Multinomial goodness-of-fit tests

The concept of entropy constitutes, together with energy, a cornerstone of contemporary physics and related areas. It was originally introduced by Clausius in 1865 along abstract lines focusing on thermodynamical irreversibility of macroscopic physical processes. In the next decade, Boltzmann made the genius connection—further developed by Gibbs—of the entropy with the microscopic world, which led to the formulation of a new and impressively successful physical theory, thereafter named statistical mechanics. The extension to quantum mechanical systems was formalized by von Neumann in 1927, and the connections with the theory of communications and, more widely, with the theory of information were respectively introduced by Shannon in 1948 and Jaynes in 1957. Since then, over fifty new entropic functionals emerged in the scientific and technological literature. The most popular among them are the additive Renyi one introduced in 1961, and the nonadditive one introduced in 1988 as a basis for the generalization of the Boltzmann–Gibbs and related equilibrium and nonequilibrium theories, focusing on natural, artificial and social complex systems. Along such lines, theoretical, experimental, observational and computational efforts, and their connections to nonlinear dynamical systems and the theory of probabilities, are currently under progress. Illustrative applications, in physics and elsewhere, of these recent developments are briefly described in the present synopsis.

Entropy

As a fundamental and critical task in various visual applications, image matching can identify then correspond the same or similar structure/content from two or more images. Over the past decades, growing amount and diversity of methods have been proposed for image matching, particularly with the development of deep learning techniques over the recent years. However, it may leave several open questions about which method would be a suitable choice for specific applications with respect to different scenarios and task requirements and how to design better image matching methods with superior performance in accuracy, robustness and efficiency. This encourages us to conduct a comprehensive and systematic review and analysis for those classical and latest techniques. Following the feature-based image matching pipeline, we first introduce feature detection, description, and matching techniques from handcrafted methods to trainable ones and provide an analysis of the development of these methods in theory and practice. Secondly, we briefly introduce several typical image matching-based applications for a comprehensive understanding of the significance of image matching. In addition, we also provide a comprehensive and objective comparison of these classical and latest techniques through extensive experiments on representative datasets. Finally, we conclude with the current status of image matching technologies and deliver insightful discussions and prospects for future works. This survey can serve as a reference for (but not limited to) researchers and engineers in image matching and related fields.

/pdf/image-matching-from-handcrafted-to-deep-features-a-survey-27kn6w026w.pdf

Image Matching from Handcrafted to Deep Features: A Survey

Feature matching, which refers to establishing reliable correspondence between two sets of features (particularly point features), is a critical prerequisite in feature-based registration. In this paper, we propose a flexible and general algorithm, which is called locally linear transforming (LLT), for both rigid and nonrigid feature matching of remote sensing images. We start by creating a set of putative correspondences based on the feature similarity and then focus on removing outliers from the putative set and estimating the transformation as well. We formulate this as a maximum-likelihood estimation of a Bayesian model with hidden/latent variables indicating whether matches in the putative set are outliers or inliers. To ensure the well-posedness of the problem, we develop a local geometrical constraint that can preserve local structures among neighboring feature points, and it is also robust to a large number of outliers. The problem is solved by using the expectation–maximization algorithm (EM), and the closed-form solutions of both rigid and nonrigid transformations are derived in the maximization step. In the nonrigid case, we model the transformation between images in a reproducing kernel Hilbert space (RKHS), and a sparse approximation is applied to the transformation that reduces the method computation complexity to linearithmic. Extensive experiments on real remote sensing images demonstrate accurate results of LLT, which outperforms current state-of-the-art methods, particularly in the case of severe outliers (even up to 80%).

