Orientation Scores should be a Piece of Cake
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915570686885888 |
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| author | Sherry, Finn M. van de Geijn, Chase Bekkers, Erik J. Duits, Remco |
| author_facet | Sherry, Finn M. van de Geijn, Chase Bekkers, Erik J. Duits, Remco |
| contents | We axiomatically derive a family of wavelets for an orientation score, lifting from position space $\mathbb{R}^2$ to position and orientation space $\mathbb{R}^2\times S^1$, with fast reconstruction property, that minimise position-orientation uncertainty. We subsequently show that these minimum uncertainty states are well-approximated by cake wavelets: for standard parameters, the uncertainty gap of cake wavelets is less than 1.1, and in the limit, we prove the uncertainty gap tends to the minimum of 1. Next, we complete a previous theoretical argument that one does not have to train the lifting layer in (PDE-)G-CNNs, but can instead use cake wavelets. Finally, we show experimentally that in this way we can reduce the network complexity and improve the interpretability of (PDE-)G-CNNs, with only a slight impact on the model's performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_00702 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orientation Scores should be a Piece of Cake Sherry, Finn M. van de Geijn, Chase Bekkers, Erik J. Duits, Remco Differential Geometry Computer Vision and Pattern Recognition We axiomatically derive a family of wavelets for an orientation score, lifting from position space $\mathbb{R}^2$ to position and orientation space $\mathbb{R}^2\times S^1$, with fast reconstruction property, that minimise position-orientation uncertainty. We subsequently show that these minimum uncertainty states are well-approximated by cake wavelets: for standard parameters, the uncertainty gap of cake wavelets is less than 1.1, and in the limit, we prove the uncertainty gap tends to the minimum of 1. Next, we complete a previous theoretical argument that one does not have to train the lifting layer in (PDE-)G-CNNs, but can instead use cake wavelets. Finally, we show experimentally that in this way we can reduce the network complexity and improve the interpretability of (PDE-)G-CNNs, with only a slight impact on the model's performance. |
| title | Orientation Scores should be a Piece of Cake |
| topic | Differential Geometry Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2504.00702 |