43 research outputs found
New contributions in overcomplete image representations inspired from the functional architecture of the primary visual cortex = Nuevas contribuciones en representaciones sobrecompletas de imágenes inspiradas por la arquitectura funcional de la corteza visual primaria
The present thesis aims at investigating parallelisms between the functional architecture of primary visual areas and image processing methods. A first objective is to refine existing models of biological vision on the base of information theory statements and a second is to develop original solutions for image processing inspired from natural vision. The available data on visual systems contains physiological and psychophysical studies, Gestalt psychology and statistics on natural images The thesis is mostly centered in overcomplete representations (i.e. representations increasing the dimensionality of the data) for multiple reasons. First because they allow to overcome existing drawbacks of critically sampled transforms, second because biological vision models appear overcomplete and third because building efficient overcomplete representations raises challenging and actual mathematical problems, in particular the problem of sparse approximation. The thesis proposes first a self-invertible log-Gabor wavelet transformation inspired from the receptive field and multiresolution arrangement of the simple cells in the primary visual cortex (V1). This transform shows promising abilities for noise elimination. Second, interactions observed between V1 cells consisting in lateral inhibition and in facilitation between aligned cells are shown efficient for extracting edges of natural images. As a third point, the redundancy introduced by the overcompleteness is reduced by a dedicated sparse approximation algorithm which builds a sparse representation of the images based on their edge content. For an additional decorrelation of the image information and for improving the image compression performances, edges arranged along continuous contours are coded in a predictive manner through chains of coefficients. This offers then an efficient representation of contours. Fourth, a study on contour completion using the tensor voting framework based on Gestalt psychology is presented. There, the use of iterations and of the curvature information allow to improve the robustness and the perceptual quality of the existing method.
La presente tesis doctoral tiene como objetivo indagar en algunos paralelismos entre la arquitectura funcional de las áreas visuales primarias y el tratamiento de imágenes. Un primer objetivo consiste en mejorar los modelos existentes de visión biológica basándose en la teoría de la información. Un segundo es el desarrollo de nuevos algoritmos de tratamiento de imágenes inspirados de la visión natural. Los datos disponibles sobre el sistema visual abarcan estudios fisiológicos y psicofísicos, psicología Gestalt y estadísticas de las imágenes naturales. La tesis se centra principalmente en las representaciones sobrecompletas (i.e. representaciones que incrementan la dimensionalidad de los datos) por las siguientes razones. Primero porque permiten sobrepasar importantes desventajas de las transformaciones ortogonales; segundo porque los modelos de visión biológica necesitan a menudo ser sobrecompletos y tercero porque construir representaciones sobrecompletas eficientes involucra problemas matemáticos relevantes y novedosos, en particular el problema de las aproximaciones dispersas. La tesis propone primero una transformación en ondículas log-Gabor auto-inversible inspirada del campo receptivo y la organización en multiresolución de las células simples del cortex visual primario (V1). Esta transformación ofrece resultados prometedores para la eliminación del ruido. En segundo lugar, las interacciones observadas entre las células de V1 que consisten en la inhibición lateral y en la facilitación entre células alineadas se han mostrado eficientes para extraer los bordes de las imágenes naturales. En tercer lugar, la redundancia introducida por la transformación sobrecompleta se reduce gracias a un algoritmo dedicado de aproximación dispersa el cual construye una representación dispersa de las imágenes sobre la base de sus bordes. Para una decorrelación adicional y para conseguir más altas tasas de compresión, los bordes alineados a lo largo de contornos continuos están codificado de manera predictiva por cadenas de coeficientes, lo que ofrece una representacion eficiente de los contornos. Finalmente se presenta un estudio sobre el cierre de contornos utilizando la metodología de tensor voting. Proponemos el uso de iteraciones y de la información de curvatura para mejorar la robustez y la calidad perceptual de los métodos existentes
The SURE-LET approach to image denoising
Denoising is an essential step prior to any higher-level image-processing tasks such as segmentation or object tracking, because the undesirable corruption by noise is inherent to any physical acquisition device. When the measurements are performed by photosensors, one usually distinguish between two main regimes: in the first scenario, the measured intensities are sufficiently high and the noise is assumed to be signal-independent. In the second scenario, only few photons are detected, which leads to a strong signal-dependent degradation. When the noise is considered as signal-independent, it is often modeled as an additive independent (typically Gaussian) random variable, whereas, otherwise, the measurements are commonly assumed to follow independent Poisson laws, whose underlying intensities are the unknown noise-free measures. We first consider the reduction of additive white Gaussian noise (AWGN). Contrary to most existing denoising algorithms, our approach does not require an explicit prior statistical modeling of the unknown data. Our driving principle is the minimization of a purely data-adaptive unbiased estimate of the mean-squared error (MSE) between the processed and the noise-free data. In the AWGN case, such a MSE estimate was first proposed by Stein, and is known as "Stein's unbiased risk estimate" (SURE). We further develop the original SURE theory and propose a general methodology for fast and efficient multidimensional image denoising, which we call the SURE-LET approach. While SURE allows the quantitative monitoring of the denoising quality, the flexibility and the low computational complexity of our approach are ensured by a linear parameterization of the denoising process, expressed as a linear expansion of thresholds (LET).We propose several pointwise, multivariate, and multichannel thresholding functions applied to arbitrary (in particular, redundant) linear transformations of the input data, with a special focus on multiscale signal representations. We then transpose the SURE-LET approach to the estimation of Poisson intensities degraded by AWGN. The signal-dependent specificity of the Poisson statistics leads to the derivation of a new unbiased MSE estimate that we call "Poisson's unbiased risk