750 research outputs found
Disparity map estimation under convex constraints using proximal algorithms
International audienceIn this paper, we propose a new approach for estimating depth maps of stereo images which are prone to various types of noise. This method, based on a parallel proximal algorithm, gives a great flexibility in the choice of the constrained criterion to be minimized, thus allowing us to take into account different types of noise distributions. Our main objective is to present an iterative estimation method based on recent convex optimization algorithms and proximal tools. Results for several error measures demonstrate the effectiveness and robustness of the proposed method for disparity map estimation even in the presence of perturbations
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
Confidence driven TGV fusion
We introduce a novel model for spatially varying variational data fusion,
driven by point-wise confidence values. The proposed model allows for the joint
estimation of the data and the confidence values based on the spatial coherence
of the data. We discuss the main properties of the introduced model as well as
suitable algorithms for estimating the solution of the corresponding biconvex
minimization problem and their convergence. The performance of the proposed
model is evaluated considering the problem of depth image fusion by using both
synthetic and real data from publicly available datasets
Light Field Super-Resolution Via Graph-Based Regularization
Light field cameras capture the 3D information in a scene with a single
exposure. This special feature makes light field cameras very appealing for a
variety of applications: from post-capture refocus, to depth estimation and
image-based rendering. However, light field cameras suffer by design from
strong limitations in their spatial resolution, which should therefore be
augmented by computational methods. On the one hand, off-the-shelf single-frame
and multi-frame super-resolution algorithms are not ideal for light field data,
as they do not consider its particular structure. On the other hand, the few
super-resolution algorithms explicitly tailored for light field data exhibit
significant limitations, such as the need to estimate an explicit disparity map
at each view. In this work we propose a new light field super-resolution
algorithm meant to address these limitations. We adopt a multi-frame alike
super-resolution approach, where the complementary information in the different
light field views is used to augment the spatial resolution of the whole light
field. We show that coupling the multi-frame approach with a graph regularizer,
that enforces the light field structure via nonlocal self similarities, permits
to avoid the costly and challenging disparity estimation step for all the
views. Extensive experiments show that the new algorithm compares favorably to
the other state-of-the-art methods for light field super-resolution, both in
terms of PSNR and visual quality.Comment: This new version includes more material. In particular, we added: a
new section on the computational complexity of the proposed algorithm,
experimental comparisons with a CNN-based super-resolution algorithm, and new
experiments on a third datase
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
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
The problem of minimizing convex functionals of probability distributions is
solved under the assumption that the density of every distribution is bounded
from above and below. A system of sufficient and necessary first-order
optimality conditions as well as a bound on the optimality gap of feasible
candidate solutions are derived. Based on these results, two numerical
algorithms are proposed that iteratively solve the system of optimality
conditions on a grid of discrete points. Both algorithms use a block coordinate
descent strategy and terminate once the optimality gap falls below the desired
tolerance. While the first algorithm is conceptually simpler and more
efficient, it is not guaranteed to converge for objective functions that are
not strictly convex. This shortcoming is overcome in the second algorithm,
which uses an additional outer proximal iteration, and, which is proven to
converge under mild assumptions. Two examples are given to demonstrate the
theoretical usefulness of the optimality conditions as well as the high
efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on
Signal Processing. In previous versions, the example in Section VI.B
contained some mistakes and inaccuracies, which have been fixed in this
versio
A proximal approach for optimization problems involving Kullback divergences
International audienceConvex optimization problems involving information measures have been extensively investigated in source and channel coding. These measures can also be successfully used in inverse problems encountered in signal and image processing. The related optimization problems are often challenging due to their large size. In this paper, we derive closed-form expressions of the proximity operators of Kullback-Leibler and Jeffreys-Kullback divergences. Building upon these results, we develop an efïŹcient primal-dual proximal approach. This allows us to address a wide range of convex optimization problems whose objective function expression includes one of these divergences. An image registration application serves as an example for illustrating the good performance of the proposed method
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