| Abstract | 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.
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