Kaniadakis Entropy and Images

Entropy has a relevant role in several applications of information theory and in the image processing. Here, we discuss the Kaniadakis entropy for images. An example of bi-level image thresholding obtained by means of this entropy is also given. Keywords: Kaniadakis Entropy, Data Segmentation, Image processing, Thresholding

Shannon, Tsallis and Kaniadakis entropies in bi-level image thresholding

The maximum entropy principle is often used for bi-level or multi-level thresholding of images. For this purpose, some methods are available based on Shannon and Tsallis entropies. In this paper, we discuss them and propose a method based on Kaniadakis entropy.Comment: Keywords: Kaniadakis Entropy, Image Processing, Image Segmentation, Image Thresholding, Texture Transition

Tsallis Entropy In Bi-level And Multi-level Image Thresholding

International audienceThe maximum entropy principle has a relevant role in image processing, in particular for thresholding and image segmentation. Different entropic formulations are available to this purpose; one of them is based on the Tsallis non-extensive entropy. Here, we propose a discussion of its use for bi-and multi-level thresholding

Tsallis Entropy In Bi-level And Multi-level Image Thresholding

The maximum entropy principle has a relevant role in image processing, in particular for thresholding and image segmentation. Different entropic formulations are available to this purpose; one of them is based on the Tsallis non-extensive entropy. Here, we propose a discussion of its use for bi-and multi-level thresholding

On The Generalized Additivity Of Kaniadakis Entropy

Since entropy has several applications in the information theory, such as, for example, in bi-level or multi-level thresholding of images, it is interesting to investigate the generalized additivity of Kaniadakis entropy for more than two systems. Here we consider the additivity for three, four and five systems, because we aim applying Kaniadakis entropy to such multi-level analyses

Edges Detection Based On Renyi Entropy with Split/Merge

Most of the classical methods for edge detection are based on the first and second order derivatives of gray levels of the pixels of the original image. These processes give rise to the exponential increment of computational time, especially with large size of images, and therefore requires more time for processing. This paper shows the new algorithm based on both the Rényi entropy and the Shannon entropy together for edge detection using split and merge technique. The objective is to find the best edge representation and decrease the computation time. A set of experiments in the domain of edge detection are presented. The system yields edge detection performance comparable to the classic methods, such as Canny, LOG, and Sobel.  The experimental results show that the effect of this method is better to LOG, and Sobel methods. In addition, it is better to other three methods in CPU time. Another benefit comes from easy implementation of this method. Keywords: Rényi Entropy, Information content, Edge detection, Thresholdin

Wavelet regression using a Lévy prior model

This thesis is concerned with nonparametric regression and regularization. In particular, wavelet regression using a Lévy prior model is investigated. The use of this prior is motivated by the statistical properties, such as heavy-tails, common in many datasets of interest, such as those in financial time series. The Lévy process we propose captures the heavy tails of the wavelet coefficients of an unknown function. We study the Besov regularity of the wavelet coefficients and establish the connection between the parameters of the Lévy wavelet prior model and Besov spaces. At first, we gave a necessary and sufficient condition such that the realizations of the prior model fall into a certain class of Besov spaces. We show that the tempered stable distribution preserves its functional form for different time scales. We prove that this scaling behaviour can model the exponential-decay-across-scale property of the wavelet coefficients without imposing any specified structure on the coefficients’ energy. We also introduce a Lévy wavelet mixture model to capture the sparseness of the wavelet coefficients. We show that this sparse model exhibits a thresholding rule. We also study the Lévy tempered stable prior model under a Bayesian framework. For the prior specified, we gave a closed form to the posterior Lévy measure of the wavelet coefficients and estimate the hyperparameters of the prior model in both a simulation study and for the S&P 500 time series. We focus on density estimation using a penalized likelihood approach. Primarily, we study the wavelet Tsallis entropy and Fisher information and give closed-form expressions for these measures when the wavelet coefficients are driven by a tempered stable process. Then, we develop an entropic regularization based on the wavelet Tsallis entropy and show that the penalized maximum likelihood method improves the convergence of the estimates