Statistical optimization and geometric inference in computer vision

This paper gives a mathematical formulation to the computer vision task of inferring three-dimensional structures of the scene based on image data and geometric constraints. Introducing a statistical model of image noise, we define a geometric model as a manifold determined by the constraints and vi...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 1998-05, Vol.356 (1740), p.1303-1320
Main Author: Kanatani, Kenichi
Format: Article
Language:English
Subjects:
Accuracy Bound
AIC
Computer vision
Covariance matrices
Cramer-Rao Lower Bound
Curve Fitting
Degrees of freedom
Estimators
Geometry and Statistics
Inference
Mathematical manifolds
Mathematical vectors
Maximum likelihood estimation
Model Selection
Modeling
Rotation
Structure From Motion
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Summary:This paper gives a mathematical formulation to the computer vision task of inferring three-dimensional structures of the scene based on image data and geometric constraints. Introducing a statistical model of image noise, we define a geometric model as a manifold determined by the constraints and view the problem as model fitting. We then present a general mathematical framework for proving optimality of estimation, deriving optimal schemes, and selecting appropriate models. Finally, we illustrate our theory by applying it to curve fitting and structure from motion.
ISSN:1364-503X
1471-2962
DOI:10.1098/rsta.1998.0223