The dependence between random variables may be measured by mutual information. However, the estimation of mutual information is difficult since the estimation of the joint probability density function (PDF) of non-Gaussian distributed data is a hard problem. Copulas offer a natural approach for estimating mutual information, since the joint probability density function of random variables can be expressed as the product of the associated copula density function and marginal PDFs. The experiment demonstrates that the proposed copulas-based mutual information is much more accurate than conventional methods such as the joint histogram and Parzen window based mutual information that are widely used in image processing

Copulas offer interesting insights into the dependence structures between the distributions of random variables. This report introduces new copulas, and provides an analysis for copulas, associated with bivariate exponential and Rayleigh distributions that have relevance to signal processing

This paper explores a new measure for band selection of hyperspectral images using copulas-based mutual information. Mutual information offers a measure of the dependence between random variables, which can be used to select specific bands for the analysis of hyperspectral images. This is achieved by comparing mutual information values between the band images and a reference map. In this paper, copula density functions are exploited for the estimation of mutual information between the images. Due to the special relationship between copula density functions and joint probability density functions, copulas offer a natural and robust way for the estimation of the mutual information

Existing works on multivariate distributions mainly focus on limited distribution functions and require that the associated marginal distributions belong to the same family. Although this simplifies problems, it may fail to deal with practical cases when the marginal distributions are arbitrary. To this end, copula function is employed since it provides a flexible way in decoupling the marginal distributions and dependence structure for random variables. Among different copula functions, most researches focus on Gaussian, Student's t and Archimedean copulas for simplicity. In this paper, to extend bivariate copula families, we have constructed new bivariate copulas for exponential, Weibull and Rician distributions. We have proved that the three copula functions of exponential, Rayleigh and Weibull distributions are equivalent, constrained by only one parameter, thus greatly facilitating practical applications of them. We have also proved that the copula function of log-normal distribution is equivalent to the Gaussian copula. Moreover, we have derived the Rician copula with two parameters. In addition, the modified Bessel function or incomplete Gamma function with double integrals in the copula functions are simplified by single integral or infinite series for computational efficiency. Associated copula density functions for exponential, Rayleigh, Weibull, log-normal, Nakagami-m and Rician distributions are also derived.

This paper explores a new class of measures for the detection of changes in images, specially for images acquired from different classes of sensors such as synthetic aperture radar (SAR) systems or computerized axial tomography (CAT) systems, monitoring patients. The problems become very challenging as the local statistics may be different even though the observations in the images may be similar. By exploiting this similarity new approaches are proposed for change detection. Based on the assumption that some form of dependence exists between the images, this dependence can be modeled by copulas. By using the conditional copula and the second image to simulate the distribution of first image, the dependence between the two images may be more closely modeled by the ensuing joint distribution. As a follow on, the symmetrical Kullback-Leibler distance can be used to obtain the change indicator between the distributions associated with the two images. In this paper the conditional copula is used as a change detector and applied to scenes from two distinct and different image families -SAR and CAT, and its performance compared with that of conventional change detection algorithms, based on a pixel based difference measure and on local pixel statistics