TY - CONF
T1 - Statistical bias and the accuracy of 3d reconstruction from video
T2 - in International Journal of Computer Vision
Y1 - 2003
A1 - Chowdhury, A.R.
A1 - Chellapa, Rama
AB - The present state of the art in determining the error statistics in3D reconstruction from video concentrates on estimating the error covariance. A different source of error which has not received much attention in the computer vision community, but has been noted by psychophysicists, is the fact "that it is hard to explain ... the existence of systematic biases in observers' magnitude estimation of perceived depth" (Todd, 1998). In this paper, we prove that the depth estimate is statistically biased, derive a precise expression for it, and hypothesize that our analysis can be a possible explanation for the experimental observations. Many structure from motion (SfM) algorithms that reconstruct a scene from a video sequence pose the problem in a linear least squares framework Ax = b. It is a well- known fact that the least squares estimate is biased if the system matrix A is noisy. In SfM, the matrix A contains the image coordinates, 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. Though previous authors have analyzed the bias in 3D motion estimation from stereo, to the best of our knowledge, the statistical bias in 3D reconstruction from video has not been studied in the vision community. We show that even with a perfect motion estimate, the depth estimate is statistically biased. Existing results on the minimum achievable variance of the estimator are extended by deriving a generalized Cramer-Rao lower bound. Through simulations, we demonstrate the effects of camera motion parameters on the bias and give numerical examples to highlight the importance of compensating for it.
JA - in International Journal of Computer Vision
ER -