Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold
Geometric transformations of images are the predominant factor, which influences the effectiveness of visual tracking and detection tasks in computer vision. Naturally, although it makes significant sense to grasp the process of image geometric transformations, the numerical relationship of geometri...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
IEEE
2019-01-01
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| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/8784183/ |
| _version_ | 1818949215413338112 |
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| author | Tianci Liu Zelin Shi Yunpeng Liu |
| author_facet | Tianci Liu Zelin Shi Yunpeng Liu |
| author_sort | Tianci Liu |
| collection | DOAJ |
| description | Geometric transformations of images are the predominant factor, which influences the effectiveness of visual tracking and detection tasks in computer vision. Naturally, although it makes significant sense to grasp the process of image geometric transformations, the numerical relationship of geometric transformations cannot be revealed directly from images themselves. Even if the geometric transformation matrices form the three-dimensional special linear group, Sl(3, ℝ) group, it is difficult to comprehend the manifold of this invisible visual motion, which resides in the high-dimensional space. Furthermore, the main challenge is the deficiency of analytic expressions of the Riemannian logarithmic map to compute the geodesic distance on the Sl(3, ℝ) manifold. Facing these issues, this paper comes up with a novel approach to visualize the geometric transformation in images by presenting a new metric, and then, computes a set of coordinate-vectors in the three-dimensional state transition space for visualization using the Riemannian stress majorization. The superiority of the presented framework for visualization, in terms of accuracy and efficiency, is demonstrated through abundant experiments on aerial images and moving objects. |
| first_indexed | 2024-12-20T08:59:09Z |
| format | Article |
| id | doaj.art-a3dc979b6c094154b2e3724d76eb7161 |
| institution | Directory Open Access Journal |
| issn | 2169-3536 |
| language | English |
| last_indexed | 2024-12-20T08:59:09Z |
| publishDate | 2019-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj.art-a3dc979b6c094154b2e3724d76eb71612022-12-21T19:45:55ZengIEEEIEEE Access2169-35362019-01-01710553110554510.1109/ACCESS.2019.29324128784183Visualization of the Image Geometric Transformation Group Based on Riemannian ManifoldTianci Liu0https://orcid.org/0000-0002-4601-9554Zelin Shi1https://orcid.org/0000-0001-7059-6477Yunpeng Liu2https://orcid.org/0000-0002-0959-0209Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, ChinaShenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, ChinaShenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, ChinaGeometric transformations of images are the predominant factor, which influences the effectiveness of visual tracking and detection tasks in computer vision. Naturally, although it makes significant sense to grasp the process of image geometric transformations, the numerical relationship of geometric transformations cannot be revealed directly from images themselves. Even if the geometric transformation matrices form the three-dimensional special linear group, Sl(3, ℝ) group, it is difficult to comprehend the manifold of this invisible visual motion, which resides in the high-dimensional space. Furthermore, the main challenge is the deficiency of analytic expressions of the Riemannian logarithmic map to compute the geodesic distance on the Sl(3, ℝ) manifold. Facing these issues, this paper comes up with a novel approach to visualize the geometric transformation in images by presenting a new metric, and then, computes a set of coordinate-vectors in the three-dimensional state transition space for visualization using the Riemannian stress majorization. The superiority of the presented framework for visualization, in terms of accuracy and efficiency, is demonstrated through abundant experiments on aerial images and moving objects.https://ieeexplore.ieee.org/document/8784183/Geometric transformationvisualizationmotion groupRiemannian manifold |
| spellingShingle | Tianci Liu Zelin Shi Yunpeng Liu Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold IEEE Access Geometric transformation visualization motion group Riemannian manifold |
| title | Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold |
| title_full | Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold |
| title_fullStr | Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold |
| title_full_unstemmed | Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold |
| title_short | Visualization of the Image Geometric Transformation Group Based on Riemannian Manifold |
| title_sort | visualization of the image geometric transformation group based on riemannian manifold |
| topic | Geometric transformation visualization motion group Riemannian manifold |
| url | https://ieeexplore.ieee.org/document/8784183/ |
| work_keys_str_mv | AT tianciliu visualizationoftheimagegeometrictransformationgroupbasedonriemannianmanifold AT zelinshi visualizationoftheimagegeometrictransformationgroupbasedonriemannianmanifold AT yunpengliu visualizationoftheimagegeometrictransformationgroupbasedonriemannianmanifold |