estimate" (PURE) and requires more adaptive transform-domain thresholding rules. In a general PURE-LET framework, we first devise a fast interscale thresholding method restricted to the use of the (unnormalized) Haar wavelet transform. We then lift this restriction and show how the PURE-LET strategy can be used to design and optimize a wide class of nonlinear processing applied in an arbitrary (in particular, redundant) transform domain. We finally apply some of the proposed denoising algorithms to real multidimensional fluorescence microscopy images. Such in vivo imaging modality often operates under low-illumination conditions and short exposure time; consequently, the random fluctuations of the measured fluorophore radiations are well described by a Poisson process degraded (or not) by AWGN. We validate experimentally this statistical measurement model, and we assess the performance of the PURE-LET algorithms in comparison with some state-of-the-art denoising methods. Our solution turns out to be very competitive both qualitatively and computationally, allowing for a fast and efficient denoising of the huge volumes of data that are nowadays routinely produced in biomedical imaging
Image Denoising in Mixed Poisson-Gaussian Noise
We propose a general methodology (PURE-LET) to design and optimize a wide class of transform-domain thresholding algorithms for denoising images corrupted by mixed Poisson-Gaussian noise. We express the denoising process as a linear expansion of thresholds (LET) that we optimize by relying on a purely data-adaptive unbiased estimate of the mean-squared error (MSE), derived in a non-Bayesian framework (PURE: Poisson-Gaussian unbiased risk estimate). We provide a practical approximation of this theoretical MSE estimate for the tractable optimization of arbitrary transform-domain thresholding. We then propose a pointwise estimator for undecimated filterbank transforms, which consists of subband-adaptive thresholding functions with signal-dependent thresholds that are globally optimized in the image domain. We finally demonstrate the potential of the proposed approach through extensive comparisons with state-of-the-art techniques that are specifically tailored to the estimation of Poisson intensities. We also present denoising results obtained on real images of low-count fluorescence microscopy
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
Adaptive Representations for Image Restoration
In the �eld of image processing, building good representation models for
natural images is crucial for various applications, such as image restora-
tion, sampling, segmentation, etc. Adaptive image representation models
are designed for describing the intrinsic structures of natural images. In
the classical Bayesian inference, this representation is often known as the
prior of the intensity distribution of the input image. Early image priors
have forms such as total variation norm, Markov Random Fields (MRF),
and wavelets. Recently, image priors obtained from machine learning tech-
niques tend to be more adaptive, which aims at capturing the natural image
models via learning from larger databases. In this thesis, we study adaptive
representations of natural images for image restoration.
The purpose of image restoration is to remove the artifacts which degrade
an image. The degradation comes in many forms such as image blurs,
noises, and artifacts from the codec. Take image denoising for an example.
There are several classic representation methods which can generate state-
of-the-art results. The �rst one is the assumption of image self-similarity.
However, this representation has the issue that sometimes the self-similarity
assumption would fail because of high noise levels or unique image contents.
The second one is the wavelet based nonlocal representation, which also has
a problem in that the �xed basis function is not adaptive enough for any
arbitrary type of input images. The third is the sparse coding using over-
complete dictionaries, which does not have the hierarchical structure that is
similar to the one in human visual system and is therefore prone to denoising
artifacts.
My research started from image denoising. Through the thorough review
and evaluation of state-of-the-art denoising methods, it was found that the representation of images is substantially important for the denoising tech-
nique. At the same time, an improvement on one of the nonlocal denoising
method was proposed, which improves the representation of images by the
integration of Gaussian blur, clustering and Rotationally Invariant Block
Matching. Enlightened by the successful application of sparse coding in
compressive sensing, we exploited the image self-similarity by using a sparse
representation based on wavelet coe�cients in a nonlocal and hierarchical
way, which generates competitive results compared to the state-of-the-art
denoising algorithms. Meanwhile, another adaptive local �lter learned by
Genetic Programming (GP) was proposed for e�cient image denoising. In
this work, we employed GP to �nd the optimal representations for local im-
age patches through training on massive datasets, which yields competitive
results compared to state-of-the-art local denoising �lters. After success-
fully dealt with the denoising part, we moved to the parameter estimation
for image degradation models. For instance, image blur identi�cation uses
deep learning, which has recently been proposed as a popular image repre-
sentation approach. This work has also been extended to blur estimation
based on the fact that the second step of the framework has been replaced
with general regression neural network. In a word, in this thesis, spatial cor-
relations, sparse coding, genetic programming, deep learning are explored
as adaptive image representation models for both image restoration and
parameter estimation.
We conclude this thesis by considering methods based on machine learning
to be the best adaptive representations for natural images. We have shown
that they can generate better results than conventional representation mod-
els for the tasks of image denoising and deblurring
A nonlinear Stein based estimator for multichannel image denoising
The use of multicomponent images has become widespread with the improvement
of multisensor systems having increased spatial and spectral resolutions.
However, the observed images are often corrupted by an additive Gaussian noise.
In this paper, we are interested in multichannel image denoising based on a
multiscale representation of the images. A multivariate statistical approach is
adopted to take into account both the spatial and the inter-component
correlations existing between the different wavelet subbands. More precisely,
we propose a new parametric nonlinear estimator which generalizes many reported
denoising methods. The derivation of the optimal parameters is achieved by
applying Stein's principle in the multivariate case. Experiments performed on
multispectral remote sensing images clearly indicate that our method
outperforms conventional wavelet denoising technique