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This paper deals with area-based subpixel image registration under the rotation-isometric scaling-translation transformation hypothesis. Our approach is based on parametrical modeling of geometrically transformed textural image fragments and maximum-likelihood estimation of the transformation vector between them. Due to the parametrical approach based on the fractional Brownian motion modeling of the local fragments' texture, the proposed estimator \mboxML_\mathrmfBm (ML stands for “maximum likelihood” and fBm stands for “fractal Brownian motion”) has the ability to better adapt to real image texture content compared with other methods relying on universal similarity measures such as mutual information or normalized correlation. The main benefits are observed when assumptions underlying the fBm model are fully satisfied, e.g., for isotropic normally distributed textures with stationary increments. Experiments on both simulated and real images and for high and weak correlations between registered images show that the \mboxML_\mathrmfBm estimator offers significant improvement compared with other state-of-the-art methods. It reduces translation vector, rotation angle, and scaling factor estimation errors by a factor of about 1.75–2, and it decreases the probability of false match by up to five times. In addition, an accurate confidence interval for \mboxML_\mathrmfBm estimates can be obtained from the Cramér–Rao lower bound on rotation-scaling-translation parameter estimation error. This bound depends on texture roughness, noise level in reference and template images, correlation between these images, and geometrical transformation parameters. [ABSTRACT FROM AUTHOR]

Many of the classical and recent relations between information and estimation in the presence of Gaussian noise can be viewed as identities between expectations of random quantities. These include the relationship between mutual information and minimum mean square error (I-MMSE) of Guo ; the relative entropy and mismatched estimation relationship of Verdú; the relationship between causal estimation and mutual information of Duncan, and its extension to the presence of feedback by Kadota ; the relationship between causal and non-casual estimation of Guo , and its mismatched version of Weissman. We dispense with the expectations and explore the nature of the pointwise relations between the respective random quantities. The pointwise relations that we find are as succinctly stated as—and give considerable insight into—the original expectation identities. As an illustration of our results, consider Duncan's 1970 discovery that the mutual information is equal to the causal MMSE in the additive white Gaussian noise channel, which can equivalently be expressed saying that the difference between the input–output information density and half the causal estimation error is a zero-mean random variable (regardless of the distribution of the channel input). We characterize this random variable explicitly, rather than merely its expectation. Classical estimation and information theoretic quantities emerge with new and surprising roles. For example, the variance of this random variable turns out to be given by the causal MMSE (which, in turn, is equal to twice the mutual information by Duncan's result). [ABSTRACT FROM PUBLISHER]