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Image registration algorithm based on stochastic gradient optimisation of mutual information between images


A.G. Tashlinsky – Dr.Sc.(Eng.), Professor, Head of Department «Radio Engineering», Ulyanovsk State Technical University
S.V. Voronov – Ph.D.(Eng.), Associate Professor, Department «Radio Engineering», Ulyanovsk State Technical University
A.V. Zhukova – Post-graduate Student, Ulyanovsk State Technical University

One of the problems of processing digital images is their registration (matching). There are various algorithms solving this problem and operating both in the frequency and spatial domains. Mean squared error and correlation coefficient are a common choice for the objective function in this problem. However, these measures are ineffective when matching multimodal images and images with sig-nificant nonlinear intensity distortions. Among the similarity measures mutual information is most resistant to the types of distortions indicated. Therefore, this paper is devoted to development of a recurrent image registration algorithm based on this measure. The algorithm is based on stochastic gradient optimisation of registration parameters.
In the development of the algorithm, the problems of finding the probability density function of image intensities from a small image sample, estimation of the derivative of image entropy and calculation of the components of mutual information gradient with respect to the parameters of the given registration model are solved. In order to restore the probability density function of image intensities, Parzen window method is applied to the intensities in the sample drawn on each. iteration. This allows us to estimate the density function using a small sample size. To estimate the entropy of the image from the reconstructed probability density function, a method based on the use of an additional sample is used. Finite differences approach is applied for finding mutual information gradient estimates with respect to image base axis. The estimates of the chosen registration model with respect to registration parameters are calculated analytically. This approach requires only two estimates of mutual information at each iteration which ensures high processing speed.
The developed algorithm is tested on synthetic and real images. The tests show high effectiveness of the algorithm proposed. When matching multimodal images and images with significant non-linear intensity distortions the algorithm shows higher processing speed and stability of estimates in comparison with algorithms which use mean squared error and correlation coefficient as the objective function.

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