Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model
The pair-wise Markov chain (PMC) model serves as an extension to the hidden Markov chain (HMC) model and has been widely used in unsupervised restoration tasks associated with reconstructing the hidden data. In fact, the PMC model can treat fairly complicated situations for which application of Baye...
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2024-10-01
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| author | A. Joumad A. El Moutaouakkil A. Nasroallah 2. Department of mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B. P. 2390, Marrakesh, Morocco Mejdl Safran Sultan Alfarhood Imran Ashraf |
| author_facet | A. Joumad A. El Moutaouakkil A. Nasroallah 2. Department of mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B. P. 2390, Marrakesh, Morocco Mejdl Safran Sultan Alfarhood Imran Ashraf |
| author_sort | A. Joumad |
| collection | DOAJ |
| description | The pair-wise Markov chain (PMC) model serves as an extension to the hidden Markov chain (HMC) model and has been widely used in unsupervised restoration tasks associated with reconstructing the hidden data. In fact, the PMC model can treat fairly complicated situations for which application of Bayesian restoration estimators such as maximum A Posteriori (MAP), or maximal Posterior mode (MPM) remains possible. The major novelty in this work is to construct a PMC model with observational data in two dimensions, and subsequently adapt the estimation algorithms, as well as, image restoration methods for that context. Often, the transformation of an image from a two-dimensional format to a one-dimensional sequence occurs via Hilbert-Peano scan (HPS), whereas in the proposed model, the second component of the observed process takes over this role to exceed the situation of pixel missing information after transformation for a to be segmented image. To reconstruct the hidden process, we used the MPM decision criterion after estimating the model's parameters with two algorithms: Stochastic expectation maximization (SEM) and iterative conditional estimation (ICE). In this study, experimental, numerical, and visual results are shown to demonstrate the superiority of the proposed model over the classical PMC for unsupervised restorations. |
| format | Article |
| id | doaj-art-2ec7439e321f4564afab219cf3df6eb2 |
| institution | Kabale University |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-2ec7439e321f4564afab219cf3df6eb22024-11-12T01:36:03ZengAIMS PressAIMS Mathematics2473-69882024-10-01911310573108610.3934/math.20241498Unsupervised segmentation of images using bi-dimensional pairwise Markov chains modelA. Joumad 0A. El Moutaouakkil 1A. Nasroallah 22. Department of mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B. P. 2390, Marrakesh, Morocco3Mejdl Safran4Sultan Alfarhood 5Imran Ashraf61. Department of informatics, Chouaib Doukkali University, Faculty of Sciences, B. P. 299-24000, El Jadida, Morocco1. Department of informatics, Chouaib Doukkali University, Faculty of Sciences, B. P. 299-24000, El Jadida, Morocco2. Department of mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B. P. 2390, Marrakesh, Morocco1. Department of informatics, Chouaib Doukkali University, Faculty of Sciences, B. P. 299-24000, El Jadida, Morocco3. Department of Computer Science, College of Computer and Information Sciences, King Saud University, P.O.Box 51178, Riyadh 11543, Saudi Arabia3. Department of Computer Science, College of Computer and Information Sciences, King Saud University, P.O.Box 51178, Riyadh 11543, Saudi Arabia4. Department of Information and Communication Engineering, Yeungnam University, Gyeongsan 38541, Republic of KoreaThe pair-wise Markov chain (PMC) model serves as an extension to the hidden Markov chain (HMC) model and has been widely used in unsupervised restoration tasks associated with reconstructing the hidden data. In fact, the PMC model can treat fairly complicated situations for which application of Bayesian restoration estimators such as maximum A Posteriori (MAP), or maximal Posterior mode (MPM) remains possible. The major novelty in this work is to construct a PMC model with observational data in two dimensions, and subsequently adapt the estimation algorithms, as well as, image restoration methods for that context. Often, the transformation of an image from a two-dimensional format to a one-dimensional sequence occurs via Hilbert-Peano scan (HPS), whereas in the proposed model, the second component of the observed process takes over this role to exceed the situation of pixel missing information after transformation for a to be segmented image. To reconstruct the hidden process, we used the MPM decision criterion after estimating the model's parameters with two algorithms: Stochastic expectation maximization (SEM) and iterative conditional estimation (ICE). In this study, experimental, numerical, and visual results are shown to demonstrate the superiority of the proposed model over the classical PMC for unsupervised restorations.https://www.aimspress.com/article/doi/10.3934/math.20241498?viewType=HTMLbayesian restorationhidden markov chain modelpairwise markov chain modelunsupervised segmentationhilbert-peano scanice algorithmsem algorithmbi-dimensional parwise markov chain |
| spellingShingle | A. Joumad A. El Moutaouakkil A. Nasroallah 2. Department of mathematics, Cadi Ayyad University, Faculty of Sciences Semlalia, B. P. 2390, Marrakesh, Morocco Mejdl Safran Sultan Alfarhood Imran Ashraf Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model AIMS Mathematics bayesian restoration hidden markov chain model pairwise markov chain model unsupervised segmentation hilbert-peano scan ice algorithm sem algorithm bi-dimensional parwise markov chain |
| title | Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model |
| title_full | Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model |
| title_fullStr | Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model |
| title_full_unstemmed | Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model |
| title_short | Unsupervised segmentation of images using bi-dimensional pairwise Markov chains model |
| title_sort | unsupervised segmentation of images using bi dimensional pairwise markov chains model |
| topic | bayesian restoration hidden markov chain model pairwise markov chain model unsupervised segmentation hilbert-peano scan ice algorithm sem algorithm bi-dimensional parwise markov chain |
| url | https://www.aimspress.com/article/doi/10.3934/math.20241498?viewType=HTML |
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