4 research outputs found
A Panorama on Multiscale Geometric Representations, Intertwining Spatial, Directional and Frequency Selectivity
The richness of natural images makes the quest for optimal representations in
image processing and computer vision challenging. The latter observation has
not prevented the design of image representations, which trade off between
efficiency and complexity, while achieving accurate rendering of smooth regions
as well as reproducing faithful contours and textures. The most recent ones,
proposed in the past decade, share an hybrid heritage highlighting the
multiscale and oriented nature of edges and patterns in images. This paper
presents a panorama of the aforementioned literature on decompositions in
multiscale, multi-orientation bases or dictionaries. They typically exhibit
redundancy to improve sparsity in the transformed domain and sometimes its
invariance with respect to simple geometric deformations (translation,
rotation). Oriented multiscale dictionaries extend traditional wavelet
processing and may offer rotation invariance. Highly redundant dictionaries
require specific algorithms to simplify the search for an efficient (sparse)
representation. We also discuss the extension of multiscale geometric
decompositions to non-Euclidean domains such as the sphere or arbitrary meshed
surfaces. The etymology of panorama suggests an overview, based on a choice of
partially overlapping "pictures". We hope that this paper will contribute to
the appreciation and apprehension of a stream of current research directions in
image understanding.Comment: 65 pages, 33 figures, 303 reference
Mathematical Approaches for Image Enhancement Problems
This thesis develops novel techniques that can solve some image enhancement problems using theoretically and technically proven and very useful mathematical tools to image processing such as wavelet transforms, partial differential equations, and variational models. Three subtopics are mainly covered. First, color image denoising framework is introduced to achieve high quality denoising results by considering correlations between color components while existing denoising approaches can be plugged in flexibly. Second, a new and efficient framework for image contrast and color enhancement in the compressed wavelet domain is proposed. The proposed approach is capable of enhancing both global and local contrast and brightness as well as preserving color consistency. The framework does not require inverse transform for image enhancement since linear scale factors are directly applied to both scaling and wavelet coefficients in the compressed domain, which results in high computational efficiency. Also contaminated noise in the image can be efficiently reduced by introducing wavelet shrinkage terms adaptively in different scales. The proposed method is able to enhance a wavelet-coded image computationally efficiently with high image quality and less noise or other artifact. The experimental results show that the proposed method produces encouraging results both visually and numerically compared to some existing approaches. Finally, image inpainting problem is discussed. Literature review, psychological analysis, and challenges on image inpainting problem and related topics are described. An inpainting algorithm using energy minimization and texture mapping is proposed. Mumford-Shah energy minimization model detects and preserves edges in the inpainting domain by detecting both the main structure and the detailed edges. This approach utilizes faster hierarchical level set method and guarantees convergence independent of initial conditions. The estimated segmentation results in the inpainting domain are stored in segmentation map, which is referred by a texture mapping algorithm for filling textured regions. We also propose an inpainting algorithm using wavelet transform that can expect better global structure estimation of the unknown region in addition to shape and texture properties since wavelet transforms have been used for various image analysis problems due to its nice multi-resolution properties and decoupling characteristics
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