Fast High‐Dimensional Filtering Using the Permutohedral Lattice
Abstract
Many useful algorithms for processing images and geometry fall under the general framework of high‐dimensional Gaussian filtering. This family of algorithms includes bilateral filtering and non‐local means. We propose a new way to perform such filters using the permutohedral lattice, which tessellates high‐dimensional space with uniform simplices. Our algorithm is the first implementation of a high‐dimensional Gaussian filter that is both linear in input size and polynomial in dimensionality. Furthermore it is parameter‐free, apart from the filter size, and achieves a consistently high accuracy relative to ground truth (> 45 dB). We use this to demonstrate a number of interactive‐rate applications of filters in as high as eight dimensions.
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In CRF-RNN, pair-wise potentials are limited to weighted Gaussians and not all parameters are trainable due to the Permutohedral lattice implementation.
“However, the pair-wise potentials in [50] are limited to weighted Gaussians and not all the parameters are trainable due to the Permutohedral lattice implementation [51].”
From DeepIGeoS: A Deep Interactive Geodesic Framework for Medical Image Segmentation (2019) · cites this paper as [51]
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Cites
Bilateral Filtering for Gray and Color Images
Tomasi, C., & Manduchi, R. (2002) · Sixth International Conference on Computer Vision (IEEE Cat. No.98CH36271) · doi:10.1109/iccv.1998.710815 · Cited by 8,177 · see citing works
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Chen, L.-C., Papandreou, G., Kokkinos, I., Murphy, K., & Yuille, A. L. (2018) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2017.2699184 · Cited by 22,392 · see citing works
Encoder-Decoder with Atrous Separable Convolution for Semantic Image Segmentation
Chen, L.-C., Zhu, Y., Papandreou, G., Schroff, F., & Adam, H. (2018) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-01234-2_49 · Cited by 20,054 · see citing works
He, K., Sun, J., & Tang, X. (2013) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2012.213 · Cited by 5,503 · see citing works
Conditional Random Fields as Recurrent Neural Networks
Zheng, S., Jayasumana, S., Romera-Paredes, B., Vineet, V., Su, Z., Du, D., Huang, C., & Torr, P. H. S. (2015) · 2015 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2015.179 · Cited by 2,386 · see citing works
“Following [29], we use the Permutohedral lattice implementation [1], which can compute the filter response in O(N) time, where N is the number of pixels of the image [1].”
MethodLarge Kernel Matters — Improve Semantic Segmentation by Global Convolutional Network
Peng, C., Zhang, X., Yu, G., Luo, G., & Sun, J. (2017) · 2017 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2017.189 · Cited by 1,750 · see citing works
DeepIGeoS: A Deep Interactive Geodesic Framework for Medical Image Segmentation
Wang, G., Zuluaga, M. A., Li, W., Pratt, R., Patel, P. A., Aertsen, M., Doel, T., David, A. L., Deprest, J., Ourselin, S., et al. (2019) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2018.2840695 · Cited by 502 · see citing works
“However, the pair-wise potentials in [17] are limited to weighted Gaussians and not all the parameters are trainable due to the Per-mutohedral lattice implementation [49].”
BackgroundPixel-Adaptive Convolutional Neural Networks
Su, H., Jampani, V., Sun, D., Gallo, O., Learned-Miller, E., & Kautz, J. (2019) · 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2019.01142 · Cited by 348 · see citing works
Segmentation-Aware Convolutional Networks Using Local Attention Masks
Harley, A. W., Derpanis, K. G., & Kokkinos, I. (2017) · 2017 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.539 · Cited by 142 · see citing works
- Authors
- Adams, A., Baek, J., & Davis, M. A.
- Affiliations
- Stanford University (US)
- Venue
- Computer Graphics Forum
- Publisher
- Wiley
- Published
- 2010-05
- Volume
- 29
- Issue
- 2
- Pages
- 753-762
- ISSN
- 0167-7055 (ISSN-L)
- 1467-8659
- OpenAlex
- W1964772475
- Cited by
- 394
- References
- 1
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 17 · 2023: 18 · 2022: 23 · 2021: 29 · 2020: 35 · 2019: 43 · 2018: 39 · 2017: 31 · 2016: 37 · 2015: 30 · 2014: 31 · 2013: 19 · 2012: 15
- FWCI
- 38.06
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Computer Graphics Forum (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Graphics and Computer-Aided Design › Computer Graphics and Visualization Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Digital Image Processing Techniques
- Keywords
- bilateral filter, non-local means, simplices, image filtering
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