TY - JOUR
T1 - Statistical bias in 3-D reconstruction from a monocular video
JF - Image Processing, IEEE Transactions on
Y1 - 2005
A1 - Roy-Chowdhury, A.K.
A1 - Chellapa, Rama
KW - 3D face models
KW - 3D video reconstruction
KW - algorithms
KW - artifacts
KW - Artificial intelligence
KW - Automated;Signal Processing
KW - bias compensation
KW - bundle adjustment
KW - camera motion estimation
KW - Computer simulation
KW - Computer-Assisted;Imaging
KW - Computer-Assisted;Subtraction Technique;Video Recording;
KW - depth estimate
KW - error covariance estimation
KW - error statistics
KW - generalized Cramer-Rao lower bound
KW - Image Enhancement
KW - Image Interpretation
KW - Image reconstruction
KW - initialization procedures
KW - least squares approximations
KW - linear least-squares framework
KW - monocular video
KW - motion compensation
KW - Motion estimation
KW - statistical bias
KW - Statistical;Pattern Recognition
KW - structure from motion algorithms
KW - Three-Dimensional;Information Storage and Retrieval;Models
KW - video signal processing
AB - 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.
VL - 14
SN - 1057-7149
CP - 8
M3 - 10.1109/TIP.2005.849775
ER -