3,868 research outputs found
Factorization of natural 4 × 4 patch distributions
The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-540-30212-4_15Revised and Selected Papers of ECCV 2004 Workshop SMVP 2004, Prague, Czech Republic, May 16, 2004The lack of sufficient machine readable images makes impossible the direct computation of natural image 4 × 4 block statistics and one has to resort to indirect approximated methods to reduce their domain space. A natural approach to this is to collect statistics over compressed images; if the reconstruction quality is good enough, these statistics will be sufficiently representative. However, a requirement for easier statistics collection is that the method used provides a uniform representation of the compression information across all patches, something for which codebook techniques are well suited. We shall follow this approach here, using a fractal compression–inspired quantization scheme to approximate a given patch B by a triplet (D B , μ B , σ B ) with σ B the patch’s contrast, μ B its brightness and D B a codebook approximation to the mean–variance normalization (B – μ B )/σ B of B. The resulting reduction of the domain space makes feasible the computation of entropy and mutual information estimates that, in turn, suggest a factorization of the approximation of p(B) ≃ p(D B , μ B , σ B ) as p(D B , μ B , σ B ) ≃ p(D B )p(μ)p(σ)Φ(|| ∇ ||), with Φ being a high contrast correction.With partial support of Spain’s CICyT, TIC 01–57
Image patch analysis of sunspots and active regions. II. Clustering via matrix factorization
Separating active regions that are quiet from potentially eruptive ones is a
key issue in Space Weather applications. Traditional classification schemes
such as Mount Wilson and McIntosh have been effective in relating an active
region large scale magnetic configuration to its ability to produce eruptive
events. However, their qualitative nature prevents systematic studies of an
active region's evolution for example. We introduce a new clustering of active
regions that is based on the local geometry observed in Line of Sight
magnetogram and continuum images. We use a reduced-dimension representation of
an active region that is obtained by factoring the corresponding data matrix
comprised of local image patches. Two factorizations can be compared via the
definition of appropriate metrics on the resulting factors. The distances
obtained from these metrics are then used to cluster the active regions. We
find that these metrics result in natural clusterings of active regions. The
clusterings are related to large scale descriptors of an active region such as
its size, its local magnetic field distribution, and its complexity as measured
by the Mount Wilson classification scheme. We also find that including data
focused on the neutral line of an active region can result in an increased
correspondence between our clustering results and other active region
descriptors such as the Mount Wilson classifications and the value. We
provide some recommendations for which metrics, matrix factorization
techniques, and regions of interest to use to study active regions.Comment: Accepted for publication in the Journal of Space Weather and Space
Climate (SWSC). 33 pages, 12 figure
Poisson noise reduction with non-local PCA
Photon-limited imaging arises when the number of photons collected by a
sensor array is small relative to the number of detector elements. Photon
limitations are an important concern for many applications such as spectral
imaging, night vision, nuclear medicine, and astronomy. Typically a Poisson
distribution is used to model these observations, and the inherent
heteroscedasticity of the data combined with standard noise removal methods
yields significant artifacts. This paper introduces a novel denoising algorithm
for photon-limited images which combines elements of dictionary learning and
sparse patch-based representations of images. The method employs both an
adaptation of Principal Component Analysis (PCA) for Poisson noise and recently
developed sparsity-regularized convex optimization algorithms for
photon-limited images. A comprehensive empirical evaluation of the proposed
method helps characterize the performance of this approach relative to other
state-of-the-art denoising methods. The results reveal that, despite its
conceptual simplicity, Poisson PCA-based denoising appears to be highly
competitive in very low light regimes.Comment: erratum: Image man is wrongly name pepper in the journal versio
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
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