25,713 research outputs found
Robust Recovery of Subspace Structures by Low-Rank Representation
In this work we address the subspace recovery problem. Given a set of data
samples (vectors) approximately drawn from a union of multiple subspaces, our
goal is to segment the samples into their respective subspaces and correct the
possible errors as well. To this end, we propose a novel method termed Low-Rank
Representation (LRR), which seeks the lowest-rank representation among all the
candidates that can represent the data samples as linear combinations of the
bases in a given dictionary. It is shown that LRR well solves the subspace
recovery problem: when the data is clean, we prove that LRR exactly captures
the true subspace structures; for the data contaminated by outliers, we prove
that under certain conditions LRR can exactly recover the row space of the
original data and detect the outlier as well; for the data corrupted by
arbitrary errors, LRR can also approximately recover the row space with
theoretical guarantees. Since the subspace membership is provably determined by
the row space, these further imply that LRR can perform robust subspace
segmentation and error correction, in an efficient way.Comment: IEEE Trans. Pattern Analysis and Machine Intelligenc
Learning and Matching Multi-View Descriptors for Registration of Point Clouds
Critical to the registration of point clouds is the establishment of a set of
accurate correspondences between points in 3D space. The correspondence problem
is generally addressed by the design of discriminative 3D local descriptors on
the one hand, and the development of robust matching strategies on the other
hand. In this work, we first propose a multi-view local descriptor, which is
learned from the images of multiple views, for the description of 3D keypoints.
Then, we develop a robust matching approach, aiming at rejecting outlier
matches based on the efficient inference via belief propagation on the defined
graphical model. We have demonstrated the boost of our approaches to
registration on the public scanning and multi-view stereo datasets. The
superior performance has been verified by the intensive comparisons against a
variety of descriptors and matching methods
redMaPPer III: A Detailed Comparison of the Planck 2013 and SDSS DR8 RedMaPPer Cluster Catalogs
We compare the Planck Sunyaev-Zeldovich (SZ) cluster sample (PSZ1) to the
Sloan Digital Sky Survey (SDSS) redMaPPer catalog, finding that all Planck
clusters within the redMaPPer mask and within the redshift range probed by
redMaPPer are contained in the redMaPPer cluster catalog. These common clusters
define a tight scaling relation in the richness-SZ mass (--)
plane, with an intrinsic scatter in richness of . The corresponding intrinsic scatter in true cluster halo mass
at fixed richness is . The regularity of this scaling relation is
used to identify failures in both the redMaPPer and Planck cluster catalogs. Of
the 245 galaxy clusters in common, we identify three failures in redMaPPer and
36 failures in the PSZ1. Of these, at least 12 are due to clusters whose
optical counterpart was correctly identified in the PSZ1, but where the quoted
redshift for the optical counterpart in the external data base used in the PSZ1
was incorrect. The failure rates for redMaPPer and the PSZ1 are and
respectively, or 9.8% in the PSZ1 after subtracting the external data
base errors. We have further identified 5 PSZ1 sources that suffer from
projection effects (multiple rich systems along the line-of-sight of the SZ
detection) and 17 new high redshift () cluster candidates of
varying degrees of confidence. Should all of the high-redshift cluster
candidates identified here be confirmed, we will have tripled the number of
high redshift Planck clusters in the SDSS region. Our results highlight the
power of multi-wavelength observations to identify and characterize systematic
errors in galaxy cluster data sets, and clearly establish photometric data both
as a robust cluster finding method, and as an important part of defining clean
galaxy cluster samples.Comment: comments welcom
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