Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification
The space of symmetric positive definite (SPD) matrices, denoted as <inline-formula> <tex-math notation="LaTeX">$P_{m}$ </tex-math></inline-formula>, plays a crucial role in various domains, including computer vision, medical imaging, and signal processing. Its sign...
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| Format: | Article |
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IEEE
2024-01-01
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| Series: | IEEE Access |
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| Online Access: | https://ieeexplore.ieee.org/document/10436648/ |
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| author | Zakariae Abbad Ahmed Drissi El Maliani Mohammed El Hassouni Mohamed Tahar Kadaoui Abbassi Lionel Bombrun Yannick Berthoumieu |
| author_facet | Zakariae Abbad Ahmed Drissi El Maliani Mohammed El Hassouni Mohamed Tahar Kadaoui Abbassi Lionel Bombrun Yannick Berthoumieu |
| author_sort | Zakariae Abbad |
| collection | DOAJ |
| description | The space of symmetric positive definite (SPD) matrices, denoted as <inline-formula> <tex-math notation="LaTeX">$P_{m}$ </tex-math></inline-formula>, plays a crucial role in various domains, including computer vision, medical imaging, and signal processing. Its significance lies in its capacity to represent the underlying structure in nonlinear data using its Riemannian geometry. Nevertheless, a notable gap exists in the absence of statistical distributions capable of characterizing the statistical properties of data within this space. This paper proposes a new Riemannian Generalized Gaussian distribution (RGGD) on that space. The major contributions of this paper are, first of all, providing the exact expression of the probability density function (PDF) of the RGGD model, as well as an exact expression of the normalizing factor. Furthermore, an estimation of parameters is given using the maximum likelihood of this distribution. The second contribution involves exploiting the second-order statistics of feature maps derived from the first layers of deep convolutional neural networks (DCNNs) through the RGGD stochastic model in an image classification framework. Experiments were carried out on four well-known datasets, and the results demonstrate the efficiency and competitiveness of the proposed model. |
| first_indexed | 2024-03-07T22:03:04Z |
| format | Article |
| id | doaj.art-3c9fcfa37c424d50917b211145352fd9 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-03-07T22:03:04Z |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-3c9fcfa37c424d50917b211145352fd92024-02-24T00:01:09ZengIEEEIEEE Access2169-35362024-01-0112260962610910.1109/ACCESS.2024.336649410436648Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image ClassificationZakariae Abbad0https://orcid.org/0000-0003-4911-2022Ahmed Drissi El Maliani1https://orcid.org/0009-0006-2464-2296Mohammed El Hassouni2https://orcid.org/0000-0002-6741-4799Mohamed Tahar Kadaoui Abbassi3https://orcid.org/0000-0001-7802-0624Lionel Bombrun4https://orcid.org/0000-0001-9036-3988Yannick Berthoumieu5https://orcid.org/0000-0002-7559-0602ENSIAS, Mohammed V University in Rabat, Rabat, MoroccoLRIT Rabat IT Center, Faculty of Sciences, Mohammed V University in Rabat, Rabat, MoroccoFLSH, Mohammed V University in Rabat, Rabat, MoroccoLaboratory of Mathematical Sciences and Applications, Faculty of Sciences Dhar El Mahraz, Sidi Mohamed Ben Abdellah University, Fes, MoroccoCNRS, Bordeaux INP, IMS, UMR 5218, University of Bordeaux, Bordeaux, Talence, FranceCNRS, Bordeaux INP, IMS, UMR 5218, University of Bordeaux, Bordeaux, Talence, FranceThe space of symmetric positive definite (SPD) matrices, denoted as <inline-formula> <tex-math notation="LaTeX">$P_{m}$ </tex-math></inline-formula>, plays a crucial role in various domains, including computer vision, medical imaging, and signal processing. Its significance lies in its capacity to represent the underlying structure in nonlinear data using its Riemannian geometry. Nevertheless, a notable gap exists in the absence of statistical distributions capable of characterizing the statistical properties of data within this space. This paper proposes a new Riemannian Generalized Gaussian distribution (RGGD) on that space. The major contributions of this paper are, first of all, providing the exact expression of the probability density function (PDF) of the RGGD model, as well as an exact expression of the normalizing factor. Furthermore, an estimation of parameters is given using the maximum likelihood of this distribution. The second contribution involves exploiting the second-order statistics of feature maps derived from the first layers of deep convolutional neural networks (DCNNs) through the RGGD stochastic model in an image classification framework. Experiments were carried out on four well-known datasets, and the results demonstrate the efficiency and competitiveness of the proposed model.https://ieeexplore.ieee.org/document/10436648/Symmetric positive definite matricesgeneralized Gaussian distributiontextureRiemannian geometryRao’s distanceRiemannian metric |
| spellingShingle | Zakariae Abbad Ahmed Drissi El Maliani Mohammed El Hassouni Mohamed Tahar Kadaoui Abbassi Lionel Bombrun Yannick Berthoumieu Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification IEEE Access Symmetric positive definite matrices generalized Gaussian distribution texture Riemannian geometry Rao’s distance Riemannian metric |
| title | Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification |
| title_full | Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification |
| title_fullStr | Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification |
| title_full_unstemmed | Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification |
| title_short | Riemannian Generalized Gaussian Distributions on the Space of SPD Matrices for Image Classification |
| title_sort | riemannian generalized gaussian distributions on the space of spd matrices for image classification |
| topic | Symmetric positive definite matrices generalized Gaussian distribution texture Riemannian geometry Rao’s distance Riemannian metric |
| url | https://ieeexplore.ieee.org/document/10436648/ |
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