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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2412.16619 |
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| _version_ | 1866916793655754752 |
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| author | Shen, Tianqi Liu, Shaohua Feng, Jiaqi Ma, Ziye An, Ning |
| author_facet | Shen, Tianqi Liu, Shaohua Feng, Jiaqi Ma, Ziye An, Ning |
| contents | Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces Topology-Aware 3D Gaussian Splatting (Topology-GS), which addresses two key limitations in current approaches: compromised pixel-level structural integrity due to incomplete initial geometric coverage, and inadequate feature-level integrity from insufficient topological constraints during optimization. To overcome these limitations, Topology-GS incorporates a novel interpolation strategy, Local Persistent Voronoi Interpolation (LPVI), and a topology-focused regularization term based on persistent barcodes, named PersLoss. LPVI utilizes persistent homology to guide adaptive interpolation, enhancing point coverage in low-curvature areas while preserving topological structure. PersLoss aligns the visual perceptual similarity of rendered images with ground truth by constraining distances between their topological features. Comprehensive experiments on three novel-view synthesis benchmarks demonstrate that Topology-GS outperforms existing methods in terms of PSNR, SSIM, and LPIPS metrics, while maintaining efficient memory usage. This study pioneers the integration of topology with 3D-GS, laying the groundwork for future research in this area. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_16619 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity Shen, Tianqi Liu, Shaohua Feng, Jiaqi Ma, Ziye An, Ning Computer Vision and Pattern Recognition Machine Learning Image and Video Processing Algebraic Topology Geometric Topology 55N31, 68T45 I.2.10; I.3.7; I.4.5 Gaussian Splatting (GS) has emerged as a crucial technique for representing discrete volumetric radiance fields. It leverages unique parametrization to mitigate computational demands in scene optimization. This work introduces Topology-Aware 3D Gaussian Splatting (Topology-GS), which addresses two key limitations in current approaches: compromised pixel-level structural integrity due to incomplete initial geometric coverage, and inadequate feature-level integrity from insufficient topological constraints during optimization. To overcome these limitations, Topology-GS incorporates a novel interpolation strategy, Local Persistent Voronoi Interpolation (LPVI), and a topology-focused regularization term based on persistent barcodes, named PersLoss. LPVI utilizes persistent homology to guide adaptive interpolation, enhancing point coverage in low-curvature areas while preserving topological structure. PersLoss aligns the visual perceptual similarity of rendered images with ground truth by constraining distances between their topological features. Comprehensive experiments on three novel-view synthesis benchmarks demonstrate that Topology-GS outperforms existing methods in terms of PSNR, SSIM, and LPIPS metrics, while maintaining efficient memory usage. This study pioneers the integration of topology with 3D-GS, laying the groundwork for future research in this area. |
| title | Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity |
| topic | Computer Vision and Pattern Recognition Machine Learning Image and Video Processing Algebraic Topology Geometric Topology 55N31, 68T45 I.2.10; I.3.7; I.4.5 |
| url | https://arxiv.org/abs/2412.16619 |