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On the Metric on Images Invariant with Respect to the Monotonic Brightness Transformation

  • MATHEMATICAL THEORY OF IMAGES AND SIGNALS REPRESENTING, PROCESSING, ANALYSIS, RECOGNITION, AND UNDERSTANDING
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Abstract—

It is described how to construct a distance on analog and quantized images, which is invariant with respect to strictly monotonic increasing transformations of the brightness function. The distance function takes into account possible normal noise on the image. The maximal value of such a distance for any number of quantizing levels and noise parameters is calculated. The experimental results, which make it possible to compare the invariant distance measure with classical measures, are presented.

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Funding

This study was supported by the Russian Foundation for Basic Researches, projects no. 19-07-00873 and 17-20-02017.

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Authors and Affiliations

  1. Southern Federal University, 347928, Taganrog, Russia

    A. N. Karkishchenko & V. B. Mnukhin

Authors
  1. A. N. Karkishchenko
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  2. V. B. Mnukhin
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Correspondence to A. N. Karkishchenko or V. B. Mnukhin.

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The authors declare that they do not have a conflict of interest.

Additional information

Karkishchenko Alexander Nikolaevich was born in 1956. In 1978 he graduated from Taganrog State University of Radio Engineering, specialty “Applied Mathematics”. He received the degree of Candidate of Sciences in 1983, and Doctor of Sciences in 1997. Now he is a Professor at Southern Federal University. Field of interests: graph theory; combinatorial analysis, theory of possibilities, theory of nonadditive measures, mathematical models for classification, image processing and analysis, pattern recognition. He is the author of more than 200 scientific papers.

Mnukhin Valeriy Borisovich was born in 1958. In 1979 he graduated from Taganrog State University of Radio Engineering, specialty “Applied Mathematics”. He received the degree of Candidate of Sciences from the Institute of Mathematics with the Computing Center of the Academy of Sciences of the Moldavian SSR in 1985. Now he is an Associate Professor at Southern Federal University. Field of interests: mathematical methods for pattern recognition, algebraic and topological combinatorial analysis, problems of graph reconstruction, spectral graph theory. He is the author of more than 80 scientific papers.

Translated by Yu. Zikeeva

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Karkishchenko, A.N., Mnukhin, V.B. On the Metric on Images Invariant with Respect to the Monotonic Brightness Transformation. Pattern Recognit. Image Anal. 30, 359–371 (2020). https://doi.org/10.1134/S1054661820030104

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  • DOI: https://doi.org/10.1134/S1054661820030104

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