328 research outputs found
Playing with Duality: An Overview of Recent Primal-Dual Approaches for Solving Large-Scale Optimization Problems
Optimization methods are at the core of many problems in signal/image
processing, computer vision, and machine learning. For a long time, it has been
recognized that looking at the dual of an optimization problem may drastically
simplify its solution. Deriving efficient strategies which jointly brings into
play the primal and the dual problems is however a more recent idea which has
generated many important new contributions in the last years. These novel
developments are grounded on recent advances in convex analysis, discrete
optimization, parallel processing, and non-smooth optimization with emphasis on
sparsity issues. In this paper, we aim at presenting the principles of
primal-dual approaches, while giving an overview of numerical methods which
have been proposed in different contexts. We show the benefits which can be
drawn from primal-dual algorithms both for solving large-scale convex
optimization problems and discrete ones, and we provide various application
examples to illustrate their usefulness
Discrete Visual Perception
International audienceComputational vision and biomedical image have made tremendous progress of the past decade. This is mostly due the development of efficient learning and inference algorithms which allow better, faster and richer modeling of visual perception tasks. Graph-based representations are among the most prominent tools to address such perception through the casting of perception as a graph optimization problem. In this paper, we briefly introduce the interest of such representations, discuss their strength and limitations and present their application to address a variety of problems in computer vision and biomedical image analysis
Deformable Registration through Learning of Context-Specific Metric Aggregation
We propose a novel weakly supervised discriminative algorithm for learning
context specific registration metrics as a linear combination of conventional
similarity measures. Conventional metrics have been extensively used over the
past two decades and therefore both their strengths and limitations are known.
The challenge is to find the optimal relative weighting (or parameters) of
different metrics forming the similarity measure of the registration algorithm.
Hand-tuning these parameters would result in sub optimal solutions and quickly
become infeasible as the number of metrics increases. Furthermore, such
hand-crafted combination can only happen at global scale (entire volume) and
therefore will not be able to account for the different tissue properties. We
propose a learning algorithm for estimating these parameters locally,
conditioned to the data semantic classes. The objective function of our
formulation is a special case of non-convex function, difference of convex
function, which we optimize using the concave convex procedure. As a proof of
concept, we show the impact of our approach on three challenging datasets for
different anatomical structures and modalities.Comment: Accepted for publication in the 8th International Workshop on Machine
Learning in Medical Imaging (MLMI 2017), in conjunction with MICCAI 201
DPP-PMRF: Rethinking Optimization for a Probabilistic Graphical Model Using Data-Parallel Primitives
We present a new parallel algorithm for probabilistic graphical model
optimization. The algorithm relies on data-parallel primitives (DPPs), which
provide portable performance over hardware architecture. We evaluate results on
CPUs and GPUs for an image segmentation problem. Compared to a serial baseline,
we observe runtime speedups of up to 13X (CPU) and 44X (GPU). We also compare
our performance to a reference, OpenMP-based algorithm, and find speedups of up
to 7X (CPU).Comment: LDAV 2018, October 201
Large-scale Binary Quadratic Optimization Using Semidefinite Relaxation and Applications
In computer vision, many problems such as image segmentation, pixel
labelling, and scene parsing can be formulated as binary quadratic programs
(BQPs). For submodular problems, cuts based methods can be employed to
efficiently solve large-scale problems. However, general nonsubmodular problems
are significantly more challenging to solve. Finding a solution when the
problem is of large size to be of practical interest, however, typically
requires relaxation. Two standard relaxation methods are widely used for
solving general BQPs--spectral methods and semidefinite programming (SDP), each
with their own advantages and disadvantages. Spectral relaxation is simple and
easy to implement, but its bound is loose. Semidefinite relaxation has a
tighter bound, but its computational complexity is high, especially for large
scale problems. In this work, we present a new SDP formulation for BQPs, with
two desirable properties. First, it has a similar relaxation bound to
conventional SDP formulations. Second, compared with conventional SDP methods,
the new SDP formulation leads to a significantly more efficient and scalable
dual optimization approach, which has the same degree of complexity as spectral
methods. We then propose two solvers, namely, quasi-Newton and smoothing Newton
methods, for the dual problem. Both of them are significantly more efficiently
than standard interior-point methods. In practice, the smoothing Newton solver
is faster than the quasi-Newton solver for dense or medium-sized problems,
while the quasi-Newton solver is preferable for large sparse/structured
problems. Our experiments on a few computer vision applications including
clustering, image segmentation, co-segmentation and registration show the
potential of our SDP formulation for solving large-scale BQPs.Comment: Fixed some typos. 18 pages. Accepted to IEEE Transactions on Pattern
Analysis and Machine Intelligenc
Prior-based Coregistration and Cosegmentation
We propose a modular and scalable framework for dense coregistration and
cosegmentation with two key characteristics: first, we substitute ground truth
data with the semantic map output of a classifier; second, we combine this
output with population deformable registration to improve both alignment and
segmentation. Our approach deforms all volumes towards consensus, taking into
account image similarities and label consistency. Our pipeline can incorporate
any classifier and similarity metric. Results on two datasets, containing
annotations of challenging brain structures, demonstrate the potential of our
method.Comment: The first two authors contributed equall
Early Vision Optimization: Parametric Models, Parallelization and Curvature
Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Many of these tasks are formulated as optimization problems and one of the key factors for the success of recent methods is that they seek to compute globally optimal solutions. This thesis is concerned with improving the efficiency and extending the applicability of the current state of the art. This is achieved by introducing new methods of computing solutions to image segmentation and other problems of early vision. The first part studies parametric problems where model parameters are estimated in addition to an image segmentation. For a small number of parameters these problems can still be solved optimally. In the second part the focus is shifted toward curvature regularization, i.e. when the commonly used length and area regularization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes are compared to square ones and a method for generating adaptive methods is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Thirdly, fast methods for finding minimal graph cuts and solving related problems on modern parallel hardware are developed and extensively evaluated. Finally, the thesis is concluded with two applications to early vision problems: heart segmentation and image registration
An Unsupervised Learning Model for Deformable Medical Image Registration
We present a fast learning-based algorithm for deformable, pairwise 3D
medical image registration. Current registration methods optimize an objective
function independently for each pair of images, which can be time-consuming for
large data. We define registration as a parametric function, and optimize its
parameters given a set of images from a collection of interest. Given a new
pair of scans, we can quickly compute a registration field by directly
evaluating the function using the learned parameters. We model this function
using a convolutional neural network (CNN), and use a spatial transform layer
to reconstruct one image from another while imposing smoothness constraints on
the registration field. The proposed method does not require supervised
information such as ground truth registration fields or anatomical landmarks.
We demonstrate registration accuracy comparable to state-of-the-art 3D image
registration, while operating orders of magnitude faster in practice. Our
method promises to significantly speed up medical image analysis and processing
pipelines, while facilitating novel directions in learning-based registration
and its applications. Our code is available at
https://github.com/balakg/voxelmorph .Comment: 9 pages, in CVPR 201
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