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Statistical bias in 3-D reconstruction from a monocular video
Amit K Roy-Chowdhury1, Rama Chellappa
1Department of Electrical Engineering, University of California, Riverside, CA 92521, USA.
Summary
This study quantifies statistical bias in 3-D reconstruction, a common error source in structure from motion (SfM). We present a precise bias expression and analyze its impact on 3-D face models.
Area of Science:
- Computer Vision
- Robotics
- Computational Geometry
Background:
- Current 3-D reconstruction methods focus on error covariance, often neglecting statistical bias.
- Structure from motion (SfM) algorithms frequently employ linear least-squares (LS) frameworks.
- Noisy point correspondences in SfM's system matrix lead to biased estimates.
Purpose of the Study:
- To derive a precise expression for bias in depth estimates within SfM.
- To extend existing bounds on SfM estimator variance.
- To analyze the influence of camera motion on bias and its effect on 3-D face reconstruction.
Main Methods:
- Derivation of a precise bias expression for depth estimates using continuous SfM.
- Extension of the generalized Cramer-Rao lower bound for SfM estimators.
- Analysis of camera motion parameters' effect on bias.
Main Results:
- A precise mathematical expression for bias in SfM depth estimation is derived.
- The generalized Cramer-Rao lower bound is established for SfM.
- Camera motion parameters significantly affect the bias in 3-D reconstructions.
Conclusions:
- Statistical bias is a critical, often overlooked, error source in 3-D reconstruction.
- Bias compensation can improve the accuracy of 3-D face models reconstructed from video.
- The derived bias expression and analysis provide a foundation for more robust SfM algorithms.