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| Main Authors: | , , |
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| Format: | Preprint |
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2025
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| Online Access: | https://arxiv.org/abs/2505.11099 |
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| _version_ | 1866908773692473344 |
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| author | Liu, Bin Wang, Chunyang Liu, Xuelian |
| author_facet | Liu, Bin Wang, Chunyang Liu, Xuelian |
| contents | Point clouds are a fundamental 3D data representation that underpins various computer vision tasks. Recently, Mamba has demonstrated strong potential for 3D point cloud understanding. However, existing approaches primarily focus on point serialization, overlooking a more fundamental limitation: State Space Models (SSMs) inherently exhibit a spectral low-pass bias arising from their recursive formulation. In serialized point clouds, this bias is particularly detrimental, as it suppresses high-frequency geometric structures and progressively dilutes semantic discriminability across deep layers. To address these limitations, we propose SM3D, a spectral-aware framework designed to jointly preserve geometric fidelity and semantic consistency. First, a Geometric Spectral Compensator (GSC) is introduced to counteract the low-pass bias by explicitly injecting graph-guided high-frequency components through local Laplacian analysis, thereby restoring structural sensitivity. Second, we design a Semantic Coherence Refiner (SCR) to rectify semantic drift through frequency-aware channel recalibration. To balance theoretical precision and computational efficiency, SCR is instantiated via two pathways: an exact Laplacian eigendecomposition (SCR-L) and a linear-complexity Chebyshev polynomial approximation (SCR-C). Extensive experiments demonstrate that SM3D achieves state-of-the-art performance, including 96.0% accuracy on ModelNet40 and 86.5% mIoU on ShapeNetPart, validating its effectiveness in mitigating spectral low-pass bias and semantic dilution (Code: https://github.com/L1277471578/SM3D). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_11099 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | SM3D: Mitigating Spectral Bias and Semantic Dilution in Point Cloud State Space Models Liu, Bin Wang, Chunyang Liu, Xuelian Computer Vision and Pattern Recognition Point clouds are a fundamental 3D data representation that underpins various computer vision tasks. Recently, Mamba has demonstrated strong potential for 3D point cloud understanding. However, existing approaches primarily focus on point serialization, overlooking a more fundamental limitation: State Space Models (SSMs) inherently exhibit a spectral low-pass bias arising from their recursive formulation. In serialized point clouds, this bias is particularly detrimental, as it suppresses high-frequency geometric structures and progressively dilutes semantic discriminability across deep layers. To address these limitations, we propose SM3D, a spectral-aware framework designed to jointly preserve geometric fidelity and semantic consistency. First, a Geometric Spectral Compensator (GSC) is introduced to counteract the low-pass bias by explicitly injecting graph-guided high-frequency components through local Laplacian analysis, thereby restoring structural sensitivity. Second, we design a Semantic Coherence Refiner (SCR) to rectify semantic drift through frequency-aware channel recalibration. To balance theoretical precision and computational efficiency, SCR is instantiated via two pathways: an exact Laplacian eigendecomposition (SCR-L) and a linear-complexity Chebyshev polynomial approximation (SCR-C). Extensive experiments demonstrate that SM3D achieves state-of-the-art performance, including 96.0% accuracy on ModelNet40 and 86.5% mIoU on ShapeNetPart, validating its effectiveness in mitigating spectral low-pass bias and semantic dilution (Code: https://github.com/L1277471578/SM3D). |
| title | SM3D: Mitigating Spectral Bias and Semantic Dilution in Point Cloud State Space Models |
| topic | Computer Vision and Pattern Recognition |
| url | https://arxiv.org/abs/2505.11099 |