Robust Feature Matching for Remote Sensing Image Registration via Locally Linear Transforming

In the last 10 years, development in robotics, computer vision, and sensor technology has provided new spectral remote sensing tools to capture unprecedented ultra-high spatial and high spectral resolution with unmanned aerial vehicles (UAVs). This development has led to a revolution in geospatial data collection in which not only few specialist data providers collect and deliver remotely sensed data, but a whole diverse community is potentially able to gather geospatial data that fit their needs. However, the diversification of sensing systems and user applications challenges the common application of good practice procedures that ensure the quality of the data. This challenge can only be met by establishing and communicating common procedures that have had demonstrated success in scientific experiments and operational demonstrations. In this review, we evaluate the state-of-the-art methods in UAV spectral remote sensing and discuss sensor technology, measurement procedures, geometric processing, and radiometric calibration based on the literature and more than a decade of experimentation. We follow the 'journey' of the reflected energy from the particle in the environment to its representation as a pixel in a 2D or 2.5D map, or 3D spectral point cloud. Additionally, we reflect on the current revolution in remote sensing, and identify trends, potential opportunities, and limitations.

/pdf/quantitative-remote-sensing-at-ultra-high-resolution-with-1fowvgc7qt.pdf

Quantitative Remote Sensing at Ultra-High Resolution with UAV Spectroscopy: A Review of Sensor Technology, Measurement Procedures, and Data Correction Workflows

In the present paper, based on the concept of fuzzy entropy, an exponential intuitionistic fuzzy entropy measure is proposed in the setting of Atanassov's intuitionistic fuzzy set theory. This measure is a generalized version of exponential fuzzy entropy proposed by Pal and Pal. A connection between exponential fuzzy entropy and exponential intuitionistic fuzzy entropy is also established. Some interesting properties of this measure are analyzed. Finally, a numerical example is given to show that the proposed entropy measure for Atanassov's intuitionistic fuzzy set is consistent by comparing it with other existing entropies.

http://www.kybernetika.cz/content/2013/1/114/paper.pdf

Exponential entropy on intuitionistic fuzzy sets

Gallager in 1965 IEEE Trans. Inform. Theory IT-11, 3) gave an elegant proof of coding theorem and obtained an upper bound over the probability of error in terms of reliability function. Its dual has recently been proved by Arimoto [(1973), IEEE Trans. Inform. Theory 19, 357]. We have modified the decoding scheme by bringing in the distortion. This provides an upper bound over distortion due to error when rate distortion function is less than capacity. When rate distortion function is above capacity a lower bound on distortion due to error gives the dual for code words of any block length.

Bounds on distortion due to error for rates below and above the channel capacity

On m-ary Gray codes

Using the idea of Renyi's entropy, intuitionistic fuzzy entropy of order-α is proposed in the setting of intuitionistic fuzzy sets theory. This measure is a generalized version of fuzzy entropy of order-α proposed by Bhandari and Pal and intuitionistic fuzzy entropy defined by Vlachos and Sergiadis. Our study of the four essential and some other properties of the proposed measure clearly establishes the validity of the measure as intuitionistic fuzzy entropy. Finally, a numerical example is given to show that the proposed entropy measure for intuitionistic fuzzy set is reasonable by comparing it with other existing entropies.

/pdf/on-intuitionistic-fuzzy-entropy-of-order-a-3nrpfuwhv3.pdf

On intuitionistic fuzzy entropy of order-α

The prioritized weighted average (PWA) operator was originally introduced by Yager. The prominent characteristic of the PWA operator is that it takes into account prioritization among attributes and decision makers. By combining the idea of generalized mean and PWA operator, we propose a new prioritized aggregation operator called fuzzy generalized prioritized weighted average (FGPWA) operator for aggregating triangular fuzzy numbers. The properties of the new aggregation operator are studied out and their special cases are examined. Furthermore, based on the FGPWA operator, an approach to deal with multiple attribute group decision making problems under triangular fuzzy environments is developed. Finally, a practical example is provided to illustrate the multiple attribute group decision making process. C � 2013 Wiley Periodicals, Inc.

Fuzzy Generalized Prioritized Weighted Average Operator and its Application to Multiple Attribute Decision Making

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