Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916784131538944 |
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| author | Bastian, Lennart Rashed, Mohammad Navab, Nassir Birdal, Tolga |
| author_facet | Bastian, Lennart Rashed, Mohammad Navab, Nassir Birdal, Tolga |
| contents | Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex dynamics, and (3) application settings can demand long-term forecasting. This work proposes modeling continuous-time rotational object dynamics on $SO(3)$ using Neural Controlled Differential Equations guided by Savitzky-Golay paths. Unlike existing methods that rely on simplified motion assumptions, our method learns a general latent dynamical system of the underlying object trajectory while respecting the geometric structure of rotations. Experimental results on real-world data demonstrate compelling forecasting capabilities compared to existing approaches. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_06780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations Bastian, Lennart Rashed, Mohammad Navab, Nassir Birdal, Tolga Computer Vision and Pattern Recognition Machine Learning Tracking and forecasting the rotation of objects is fundamental in computer vision and robotics, yet SO(3) extrapolation remains challenging as (1) sensor observations can be noisy and sparse, (2) motion patterns can be governed by complex dynamics, and (3) application settings can demand long-term forecasting. This work proposes modeling continuous-time rotational object dynamics on $SO(3)$ using Neural Controlled Differential Equations guided by Savitzky-Golay paths. Unlike existing methods that rely on simplified motion assumptions, our method learns a general latent dynamical system of the underlying object trajectory while respecting the geometric structure of rotations. Experimental results on real-world data demonstrate compelling forecasting capabilities compared to existing approaches. |
| title | Continuous-Time SO(3) Forecasting with Savitzky--Golay Neural Controlled Differential Equations |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2506.06780 |