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Computer Optics, 2022, Volume 46, Issue 6, Pages 939–947
DOI: https://doi.org/10.18287/2412-6179-CO-1080
(Mi co1089)
 

IMAGE PROCESSING, PATTERN RECOGNITION

Image decomposition method by topological features

S. V. Eremeeva, A. V. Abakumova, D. E. Andrianova, D. V. Titovb

a Murom Institute (branch), Vladimir State University named after Alexander and Nikolay Stoletovs
b Southwest State University, Kursk
Abstract: A new method for decomposing an image into separate objects of interest is proposed in the article. The developed method is based on the use of persistent homology. A process of direct and reverse image transformation is shown. Following direct transformation, the original image is represented as a set of matrices that can be divided into basic and detailing ones. The basic matrices contain information about the basic structure of objects in the images, and the detailing ones include data about the details of these objects, about small objects or the noise component. It is shown that there is a certain analogy with the Wavelet transformation, but the proposed method is based on a fundamentally different theoretical basis. A numerical example reflecting the basic essence of the method is described in detail. Properties of the decomposition and the possibility of using standard algebraic operations on decomposition matrices are described. The reverse transformation allows us to take into account the changed properties of individual objects and synthesize a new image. Prospects of using the proposed decomposition for solving practical problems are demonstrated. Algorithms have been developed for binarization of images and removal of text on a non-uniform background. Data analysis and processing is carried out using a unified approach in the space of decomposition matrices. The results of binarization have shown that, when compared with analogues, the developed algorithm will perform better when the binarization is used to isolate a multitude of individual objects. The obtained results of the algorithm for deleting text on a non-uniform background confirm that the information is completely deleted without affecting the rest image areas.
Keywords: topological data analysis, persistent homology, barcode, topological features, connectivity components, image decomposition, low-frequency and high-frequency decomposition matrices
Funding agency Grant number
Yaroslavl State University П2-ГМ3-2021
The reported study was funded by the YSU Programme under research project No. P2-GM3-2021.
Received: 06.12.2021
Accepted: 30.06.2022
Document Type: Article
Language: Russian
Citation: S. V. Eremeev, A. V. Abakumov, D. E. Andrianov, D. V. Titov, “Image decomposition method by topological features”, Computer Optics, 46:6 (2022), 939–947
Citation in format AMSBIB
\Bibitem{EreAbaAnd22}
\by S.~V.~Eremeev, A.~V.~Abakumov, D.~E.~Andrianov, D.~V.~Titov
\paper Image decomposition method by topological features
\jour Computer Optics
\yr 2022
\vol 46
\issue 6
\pages 939--947
\mathnet{http://mi.mathnet.ru/co1089}
\crossref{https://doi.org/10.18287/2412-6179-CO-1080}
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