Image registration by sequential tests of hypotheses: The relationship between Gaussian and binomial models

Abstract

In previous papers[1, 2], a method for treating translational image registration problems by sequential tests of hypotheses was presented. Two types of statistical models were used to describe the accumulated error between the images to be registered, namely, a Gaussian and a binomial model. The proposed method successfully registered a LANDSAT image against noisy versions of itself, different channels of the same image as well as images taken 6 months apart. In this paper, relationships between both models are established. First, by assuming that both images to be registered are Gaussian and one image is essentially a noisy version of the other, and that both images are thresholded at the mean value, a derivation is made of the probability curve of the binary error being equal to one, at the registration point, versus the signal-to-noise ratio. Second, by assuming that the cross correlation between the signals in both images is autoregressive of order one and separable, the set of probability curves of the binary error being equal to one versus the distance from registration point is derived. Third, under the same assumptions of the previous case, the set of curves relating the error variance versus the displacement is also obtained. The curves, for the second and third cases, are described for different values of the correlation coefficients in both directions and of the signal-to-noise ratio. Finally, a comparison between the theoretical curves and the experimental results is performed.