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...

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Bibliographic Details
Published in:2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) pp. 334 - 342
Main Authors: Straub, Julian, Campbell, Trevor, How, Jonathan P., Fisher, John W.
Format: Conference Proceeding Journal Article
Language:English
Published: IEEE 01.06.2015
Subjects:
Algorithms
Backbone
Clustering
Clustering algorithms
Computer vision
Data models
Dirichlet problem
Hidden Markov models
Inference algorithms
Mixture models
Pattern recognition
Reconstruction
Shape
Surface reconstruction
Surface treatment
Three dimensional
Three-dimensional displays
Vectors
ISSN:1063-6919, 1063-6919
Online Access:Get full text
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Summary: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.
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ISSN:1063-6919
1063-6919
DOI:10.1109/CVPR.2015.7298630