37,677 research outputs found
Mode-Seeking on Hypergraphs for Robust Geometric Model Fitting
In this paper, we propose a novel geometric model fitting method, called
Mode-Seeking on Hypergraphs (MSH),to deal with multi-structure data even in the
presence of severe outliers. The proposed method formulates geometric model
fitting as a mode seeking problem on a hypergraph in which vertices represent
model hypotheses and hyperedges denote data points. MSH intuitively detects
model instances by a simple and effective mode seeking algorithm. In addition
to the mode seeking algorithm, MSH includes a similarity measure between
vertices on the hypergraph and a weight-aware sampling technique. The proposed
method not only alleviates sensitivity to the data distribution, but also is
scalable to large scale problems. Experimental results further demonstrate that
the proposed method has significant superiority over the state-of-the-art
fitting methods on both synthetic data and real images.Comment: Proceedings of the IEEE International Conference on Computer Vision,
pp. 2902-2910, 201
Hypergraph Modelling for Geometric Model Fitting
In this paper, we propose a novel hypergraph based method (called HF) to fit
and segment multi-structural data. The proposed HF formulates the geometric
model fitting problem as a hypergraph partition problem based on a novel
hypergraph model. In the hypergraph model, vertices represent data points and
hyperedges denote model hypotheses. The hypergraph, with large and
"data-determined" degrees of hyperedges, can express the complex relationships
between model hypotheses and data points. In addition, we develop a robust
hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF
can effectively and efficiently estimate the number of, and the parameters of,
model instances in multi-structural data heavily corrupted with outliers
simultaneously. Experimental results show the advantages of the proposed method
over previous methods on both synthetic data and real images.Comment: Pattern Recognition, 201
The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters
The distribution of galaxies in position and velocity around the centers of
galaxy clusters encodes important information about cluster mass and structure.
Using the maxBCG galaxy cluster catalog identified from imaging data obtained
in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation
function. By modeling its non-Gaussianity, we measure the mean and scatter in
velocity dispersion at fixed richness. The mean velocity dispersion increases
from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large
clusters. We show the scatter to be at most 40.5+/-3.5%, declining to
14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog,
a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2
spectroscopic sample, and in mock galaxy catalogs constructed from N-body
simulations. Our methods are robust, measuring the scatter to well within
one-sigma of the true value, and the mean to within 10%, in the mock catalogs.
By convolving the scatter in velocity dispersion at fixed richness with the
observed richness space density function, we measure the velocity dispersion
function of the maxBCG galaxy clusters. Although velocity dispersion and
richness do not form a true mass-observable relation, the relationship between
velocity dispersion and mass is theoretically well characterized and has low
scatter. Thus our results provide a key link between theory and observations up
to the velocity bias between dark matter and galaxies.Comment: 25 pages, 15 figures, 2 tables, published in Ap
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