19 research outputs found
Combining local regularity estimation and total variation optimization for scale-free texture segmentation
Texture segmentation constitutes a standard image processing task, crucial to
many applications. The present contribution focuses on the particular subset of
scale-free textures and its originality resides in the combination of three key
ingredients: First, texture characterization relies on the concept of local
regularity ; Second, estimation of local regularity is based on new multiscale
quantities referred to as wavelet leaders ; Third, segmentation from local
regularity faces a fundamental bias variance trade-off: In nature, local
regularity estimation shows high variability that impairs the detection of
changes, while a posteriori smoothing of regularity estimates precludes from
locating correctly changes. Instead, the present contribution proposes several
variational problem formulations based on total variation and proximal
resolutions that effectively circumvent this trade-off. Estimation and
segmentation performance for the proposed procedures are quantified and
compared on synthetic as well as on real-world textures
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
Disparity and optical flow partitioning using extended Potts priors
This paper addresses the problems of disparity and optical flow partitioning based on the brightness invariance assumption. We investigate new variational approaches to these problems with Potts priors and possibly box constraints. For the optical flow partitioning, our model includes vector-valued data and an adapted Potts regularizer. Using the notion of asymptotically level stable (als) functions, we prove the existence of global minimizers of our functionals. We propose a modified alternating direction method of multipliers. This iterative algorithm requires the computation of global minimizers of classical univariate Potts problems which can be done efficiently by dynamic programming. We prove that the algorithm converges both for the constrained and unconstrained problems. Numerical examples demonstrate the very good performance of our partitioning method
An introduction to continuous optimization for imaging
International audienceA large number of imaging problems reduce to the optimization of a cost function , with typical structural properties. The aim of this paper is to describe the state of the art in continuous optimization methods for such problems, and present the most successful approaches and their interconnections. We place particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems. We illustrate and compare the different algorithms using classical non-smooth problems in imaging, such as denoising and deblurring. Moreover, we present applications of the algorithms to more advanced problems, such as magnetic resonance imaging, multilabel image segmentation, optical flow estimation, stereo matching, and classification
Optimization of Markov Random Fields in Computer Vision
A large variety of computer vision tasks can be formulated using
Markov Random Fields (MRF). Except in certain special cases,
optimizing an MRF is intractable, due to a large number of
variables and complex dependencies between them. In this thesis,
we present new algorithms to perform inference in MRFs, that are
either more efficient (in terms of running time and/or memory
usage) or more effective (in terms of solution quality), than the
state-of-the-art methods.
First, we introduce a memory efficient max-flow algorithm for
multi-label submodular MRFs. In fact,
such MRFs have been shown to be optimally solvable using max-flow
based on an encoding of the labels proposed by Ishikawa, in which
each variable is represented by nodes (where
is the number of labels) arranged in a column. However, this
method in general requires edges for each pair of
neighbouring variables. This makes it inapplicable to realistic
problems with many variables and labels, due to excessive memory
requirement. By contrast, our max-flow algorithm stores
values per variable pair, requiring much less storage.
Consequently, our algorithm makes it possible to optimally solve
multi-label submodular problems involving large numbers of
variables and labels on a standard computer.
Next, we present a move-making style algorithm for multi-label
MRFs with robust non-convex priors. In particular, our algorithm
iteratively approximates the original MRF energy with an
appropriately weighted surrogate energy that is easier to
minimize. Furthermore, it guarantees that the original energy
decreases at each iteration. To this end, we consider the
scenario where the weighted surrogate energy is multi-label
submodular (i.e., it can be optimally minimized by max-flow), and
show that our algorithm then lets us handle of a large variety of
non-convex priors.
Finally, we consider the fully connected Conditional Random Field
(dense CRF) with Gaussian pairwise potentials that has proven
popular and effective for multi-class semantic segmentation.
While the energy of a dense CRF can be minimized accurately using
a Linear Programming (LP) relaxation, the state-of-the-art
algorithm is too slow to be useful in practice. To alleviate this
deficiency, we introduce an efficient LP minimization algorithm
for dense CRFs. To this end, we develop a proximal minimization
framework, where the dual of each proximal problem is optimized
via block-coordinate descent. We show that each block of
variables can be optimized in a time linear in the number of
pixels and labels. Consequently, our algorithm enables efficient
and effective optimization of dense CRFs with Gaussian pairwise
potentials.
We evaluated all our algorithms on standard energy minimization
datasets consisting of computer vision problems, such as stereo,
inpainting and semantic segmentation. The experiments at the end
of each chapter provide compelling evidence that all our
approaches are either more efficient or more effective than all
existing baselines
Nonsmooth Convex Variational Approaches to Image Analysis
Variational models constitute a foundation for the formulation and understanding of models in many areas of image processing and analysis. In this work, we consider a generic variational framework for convex relaxations of multiclass labeling problems, formulated on continuous domains. We propose several relaxations for length-based regularizers, with varying expressiveness and computational cost. In contrast to graph-based, combinatorial approaches, we rely on a geometric measure theory-based formulation, which avoids artifacts caused by an early discretization in theory as well as in practice. We investigate and compare numerical first-order approaches for solving the associated nonsmooth discretized problem, based on controlled smoothing and operator splitting. In order to obtain integral solutions, we propose a randomized rounding technique formulated in the spatially continuous setting, and prove that it allows to obtain solutions with an a priori optimality bound. Furthermore, we present a method for introducing more advanced prior shape knowledge into labeling problems, based on the sparse representation framework
Advances in Image Processing, Analysis and Recognition Technology
For many decades, researchers have been trying to make computers’ analysis of images as effective as the system of human vision is. For this purpose, many algorithms and systems have previously been created. The whole process covers various stages, including image processing, representation and recognition. The results of this work can be applied to many computer-assisted areas of everyday life. They improve particular activities and provide handy tools, which are sometimes only for entertainment, but quite often, they significantly increase our safety. In fact, the practical implementation of image processing algorithms is particularly wide. Moreover, the rapid growth of computational complexity and computer efficiency has allowed for the development of more sophisticated and effective algorithms and tools. Although significant progress has been made so far, many issues still remain, resulting in the need for the development of novel approaches