Image analysis is a fundamental task for extracting information from images acquired across a range of different devices. Since reliable quantitative results are requested, image analysis requires ...highly sophisticated numerical and analytical methods—particularly for applications in medicine, security, and remote sensing, where the results of the processing may consist of vitally important data. The contributions to this book provide a good overview of the most important demands and solutions concerning this research area. In particular, the reader will find image analysis applied for feature extraction, encryption and decryption of data, color segmentation, and in the support new technologies. In all the contributions, entropy plays a pivotal role.
Based on information theory, a number of entropy measures have been proposed since the 1990s to assess systems’ irregularity, such as approximate entropy, sample entropy, permutation entropy, ...intrinsic mode entropy, and dispersion entropy, to cite only a few. Among them, sample entropy has been used in a very large variety of disciplines for both univariate and multivariate data. However, improvements to the sample entropy algorithm are still being proposed because sample entropy is unstable for short time series, may be sensitive to parameter values, and can be too time-consuming for long data. At the same time, it is worth noting that sample entropy does not take into account the multiple temporal scales inherent in complex systems. It is maximized for completely random processes and is used only to quantify the irregularity of signals on a single scale. This is why analyses of irregularity—with sample entropy or its derivatives—at multiple time scales have been proposed to assess systems’ complexity. This Book presents contributions related to new and original research based on the use of sample entropy or its derivatives.
In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing ...interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors.
The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters.
This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.
In this paper, we establish a Kantorovich duality for unbalanced optimal total variation transport problems. As consequences, we recover a version of duality formula for partial optimal transports ...established by Caffarelli and McCann; and we also get another proof of Kantorovich–Rubinstein theorem for generalized Wasserstein distance $\widetilde {W}_1^{a,b}$ proved before by Piccoli and Rossi. Then we apply our duality formula to study generalized Wasserstein barycenters. We show the existence of these barycenters for measures with compact supports. Finally, we prove the consistency of our barycenters.
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