Propagating covariance in computer vision

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. The author assumes that the vision algorithm step can be modeled as a calculation (linear or nonlinear) that produces an estimate that minimizes an implicit scaler function of the input quantity and the calculated estimate. The only assumption is that the scaler functions have finite second partial derivatives and that the random perturbations are small enough so that the relationship between the scaler function evaluated at the ideal but unknown input and output quantities and 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.