3D face models
%K 3D video reconstruction
%K algorithms
%K artifacts
%K Artificial intelligence
%K Automated;Signal Processing
%K bias compensation
%K bundle adjustment
%K camera motion estimation
%K Computer simulation
%K Computer-Assisted;Imaging
%K Computer-Assisted;Subtraction Technique;Video Recording;
%K depth estimate
%K error covariance estimation
%K error statistics
%K generalized Cramer-Rao lower bound
%K Image Enhancement
%K Image Interpretation
%K Image reconstruction
%K initialization procedures
%K least squares approximations
%K linear least-squares framework
%K monocular video
%K motion compensation
%K Motion estimation
%K statistical bias
%K Statistical;Pattern Recognition
%K structure from motion algorithms
%K Three-Dimensional;Information Storage and Retrieval;Models
%K video signal processing
%X 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.
%B Image Processing, IEEE Transactions on
%V 14
%P 1057 - 1062
%8 2005/08//
%@ 1057-7149
%G eng
%N 8
%R 10.1109/TIP.2005.849775