Equivariant Observer Design on SL(3) for Image Intensity-Based Homography Estimation
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909032857468928 |
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| author | Bouazza, Tarek van Goor, Pieter Mahony, Robert Hamel, Tarek |
| author_facet | Bouazza, Tarek van Goor, Pieter Mahony, Robert Hamel, Tarek |
| contents | This paper addresses the problem of homography estimation using a nonlinear observer designed on the Lie group $\mathbf{SL}(3)$ that exploits the full image information through direct image registration. Unlike traditional feature-based methods, which rely on extensive feature extraction and matching, the proposed approach formulates an observer that minimises a cost function defined directly in terms of image pixel intensities. Explicit conditions ensuring the non-degeneracy of the cost function are derived, and a comprehensive analysis is conducted to characterise and generate degenerate (unobservable) image configurations. Theoretical results demonstrate local exponential convergence of the observer. To improve local convergence properties, a second-order observer variant is introduced by incorporating the Hessian of the cost function into the correction term. Simulation results demonstrate the performance of the proposed solutions on real images. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_10520 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Equivariant Observer Design on SL(3) for Image Intensity-Based Homography Estimation Bouazza, Tarek van Goor, Pieter Mahony, Robert Hamel, Tarek Systems and Control This paper addresses the problem of homography estimation using a nonlinear observer designed on the Lie group $\mathbf{SL}(3)$ that exploits the full image information through direct image registration. Unlike traditional feature-based methods, which rely on extensive feature extraction and matching, the proposed approach formulates an observer that minimises a cost function defined directly in terms of image pixel intensities. Explicit conditions ensuring the non-degeneracy of the cost function are derived, and a comprehensive analysis is conducted to characterise and generate degenerate (unobservable) image configurations. Theoretical results demonstrate local exponential convergence of the observer. To improve local convergence properties, a second-order observer variant is introduced by incorporating the Hessian of the cost function into the correction term. Simulation results demonstrate the performance of the proposed solutions on real images. |
| title | Equivariant Observer Design on SL(3) for Image Intensity-Based Homography Estimation |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2605.10520 |