Histogram Ordering

5Citations
Citations of this article
17Readers
Mendeley users who have this article in their library.

Abstract

Frequency histograms are ubiquitous, being practically used in any field of science. In this paper, we present a partial order for frequency histograms and, to our knowledge, no order of this kind has been yet defined. This order is based on the stochastic order of discrete probability distributions and it has invariance properties that make it unique. First, we model a frequency histogram as a sequence of bins associated with a discrete probability (or relative frequency) distribution. Then, we consider that two histograms are ordered if they are defined on the same sequence of bins and their respective frequency distributions are stochastically ordered. The ordering can be easily spotted because the respective cumulative distribution functions of the frequencies of two ordered histograms do not cross each other. Finally, with each bin we can associate a representative value of the bin, and for two ordered histograms it holds that all quasi-arithmetic means (such as arithmetic, harmonic, and geometric mean) of the representative values weighted by the frequencies are ordered in the same direction than the histograms are. Our theoretical study is supported by three experiments in the fields of image processing, traffic flow, and income distribution.

References Powered by Scopus

Multimodality image registration by maximization of mutual information

4038Citations
N/AReaders
Get full text

A histogram modification framework and its application for image contrast enhancement

813Citations
N/AReaders
Get full text

The Essential Guide to Image Processing

366Citations
N/AReaders
Get full text

Cited by Powered by Scopus

Bayesian optimization and channel-fusion-based convolutional autoencoder network for fault diagnosis of rotating machinery

29Citations
N/AReaders
Get full text

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

11Citations
N/AReaders
Get full text

A Bayesian Adaptive Resize-Residual Deep Learning Network for Fault Diagnosis of Rotating Machinery

1Citations
N/AReaders
Get full text

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Cite

CITATION STYLE

APA

Sbert, M., Ancuti, C., Ancuti, C. O., Poch, J., Chen, S., & Vila, M. (2021). Histogram Ordering. IEEE Access, 9, 28785–28796. https://doi.org/10.1109/ACCESS.2021.3058577

Readers over time

‘21‘22‘23‘24‘2502468

Readers' Seniority

Tooltip

Professor / Associate Prof. 1

50%

Lecturer / Post doc 1

50%

Readers' Discipline

Tooltip

Engineering 2

50%

Computer Science 1

25%

Medicine and Dentistry 1

25%

Save time finding and organizing research with Mendeley

Sign up for free
0