545 research outputs found
Dictionary Learning-based Inpainting on Triangular Meshes
The problem of inpainting consists of filling missing or damaged regions in
images and videos in such a way that the filling pattern does not produce
artifacts that deviate from the original data. In addition to restoring the
missing data, the inpainting technique can also be used to remove undesired
objects. In this work, we address the problem of inpainting on surfaces through
a new method based on dictionary learning and sparse coding. Our method learns
the dictionary through the subdivision of the mesh into patches and rebuilds
the mesh via a method of reconstruction inspired by the Non-local Means method
on the computed sparse codes. One of the advantages of our method is that it is
capable of filling the missing regions and simultaneously removes noise and
enhances important features of the mesh. Moreover, the inpainting result is
globally coherent as the representation based on the dictionaries captures all
the geometric information in the transformed domain. We present two variations
of the method: a direct one, in which the model is reconstructed and restored
directly from the representation in the transformed domain and a second one,
adaptive, in which the missing regions are recreated iteratively through the
successive propagation of the sparse code computed in the hole boundaries,
which guides the local reconstructions. The second method produces better
results for large regions because the sparse codes of the patches are adapted
according to the sparse codes of the boundary patches. Finally, we present and
analyze experimental results that demonstrate the performance of our method
compared to the literature
Linear inverse problems with noise: primal and primal-dual splitting
In this paper, we propose two algorithms for solving linear inverse problems
when the observations are corrupted by noise. A proper data fidelity term
(log-likelihood) is introduced to reflect the statistics of the noise (e.g.
Gaussian, Poisson). On the other hand, as a prior, the images to restore are
assumed to be positive and sparsely represented in a dictionary of waveforms.
Piecing together the data fidelity and the prior terms, the solution to the
inverse problem is cast as the minimization of a non-smooth convex functional.
We establish the well-posedness of the optimization problem, characterize the
corresponding minimizers, and solve it by means of primal and primal-dual
proximal splitting algorithms originating from the field of non-smooth convex
optimization theory. Experimental results on deconvolution, inpainting and
denoising with some comparison to prior methods are also reported
Astronomical Data Analysis and Sparsity: from Wavelets to Compressed Sensing
Wavelets have been used extensively for several years now in astronomy for
many purposes, ranging from data filtering and deconvolution, to star and
galaxy detection or cosmic ray removal. More recent sparse representations such
ridgelets or curvelets have also been proposed for the detection of anisotropic
features such cosmic strings in the cosmic microwave background.
We review in this paper a range of methods based on sparsity that have been
proposed for astronomical data analysis. We also discuss what is the impact of
Compressed Sensing, the new sampling theory, in astronomy for collecting the
data, transferring them to the earth or reconstructing an image from incomplete
measurements.Comment: Submitted. Full paper will figures available at
http://jstarck.free.fr/IEEE09_SparseAstro.pd
Data augmentation for galaxy density map reconstruction
The matter density is an important knowledge for today cosmology as many
phenomena are linked to matter fluctuations. However, this density is not
directly available, but estimated through lensing maps or galaxy surveys. In
this article, we focus on galaxy surveys which are incomplete and noisy
observations of the galaxy density. Incomplete, as part of the sky is
unobserved or unreliable. Noisy as they are count maps degraded by Poisson
noise. Using a data augmentation method, we propose a two-step method for
recovering the density map, one step for inferring missing data and one for
estimating of the density. The results show that the missing areas are
efficiently inferred and the statistical properties of the maps are very well
preserved
Sparsity Based Poisson Denoising with Dictionary Learning
The problem of Poisson denoising appears in various imaging applications,
such as low-light photography, medical imaging and microscopy. In cases of high
SNR, several transformations exist so as to convert the Poisson noise into an
additive i.i.d. Gaussian noise, for which many effective algorithms are
available. However, in a low SNR regime, these transformations are
significantly less accurate, and a strategy that relies directly on the true
noise statistics is required. A recent work by Salmon et al. took this route,
proposing a patch-based exponential image representation model based on GMM
(Gaussian mixture model), leading to state-of-the-art results. In this paper,
we propose to harness sparse-representation modeling to the image patches,
adopting the same exponential idea. Our scheme uses a greedy pursuit with
boot-strapping based stopping condition and dictionary learning within the
denoising process. The reconstruction performance of the proposed scheme is
competitive with leading methods in high SNR, and achieving state-of-the-art
results in cases of low SNR.Comment: 13 pages, 9 figure
Learning quadrangulated patches for 3D shape parameterization and completion
We propose a novel 3D shape parameterization by surface patches, that are
oriented by 3D mesh quadrangulation of the shape. By encoding 3D surface detail
on local patches, we learn a patch dictionary that identifies principal surface
features of the shape. Unlike previous methods, we are able to encode surface
patches of variable size as determined by the user. We propose novel methods
for dictionary learning and patch reconstruction based on the query of a noisy
input patch with holes. We evaluate the patch dictionary towards various
applications in 3D shape inpainting, denoising and compression. Our method is
able to predict missing vertices and inpaint moderately sized holes. We
demonstrate a complete pipeline for reconstructing the 3D mesh from the patch
encoding. We validate our shape parameterization and reconstruction methods on
both synthetic shapes and real world scans. We show that our patch dictionary
performs successful shape completion of complicated surface textures.Comment: To be presented at International Conference on 3D Vision 2017, 201
- …