Histogram Ordering

Sbert, Mateu; Ancuti, Cosmin; Poch, Jordi; Chen, Shuning; Vila, Marius

doi:10.1109/access.2021.3058577

Cited by 5 publications

(6 citation statements)

References 15 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then, we can summarize the results from Tables A1 and A2 in Table 1. This will do to prove Equation (20). The results for Equation ( 21) are obtained as above by substituting {α k }, {α k } by {α M−k+1 }, {α M−k+1 }.…”

Section: Discussionmentioning

confidence: 96%

“…Suppose now f (x) is decreasing and that Equations (20) and Equation ( 21) hold for g (x) and for f (x) increasing. Then, the following inequalities, for g (x) increasing,…”

Section: Discussionmentioning

confidence: 99%

“…Proof. Indirect or partial proofs can be found in [17,20]. We provide a complete proof in the Appendix A.…”

Section: Quasi-arithmetic Meanmentioning

confidence: 99%

“…These relationships between weights define first stochastic order, and likelihood ratio order. Their application to multiple importance sampling (MIS), a Monte Carlo technique, has been presented in [18], its application to cross entropy in [19], and in [20] applications to image processing, traffic flow and income distribution have been shown. In [21], the invariance results on products of distributions of independent scalar r.v.…”

Section: Introductionmentioning

confidence: 99%

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Stochastic Order and Generalized Weighted Mean Invariance

Sbert

Poch

Chen

et al. 2021

Entropy

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In this paper, we present order invariance theoretical results for weighted quasi-arithmetic means of a monotonic series of numbers. The quasi-arithmetic mean, or Kolmogorov–Nagumo mean, generalizes the classical mean and appears in many disciplines, from information theory to physics, from economics to traffic flow. Stochastic orders are defined on weights (or equivalently, discrete probability distributions). They were introduced to study risk in economics and decision theory, and recently have found utility in Monte Carlo techniques and in image processing. We show in this paper that, if two distributions of weights are ordered under first stochastic order, then for any monotonic series of numbers their weighted quasi-arithmetic means share the same order. This means for instance that arithmetic and harmonic mean for two different distributions of weights always have to be aligned if the weights are stochastically ordered, this is, either both means increase or both decrease. We explore the invariance properties when convex (concave) functions define both the quasi-arithmetic mean and the series of numbers, we show its relationship with increasing concave order and increasing convex order, and we observe the important role played by a new defined mirror property of stochastic orders. We also give some applications to entropy and cross-entropy and present an example of multiple importance sampling Monte Carlo technique that illustrates the usefulness and transversality of our approach. Invariance theorems are useful when a system is represented by a set of quasi-arithmetic means and we want to change the distribution of weights so that all means evolve in the same direction.

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Section: Discussionmentioning

confidence: 96%

“…Suppose now f (x) is decreasing and that Equations (20) and Equation ( 21) hold for g (x) and for f (x) increasing. Then, the following inequalities, for g (x) increasing,…”

Section: Discussionmentioning

confidence: 99%

“…Proof. Indirect or partial proofs can be found in [17,20]. We provide a complete proof in the Appendix A.…”

Section: Quasi-arithmetic Meanmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stochastic Order and Generalized Weighted Mean Invariance

Sbert

Poch

Chen

et al. 2021

Entropy

Self Cite

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“…To solve the problem, HE is employed in this paper to enhance the image contrast and to highlight the image features. The specific principle is 45…”

Section: The Proposed Adaptive Resize-residual Networkmentioning

confidence: 99%

Adaptive resize-residual deep neural network for fault diagnosis of rotating machinery

Zou

Lam

2022

Structural Health Monitoring

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Accurate fault diagnosis technology is essential for ensuring reliable operation of rotating machinery. However, complex conditions and various damage forms bring challenges to present diagnosis technology. In this study, a novel fault diagnosis method is proposed utilizing the newly developed adaptive resize-residual deep neural networks. The usage of the proposed method consists of three steps. First, the continuous wavelet transform is used to transfer the acquired vibration signals into time–frequency images. Second, the histogram equalization algorithm is applied to enhance the contrast of these images. Finally, the enhanced images are used as the input of newly proposed adaptive resize-residual networks, in which the adaptive resize block can deduce the dimensions of input data by self-learning and feed them into the residual block for pattern recognition. Two experimental cases are designed to evaluate the performance of proposed method. The experimental results indicate that the proposed adaptive resize-residual network obtains superior recognition accuracy and outperforms many state-of-the-art methods.

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