Principles of covariance propagation

Robert M. Haralick

doi:10.1117/12.364086

23 September 1999 Principles of covariance propagation

Robert M. Haralick

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Proceedings Volume 3811, Vision Geometry VIII; (1999) https://doi.org/10.1117/12.364086
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

This paper describes how to propagate approximately additive random perturbations through any kind of vision algorithm step in which the appropriate random perturbation model for the estimated quantity produced by the vision step is also an additive random perturbation. We assume that the vision algorithm step can be modeled as a calculation (linear or non- linear) that produces an estimate that minimizes an implicit scalar function of the input quantity and the calculated estimate. The only assumption is that the scalar function be non-negative, have finite first and second partial derivatives, that its value is zero for ideal data, and that the random perturbations are small enough so that the relationship between the scalar function evaluated at the ideal but unknown input and output quantities and evaluated at the observed input quantity and perturbed output quantity can be approximated sufficiently well by a first order Taylor series expansion. The paper finally discusses the issues of verifying that the derived statistical behavior agrees with the experimentally observed statistical behavior.

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Robert M. Haralick "Principles of covariance propagation", Proc. SPIE 3811, Vision Geometry VIII, (23 September 1999); https://doi.org/10.1117/12.364086

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