1,542 research outputs found
Multi-scale morphology of the galaxy distribution
Many statistical methods have been proposed in the last years for analyzing
the spatial distribution of galaxies. Very few of them, however, can handle
properly the border effects of complex observational sample volumes. In this
paper, we first show how to calculate the Minkowski Functionals (MF) taking
into account these border effects. Then we present a multiscale extension of
the MF which gives us more information about how the galaxies are spatially
distributed. A range of examples using Gaussian random fields illustrate the
results. Finally we have applied the Multiscale Minkowski Functionals (MMF) to
the 2dF Galaxy Redshift Survey data. The MMF clearly indicates an evolution of
morphology with scale. We also compare the 2dF real catalog with mock catalogs
and found that Lambda-CDM simulations roughly fit the data, except at the
finest scale.Comment: 17 pages, 19 figures, accepted for publication in MNRA
Adaptive regularization for image reconstruction from subsampled data
Choices of regularization parameters are central to variational methods for image restoration. In this paper, a spatially adaptive (or distributed) regularization scheme is developed based on localized residuals, which properly balances the regularization weight between regions containing image details and homogeneous regions. Surrogate iterative methods are employed to handle given subsampled data in transformed domains, such as Fourier or wavelet data. In this respect, this work extends the spatially variant regularization technique previously established in [15], which depends on the fact that the given data are degraded images only. Numerical experiments for the reconstruction from partial Fourier data and for wavelet inpainting prove the efficiency of the newly proposed approach
Image Deblurring and Super-resolution by Adaptive Sparse Domain Selection and Adaptive Regularization
As a powerful statistical image modeling technique, sparse representation has
been successfully used in various image restoration applications. The success
of sparse representation owes to the development of l1-norm optimization
techniques, and the fact that natural images are intrinsically sparse in some
domain. The image restoration quality largely depends on whether the employed
sparse domain can represent well the underlying image. Considering that the
contents can vary significantly across different images or different patches in
a single image, we propose to learn various sets of bases from a pre-collected
dataset of example image patches, and then for a given patch to be processed,
one set of bases are adaptively selected to characterize the local sparse
domain. We further introduce two adaptive regularization terms into the sparse
representation framework. First, a set of autoregressive (AR) models are
learned from the dataset of example image patches. The best fitted AR models to
a given patch are adaptively selected to regularize the image local structures.
Second, the image non-local self-similarity is introduced as another
regularization term. In addition, the sparsity regularization parameter is
adaptively estimated for better image restoration performance. Extensive
experiments on image deblurring and super-resolution validate that by using
adaptive sparse domain selection and adaptive regularization, the proposed
method achieves much better results than many state-of-the-art algorithms in
terms of both PSNR and visual perception.Comment: 35 pages. This paper is under review in IEEE TI
Adaptive regularization for image reconstruction from subsampled data
Choices of regularization parameters are central to variational methods
for image restoration. In this paper, a spatially adaptive (or distributed)
regularization scheme is developed based on localized residuals, which
properly balances the regularization weight between regions containing image
details and homogeneous regions. Surrogate iterative methods are employed to
handle given subsampled data in transformed domains, such as Fourier or
wavelet data. In this respect, this work extends the spatially variant
regularization technique previously established in [15], which depends on the
fact that the given data are degraded images only. Numerical experiments for
the reconstruction from partial Fourier data and for wavelet inpainting prove
the efficiency of the newly proposed approach
BLADE: Filter Learning for General Purpose Computational Photography
The Rapid and Accurate Image Super Resolution (RAISR) method of Romano,
Isidoro, and Milanfar is a computationally efficient image upscaling method
using a trained set of filters. We describe a generalization of RAISR, which we
name Best Linear Adaptive Enhancement (BLADE). This approach is a trainable
edge-adaptive filtering framework that is general, simple, computationally
efficient, and useful for a wide range of problems in computational
photography. We show applications to operations which may appear in a camera
pipeline including denoising, demosaicing, and stylization
Learning sparse representations of depth
This paper introduces a new method for learning and inferring sparse
representations of depth (disparity) maps. The proposed algorithm relaxes the
usual assumption of the stationary noise model in sparse coding. This enables
learning from data corrupted with spatially varying noise or uncertainty,
typically obtained by laser range scanners or structured light depth cameras.
Sparse representations are learned from the Middlebury database disparity maps
and then exploited in a two-layer graphical model for inferring depth from
stereo, by including a sparsity prior on the learned features. Since they
capture higher-order dependencies in the depth structure, these priors can
complement smoothness priors commonly used in depth inference based on Markov
Random Field (MRF) models. Inference on the proposed graph is achieved using an
alternating iterative optimization technique, where the first layer is solved
using an existing MRF-based stereo matching algorithm, then held fixed as the
second layer is solved using the proposed non-stationary sparse coding
algorithm. This leads to a general method for improving solutions of state of
the art MRF-based depth estimation algorithms. Our experimental results first
show that depth inference using learned representations leads to state of the
art denoising of depth maps obtained from laser range scanners and a time of
flight camera. Furthermore, we show that adding sparse priors improves the
results of two depth estimation methods: the classical graph cut algorithm by
Boykov et al. and the more recent algorithm of Woodford et al.Comment: 12 page
Graph Spectral Image Processing
Recent advent of graph signal processing (GSP) has spurred intensive studies
of signals that live naturally on irregular data kernels described by graphs
(e.g., social networks, wireless sensor networks). Though a digital image
contains pixels that reside on a regularly sampled 2D grid, if one can design
an appropriate underlying graph connecting pixels with weights that reflect the
image structure, then one can interpret the image (or image patch) as a signal
on a graph, and apply GSP tools for processing and analysis of the signal in
graph spectral domain. In this article, we overview recent graph spectral
techniques in GSP specifically for image / video processing. The topics covered
include image compression, image restoration, image filtering and image
segmentation
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