131,913 research outputs found
Fast Approximate -Means via Cluster Closures
-means, a simple and effective clustering algorithm, is one of the most
widely used algorithms in multimedia and computer vision community. Traditional
-means is an iterative algorithm---in each iteration new cluster centers are
computed and each data point is re-assigned to its nearest center. The cluster
re-assignment step becomes prohibitively expensive when the number of data
points and cluster centers are large.
In this paper, we propose a novel approximate -means algorithm to greatly
reduce the computational complexity in the assignment step. Our approach is
motivated by the observation that most active points changing their cluster
assignments at each iteration are located on or near cluster boundaries. The
idea is to efficiently identify those active points by pre-assembling the data
into groups of neighboring points using multiple random spatial partition
trees, and to use the neighborhood information to construct a closure for each
cluster, in such a way only a small number of cluster candidates need to be
considered when assigning a data point to its nearest cluster. Using complexity
analysis, image data clustering, and applications to image retrieval, we show
that our approach out-performs state-of-the-art approximate -means
algorithms in terms of clustering quality and efficiency
Fusion of monocular cues to detect man-made structures in aerial imagery
The extraction of buildings from aerial imagery is a complex problem for automated computer vision. It requires locating regions in a scene that possess properties distinguishing them as man-made objects as opposed to naturally occurring terrain features. It is reasonable to assume that no single detection method can correctly delineate or verify buildings in every scene. A cooperative-methods paradigm is useful in approaching the building extraction problem. Using this paradigm, each extraction technique provides information which can be added or assimilated into an overall interpretation of the scene. Thus, the main objective is to explore the development of computer vision system that integrates the results of various scene analysis techniques into an accurate and robust interpretation of the underlying three dimensional scene. The problem of building hypothesis fusion in aerial imagery is discussed. Building extraction techniques are briefly surveyed, including four building extraction, verification, and clustering systems. A method for fusing the symbolic data generated by these systems is described, and applied to monocular image and stereo image data sets. Evaluation methods for the fusion results are described, and the fusion results are analyzed using these methods
Latent tree models
Latent tree models are graphical models defined on trees, in which only a
subset of variables is observed. They were first discussed by Judea Pearl as
tree-decomposable distributions to generalise star-decomposable distributions
such as the latent class model. Latent tree models, or their submodels, are
widely used in: phylogenetic analysis, network tomography, computer vision,
causal modeling, and data clustering. They also contain other well-known
classes of models like hidden Markov models, Brownian motion tree model, the
Ising model on a tree, and many popular models used in phylogenetics. This
article offers a concise introduction to the theory of latent tree models. We
emphasise the role of tree metrics in the structural description of this model
class, in designing learning algorithms, and in understanding fundamental
limits of what and when can be learned
A geometric analysis of subspace clustering with outliers
This paper considers the problem of clustering a collection of unlabeled data
points assumed to lie near a union of lower-dimensional planes. As is common in
computer vision or unsupervised learning applications, we do not know in
advance how many subspaces there are nor do we have any information about their
dimensions. We develop a novel geometric analysis of an algorithm named sparse
subspace clustering (SSC) [In IEEE Conference on Computer Vision and Pattern
Recognition, 2009. CVPR 2009 (2009) 2790-2797. IEEE], which significantly
broadens the range of problems where it is provably effective. For instance, we
show that SSC can recover multiple subspaces, each of dimension comparable to
the ambient dimension. We also prove that SSC can correctly cluster data points
even when the subspaces of interest intersect. Further, we develop an extension
of SSC that succeeds when the data set is corrupted with possibly
overwhelmingly many outliers. Underlying our analysis are clear geometric
insights, which may bear on other sparse recovery problems. A numerical study
complements our theoretical analysis and demonstrates the effectiveness of
these methods.Comment: Published in at http://dx.doi.org/10.1214/12-AOS1034 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Fast Robust PCA on Graphs
Mining useful clusters from high dimensional data has received significant
attention of the computer vision and pattern recognition community in the
recent years. Linear and non-linear dimensionality reduction has played an
important role to overcome the curse of dimensionality. However, often such
methods are accompanied with three different problems: high computational
complexity (usually associated with the nuclear norm minimization),
non-convexity (for matrix factorization methods) and susceptibility to gross
corruptions in the data. In this paper we propose a principal component
analysis (PCA) based solution that overcomes these three issues and
approximates a low-rank recovery method for high dimensional datasets. We
target the low-rank recovery by enforcing two types of graph smoothness
assumptions, one on the data samples and the other on the features by designing
a convex optimization problem. The resulting algorithm is fast, efficient and
scalable for huge datasets with O(nlog(n)) computational complexity in the
number of data samples. It is also robust to gross corruptions in the dataset
as well as to the model parameters. Clustering experiments on 7 benchmark
datasets with different types of corruptions and background separation
experiments on 3 video datasets show that our proposed model outperforms 10
state-of-the-art dimensionality reduction models. Our theoretical analysis
proves that the proposed model is able to recover approximate low-rank
representations with a bounded error for clusterable data
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