8,685 research outputs found
Sparse Subspace Clustering: Algorithm, Theory, and Applications
In many real-world problems, we are dealing with collections of
high-dimensional data, such as images, videos, text and web documents, DNA
microarray data, and more. Often, high-dimensional data lie close to
low-dimensional structures corresponding to several classes or categories the
data belongs to. In this paper, we propose and study an algorithm, called
Sparse Subspace Clustering (SSC), to cluster data points that lie in a union of
low-dimensional subspaces. The key idea is that, among infinitely many possible
representations of a data point in terms of other points, a sparse
representation corresponds to selecting a few points from the same subspace.
This motivates solving a sparse optimization program whose solution is used in
a spectral clustering framework to infer the clustering of data into subspaces.
Since solving the sparse optimization program is in general NP-hard, we
consider a convex relaxation and show that, under appropriate conditions on the
arrangement of subspaces and the distribution of data, the proposed
minimization program succeeds in recovering the desired sparse representations.
The proposed algorithm can be solved efficiently and can handle data points
near the intersections of subspaces. Another key advantage of the proposed
algorithm with respect to the state of the art is that it can deal with data
nuisances, such as noise, sparse outlying entries, and missing entries,
directly by incorporating the model of the data into the sparse optimization
program. We demonstrate the effectiveness of the proposed algorithm through
experiments on synthetic data as well as the two real-world problems of motion
segmentation and face clustering
Quality assessment by region in spot images fused by means dual-tree complex wavelet transform
This work is motivated in providing and evaluating a fusion algorithm of remotely sensed images, i.e. the fusion of a high spatial resolution panchromatic image with a multi-spectral image (also known as pansharpening) using the dual-tree complex wavelet transform (DT-CWT), an effective approach for conducting an analytic and oversampled wavelet transform to reduce aliasing, and in turn reduce shift dependence of the wavelet transform. The proposed scheme includes the definition of a model to establish how information will be extracted from the PAN band and how that information will be injected into the MS bands with low spatial resolution. The approach was applied to Spot 5 images where there are bands falling outside PANâs spectrum. We propose an optional step in the quality evaluation protocol, which is to study the quality of the merger by regions, where each region represents a specific feature of the image. The results show that DT-CWT based approach offers good spatial quality while retaining the spectral information of original images, case SPOT 5. The additional step facilitates the identification of the most affected regions by the fusion process
Kernel Spectral Curvature Clustering (KSCC)
Multi-manifold modeling is increasingly used in segmentation and data
representation tasks in computer vision and related fields. While the general
problem, modeling data by mixtures of manifolds, is very challenging, several
approaches exist for modeling data by mixtures of affine subspaces (which is
often referred to as hybrid linear modeling). We translate some important
instances of multi-manifold modeling to hybrid linear modeling in embedded
spaces, without explicitly performing the embedding but applying the kernel
trick. The resulting algorithm, Kernel Spectral Curvature Clustering, uses
kernels at two levels - both as an implicit embedding method to linearize
nonflat manifolds and as a principled method to convert a multiway affinity
problem into a spectral clustering one. We demonstrate the effectiveness of the
method by comparing it with other state-of-the-art methods on both synthetic
data and a real-world problem of segmenting multiple motions from two
perspective camera views.Comment: accepted to 2009 ICCV Workshop on Dynamical Visio
- âŠ