Minimax Entropy Principle Research Articles

Experimental Validation of Minimax Entropy Principle in Ultrasound Images

Ultrasound imaging is one of the non-invasive imaging, that diagnoses the disease inside a human body and there are numerous ultrasonic devices being used frequently. Entropy as a well known statistical measure of uncertainty has a considerable impact on the medical images. A procedure for minimizing the entropy with respect to the region of interest is demonstrated. This new approach has shown the experiments using Extracted Region Of Interest Based Sharpened image, called as (EROIS) image based on Minimax entropy principle and various filters. In this turn, the approach also validates the versatility of the entropy concept. Experiments have been performed practically on the real-time ultrasound images collected from ultrasound centers and have shown a significant performance. The present approach has been validated with showing results over ultrasound images of the Human Gallbladder.

Minimax entropy solutions of ill-posed problems

Convergent methodology for ill-posed problems is typically equivalent to application of an operator dependent on a single parameter derived from the noise level and the data (a regularization parameter or terminal iteration number). In the context of a given problem discretized for purposes of numerical analysis, these methods can be viewed as resulting from imposed prior constraints bearing the same amount of information content. We identify a new convergent method for the treatment of certain multivariate ill-posed problems, which imposes constraints of a much lower information content (i.e., having much lower bias), based on the operator’s dependence on many data-derived parameters. The associated marked performance improvements that are possible are illustrated with solution estimates for a Lyapunov equation structured by an ill-conditioned matrix. The methodology can be understood in terms of a Minimax Entropy Principle, which emerges from the Maximum Entropy Principle in some multivariate settings.

Statistical Principles in Image Modeling

Images of natural scenes contain a rich variety of visual patterns. To learn and recognize these patterns from natural images, it is necessary to construct statistical models for these patterns. In this review article we describe three statistical principles for modeling image patterns: the sparse coding principle, the minimax entropy principle, and the meaningful alignment principle. We explain these three principles and their relationships in the context of modeling images as compositions of Gabor wavelets. These three principles correspond to three regimes of composition patterns of Gabor wavelets, and these three regimes are connected by changes in scale or resolution.

Modeling Visual Patterns by Integrating Descriptive and Generative Methods

This paper presents a class of statistical models that integrate two statistical modeling paradigms in the literature: (I) Descriptive methods, such as Markov random fields and minimax entropy learning (Zhu, S.C., Wu, Y.N., and Mumford, D. 1997. Neural Computation, 9(8)), and (II) Generative methods, such as principal component analysis, independent component analysis (Bell, A.J. and Sejnowski, T.J. 1997. Vision Research, 37:3327-3338), transformed component analysis (Frey, B. and Jojic, N. 1999. ICCV), wavelet coding (Mallat, S. and Zhang, Z. 1993. IEEE Trans. on Signal Processing, 41:3397-3415; Chen, S., Donoho, D., and Saunders, M.A. 1999. Journal on Scientific Computing, 20(1):33-61), and sparse coding (Olshausen, B.A. and Field, D.J. 1996. Nature, 381:607-609; Lewicki, M.S. and Olshausen, B.A. 1999. JOSA, A. 16(7): 1587-1601). In this paper, we demonstrate the integrated framework by constructing a class of hierarchical models for texton patterns (the term "texton" was coined by psychologist Julesz in the early 80s). At the bottom level of the model, we assume that an observed texture image is generated by multiple hidden "texton maps", and textons on each map are translated, scaled, stretched, and oriented versions of a window function, like mini-templates or wavelet bases. The texton maps generate the observed image by occlusion or linear superposition. This bottom level of the model is generative in nature. At the top level of the model, the spatial arrangements of the textons in the texton maps are characterized by minimax entropy principle, which leads to embellished versions of Gibbs point process models (Stoyan, D., Kendall, W.S., and Mecke, J. 1985. Stochastic Geometry and its Applications). The top level of the model is descriptive in nature. We demonstrate the integrated model by a set of experiments.

Minimax Entropy Principle and Its Application to Texture Modeling

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle consists of two parts. The first is the maximum entropy principle for feature binding (or fusion): for a given set of observed feature statistics, a distribution can be built to bind these feature statistics together by maximizing the entropy over all distributions that reproduce them. The second part is the minimum entropy principle for feature selection: among all plausible sets of feature statistics, we choose the set whose maximum entropy distribution has the minimum entropy. Computational and inferential issues in both parts are addressed; in particular, a feature pursuit procedure is proposed for approximately selecting the optimal set of features. The minimax entropy principle is then corrected by considering the sample variation in the observed feature statistics, and an information criterion for feature pursuit is derived. The minimax entropy principle is applied to texture modeling, where a novel Markov random field (MRF) model, called FRAME (filter, random field, and minimax entropy), is derived, and encouraging results are obtained in experiments on a variety of texture images. The relationship between our theory and the mechanisms of neural computation is also discussed.

Minimax Entropy Principle and Its Application to Texture Modeling

This article proposes a general theory and methodology, called the minimax entropy principle, for building statistical models for images (or signals) in a variety of applications. This principle co...