Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917402996899840 |
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| author | Vis, Leanne Pisarenco, Maxim Smets, Bart M. N. van der Sommen, Fons Duits, Remco |
| author_facet | Vis, Leanne Pisarenco, Maxim Smets, Bart M. N. van der Sommen, Fons Duits, Remco |
| contents | Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to this problem by introducing a snake model on $\R^2 \times P^1$, where we only compute the distance map where needed. Our method introduces a geometric criterion for switching between fast spatial snakes and computing minimizing geodesics of a new projective line bundle model. The new pseudo-distance underlying our geometric model is both symmetric and cusp-free, in contrast to previous geodesic sub-Riemannian models on $\R^2 \times P^1$. Our pseudo-distance satisfies the triangle inequality on a large set that we characterize, and includes a connected-component-informed cost function, which is highly advantageous in applications. Experiments on Scanning Electron Microscopy (SEM) images demonstrate our method's robust, automatic segmentation of overlapping electronic structures. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_11254 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images Vis, Leanne Pisarenco, Maxim Smets, Bart M. N. van der Sommen, Fons Duits, Remco Differential Geometry Geodesic tracking on the projective line bundle $\R^2 \times P^1 $ has many uses, including the segmentation of objects in images. However, global tracking requires expensive distance map computations. We provide a practical solution to this problem by introducing a snake model on $\R^2 \times P^1$, where we only compute the distance map where needed. Our method introduces a geometric criterion for switching between fast spatial snakes and computing minimizing geodesics of a new projective line bundle model. The new pseudo-distance underlying our geometric model is both symmetric and cusp-free, in contrast to previous geodesic sub-Riemannian models on $\R^2 \times P^1$. Our pseudo-distance satisfies the triangle inequality on a large set that we characterize, and includes a connected-component-informed cost function, which is highly advantageous in applications. Experiments on Scanning Electron Microscopy (SEM) images demonstrate our method's robust, automatic segmentation of overlapping electronic structures. |
| title | Sub-Riemannian Snakes on the Projective Line Bundle with Applications to Segmentation of SEM Images |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2604.11254 |