Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation
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arXiv
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| Autori principali: | , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910913776320512 |
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| author | Lux, Laurin Berger, Alexander H. Weers, Alexander Stucki, Nico Rueckert, Daniel Bauer, Ulrich Paetzold, Johannes C. |
| author_facet | Lux, Laurin Berger, Alexander H. Weers, Alexander Stucki, Nico Rueckert, Daniel Bauer, Ulrich Paetzold, Johannes C. |
| contents | Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03228 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation Lux, Laurin Berger, Alexander H. Weers, Alexander Stucki, Nico Rueckert, Daniel Bauer, Ulrich Paetzold, Johannes C. Computer Vision and Pattern Recognition Machine Learning Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods. |
| title | Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation |
| topic | Computer Vision and Pattern Recognition Machine Learning |
| url | https://arxiv.org/abs/2411.03228 |