27 research outputs found
Foundations, Inference, and Deconvolution in Image Restoration
Image restoration is a critical preprocessing step in computer vision,
producing images with reduced noise, blur, and pixel defects.
This enables precise higher-level reasoning as to the scene content in
later stages of the vision pipeline (e.g., object segmentation,
detection, recognition, and tracking).
Restoration techniques have found extensive usage in a broad range of
applications from industry, medicine, astronomy, biology, and
photography.
The recovery of high-grade results requires models of the image
degradation process, giving rise to a class of often heavily
underconstrained, inverse problems.
A further challenge specific to the problem of blur removal is noise
amplification, which may cause strong distortion by ringing artifacts.
This dissertation presents new insights and problem solving procedures
for three areas of image restoration, namely (1) model
foundations, (2) Bayesian inference for high-order Markov
random fields (MRFs), and (3) blind image deblurring
(deconvolution).
As basic research on model foundations, we contribute to reconciling
the perceived differences between probabilistic MRFs on the one hand,
and deterministic variational models on the other.
To do so, we restrict the variational functional to locally supported finite
elements (FE) and integrate over the domain.
This yields a sum of terms depending locally on FE basis coefficients,
and by identifying the latter with pixels, the terms resolve to MRF
potential functions.
In contrast with previous literature, we place special emphasis on robust
regularizers used commonly in contemporary computer vision.
Moreover, we draw samples from the derived models to further
demonstrate the probabilistic connection.
Another focal issue is a class of high-order Field of Experts MRFs
which are learned generatively from natural image data and yield
best quantitative results under Bayesian estimation.
This involves minimizing an integral expression, which has no closed
form solution in general.
However, the MRF class under study has Gaussian mixture potentials,
permitting expansion by indicator variables as a technical measure.
As approximate inference method, we study Gibbs sampling in the
context of non-blind deblurring and obtain excellent results, yet
at the cost of high computing effort.
In reaction to this, we turn to the mean field algorithm, and show
that it scales quadratically in the clique size for a standard
restoration setting with linear degradation model.
An empirical study of mean field over several restoration scenarios
confirms advantageous properties with regard to both image quality and
computational runtime.
This dissertation further examines the problem of blind deconvolution,
beginning with localized blur from fast moving objects in the
scene, or from camera defocus.
Forgoing dedicated hardware or user labels, we rely only on the image
as input and introduce a latent variable model to explain the
non-uniform blur.
The inference procedure estimates freely varying kernels and we
demonstrate its generality by extensive experiments.
We further present a discriminative method for blind removal of camera
shake.
In particular, we interleave discriminative non-blind deconvolution
steps with kernel estimation and leverage the error cancellation
effects of the Regression Tree Field model to attain a deblurring
process with tightly linked sequential stages
Nonlocal Myriad Filters for Cauchy Noise Removal
The contribution of this paper is two-fold. First, we introduce a generalized
myriad filter, which is a method to compute the joint maximum likelihood
estimator of the location and the scale parameter of the Cauchy distribution.
Estimating only the location parameter is known as myriad filter. We propose an
efficient algorithm to compute the generalized myriad filter and prove its
convergence. Special cases of this algorithm result in the classical myriad
filtering, respective an algorithm for estimating only the scale parameter.
Based on an asymptotic analysis, we develop a second, even faster generalized
myriad filtering technique.
Second, we use our new approaches within a nonlocal, fully unsupervised
method to denoise images corrupted by Cauchy noise. Special attention is paid
to the determination of similar patches in noisy images. Numerical examples
demonstrate the excellent performance of our algorithms which have moreover the
advantage to be robust with respect to the parameter choice
Space adaptive and hierarchical Bayesian variational models for image restoration
The main contribution of this thesis is the proposal of novel space-variant regularization or penalty terms motivated by a strong statistical rational. In light of the connection between the classical variational framework and the Bayesian formulation, we will focus on the design of highly flexible priors characterized by a large number of unknown parameters. The latter will be automatically estimated by setting up a hierarchical modeling framework, i.e. introducing informative or non-informative hyperpriors depending on the information at hand on the parameters.
More specifically, in the first part of the thesis we will focus on the restoration of natural images, by introducing highly parametrized distribution to model the local behavior of the gradients in the image. The resulting regularizers hold the potential to adapt to the local smoothness, directionality and sparsity in the data. The estimation of the unknown parameters will be addressed by means of non-informative hyperpriors, namely uniform distributions over the parameter domain, thus leading to the classical Maximum Likelihood approach.
In the second part of the thesis, we will address the problem of designing suitable penalty terms for the recovery of sparse signals. The space-variance in the proposed penalties, corresponding to a family of informative hyperpriors, namely generalized gamma hyperpriors, will follow directly from the assumption of the independence of the components in the signal. The study of the properties of the resulting energy functionals will thus lead to the introduction of two hybrid algorithms, aimed at combining the strong sparsity promotion characterizing non-convex penalty terms with the desirable guarantees of convex optimization
Tracking the Temporal-Evolution of Supernova Bubbles in Numerical Simulations
The study of low-dimensional, noisy manifolds embedded in a higher dimensional space has been extremely useful in many applications, from the chemical analysis of multi-phase flows to simulations of galactic mergers. Building a probabilistic model of the manifolds has helped in describing their essential properties and how they vary in space. However, when the manifold is evolving through time, a joint spatio-temporal modelling is needed, in order to fully comprehend its nature. We propose a first-order Markovian process that propagates the spatial probabilistic model of a manifold at fixed time, to its adjacent temporal stages. The proposed methodology is demonstrated using a particle simulation of an interacting dwarf galaxy to describe the evolution of a cavity generated by a Supernov