This paper describes how to validate image processing algorithms when the algorithm has been designed to produce a numerical output that optimizes a given scalar criterion function having all first and second partial derivatives. The validation technique analyzes the statistical behavior of the algorithm under small random perturbations of its input. This paper gives the theory for the computation of the covariance matrix of the output when the input is perturbed by small random input perturbations. A statistical test is done examining the algorithm output under multiple instances of simulated perturbations and comparing these outputs with the ideal output and the analytically derived covariance matrix. A second level of simulations can be done that examines the test statistics of the hypothesis of the statistical test to determine whether in fact it is distributed in accordance with statistical theory. If the hypothesis is rejected that the output perturbations do not have the analytically predicted covariance matrix, then the image analysis software fails validation.