Small-variance nonparametric clustering on the hypersphere
Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane segmentation, and regularization of 3D reconstructions. Based on...
| Main Authors: | , , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Institute of Electrical and Electronics Engineers (IEEE)
2016
|
| Online Access: | http://hdl.handle.net/1721.1/105223 https://orcid.org/0000-0003-2339-1262 https://orcid.org/0000-0003-1499-0191 https://orcid.org/0000-0001-8576-1930 https://orcid.org/0000-0003-4844-3495 |
| _version_ | 1811081388513820672 |
|---|---|
| author | Straub, Julian Campbell, Trevor David How, Jonathan P Fisher, John W |
| author2 | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory |
| author_facet | Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Straub, Julian Campbell, Trevor David How, Jonathan P Fisher, John W |
| author_sort | Straub, Julian |
| collection | MIT |
| description | Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane segmentation, and regularization of 3D reconstructions. Based on the small-variance limit of Bayesian nonparametric von-Mises-Fisher (vMF) mixture distributions, we propose two new flexible and efficient k-means-like clustering algorithms for directional data such as surface normals. The first, DP-vMF-means, is a batch clustering algorithm derived from the Dirichlet process (DP) vMF mixture. Recognizing the sequential nature of data collection in many applications, we extend this algorithm to DDP-vMF-means, which infers temporally evolving cluster structure from streaming data. Both algorithms naturally respect the geometry of directional data, which lies on the unit sphere. We demonstrate their performance on synthetic directional data and real 3D surface normals from RGB-D sensors. While our experiments focus on 3D data, both algorithms generalize to high dimensional directional data such as protein backbone configurations and semantic word vectors. |
| first_indexed | 2024-09-23T11:45:54Z |
| format | Article |
| id | mit-1721.1/105223 |
| institution | Massachusetts Institute of Technology |
| language | en_US |
| last_indexed | 2024-09-23T11:45:54Z |
| publishDate | 2016 |
| publisher | Institute of Electrical and Electronics Engineers (IEEE) |
| record_format | dspace |
| spelling | mit-1721.1/1052232022-10-01T05:51:11Z Small-variance nonparametric clustering on the hypersphere Straub, Julian Campbell, Trevor David How, Jonathan P Fisher, John W Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory Massachusetts Institute of Technology. Department of Aeronautics and Astronautics Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science Massachusetts Institute of Technology. Laboratory for Information and Decision Systems Straub, Julian Campbell, Trevor David How, Jonathan P Fisher, John W Structural regularities in man-made environments reflect in the distribution of their surface normals. Describing these surface normal distributions is important in many computer vision applications, such as scene understanding, plane segmentation, and regularization of 3D reconstructions. Based on the small-variance limit of Bayesian nonparametric von-Mises-Fisher (vMF) mixture distributions, we propose two new flexible and efficient k-means-like clustering algorithms for directional data such as surface normals. The first, DP-vMF-means, is a batch clustering algorithm derived from the Dirichlet process (DP) vMF mixture. Recognizing the sequential nature of data collection in many applications, we extend this algorithm to DDP-vMF-means, which infers temporally evolving cluster structure from streaming data. Both algorithms naturally respect the geometry of directional data, which lies on the unit sphere. We demonstrate their performance on synthetic directional data and real 3D surface normals from RGB-D sensors. While our experiments focus on 3D data, both algorithms generalize to high dimensional directional data such as protein backbone configurations and semantic word vectors. United States. Office of Naval Research. Multidisciplinary University Research Initiative (Grant N00014- 11-1-0688) United States. Army Research Office. Multidisciplinary University Research Initiative (Grant W911NF-11-1-0391) 2016-11-04T21:43:59Z 2016-11-04T21:43:59Z 2015-10 2015-06 Article http://purl.org/eprint/type/ConferencePaper 1063-6919 http://hdl.handle.net/1721.1/105223 Straub, Julian et al. “Small-Variance Nonparametric Clustering on the Hypersphere.” IEEE, 2015. 334–342. https://orcid.org/0000-0003-2339-1262 https://orcid.org/0000-0003-1499-0191 https://orcid.org/0000-0001-8576-1930 https://orcid.org/0000-0003-4844-3495 en_US http://dx.doi.org/10.1109/CVPR.2015.7298630 IEEE Conference on Computer Vision and Pattern Recognition, 2015. CVPR 2015. Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Institute of Electrical and Electronics Engineers (IEEE) MIT web domain |
| spellingShingle | Straub, Julian Campbell, Trevor David How, Jonathan P Fisher, John W Small-variance nonparametric clustering on the hypersphere |
| title | Small-variance nonparametric clustering on the hypersphere |
| title_full | Small-variance nonparametric clustering on the hypersphere |
| title_fullStr | Small-variance nonparametric clustering on the hypersphere |
| title_full_unstemmed | Small-variance nonparametric clustering on the hypersphere |
| title_short | Small-variance nonparametric clustering on the hypersphere |
| title_sort | small variance nonparametric clustering on the hypersphere |
| url | http://hdl.handle.net/1721.1/105223 https://orcid.org/0000-0003-2339-1262 https://orcid.org/0000-0003-1499-0191 https://orcid.org/0000-0001-8576-1930 https://orcid.org/0000-0003-4844-3495 |
| work_keys_str_mv | AT straubjulian smallvariancenonparametricclusteringonthehypersphere AT campbelltrevordavid smallvariancenonparametricclusteringonthehypersphere AT howjonathanp smallvariancenonparametricclusteringonthehypersphere AT fisherjohnw smallvariancenonparametricclusteringonthehypersphere |