Weiherer M, Egger B (2025)
Publication Type: Conference contribution
Publication year: 2025
Publisher: International Conference on Learning Representations, ICLR
Pages Range: 66102-66123
Conference Proceedings Title: 13th International Conference on Learning Representations, ICLR 2025
Event location: Singapore, SGP
ISBN: 9798331320850
We propose to use the family of Matérn kernels for implicit surface reconstruction, building upon the recent success of kernel methods for 3D reconstruction of oriented point clouds. As we show from a theoretical and practical perspective, Matérn kernels have some appealing properties which make them particularly well suited for surface reconstruction-outperforming state-of-the-art methods based on the arc-cosine kernel while being significantly easier to implement, faster to compute, and scalable. Being stationary, we demonstrate that Matérn kernels allow for tunable surface reconstruction in the same way as Fourier feature mappings help coordinate-based MLPs overcome spectral bias. Moreover, we theoretically analyze Matérn kernels' connection to SIREN networks as well as their relation to previously employed arc-cosine kernels. Finally, based on recently introduced Neural Kernel Fields, we present data-dependent Matérn kernels and conclude that especially the Laplace kernel (being part of the Matérn family) is extremely competitive, performing almost on par with state-of-the-art methods in the noise-free case while having a more than five times shorter training time.
APA:
Weiherer, M., & Egger, B. (2025). MATÉRN KERNELS FOR TUNABLE IMPLICIT SURFACE RECONSTRUCTION. In 13th International Conference on Learning Representations, ICLR 2025 (pp. 66102-66123). Singapore, SGP: International Conference on Learning Representations, ICLR.
MLA:
Weiherer, Maximilian, and Bernhard Egger. "MATÉRN KERNELS FOR TUNABLE IMPLICIT SURFACE RECONSTRUCTION." Proceedings of the 13th International Conference on Learning Representations, ICLR 2025, Singapore, SGP International Conference on Learning Representations, ICLR, 2025. 66102-66123.
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