10,985 research outputs found
Efficient Energy Minimization for Enforcing Statistics
Energy minimization algorithms, such as graph cuts, enable the computation of
the MAP solution under certain probabilistic models such as Markov random
fields. However, for many computer vision problems, the MAP solution under the
model is not the ground truth solution. In many problem scenarios, the system
has access to certain statistics of the ground truth. For instance, in image
segmentation, the area and boundary length of the object may be known. In these
cases, we want to estimate the most probable solution that is consistent with
such statistics, i.e., satisfies certain equality or inequality constraints.
The above constrained energy minimization problem is NP-hard in general, and
is usually solved using Linear Programming formulations, which relax the
integrality constraints. This paper proposes a novel method that finds the
discrete optimal solution of such problems by maximizing the corresponding
Lagrangian dual. This method can be applied to any constrained energy
minimization problem whose unconstrained version is polynomial time solvable,
and can handle multiple, equality or inequality, and linear or non-linear
constraints. We demonstrate the efficacy of our method on the
foreground/background image segmentation problem, and show that it produces
impressive segmentation results with less error, and runs more than 20 times
faster than the state-of-the-art LP relaxation based approaches
Convex Variational Image Restoration with Histogram Priors
We present a novel variational approach to image restoration (e.g.,
denoising, inpainting, labeling) that enables to complement established
variational approaches with a histogram-based prior enforcing closeness of the
solution to some given empirical measure. By minimizing a single objective
function, the approach utilizes simultaneously two quite different sources of
information for restoration: spatial context in terms of some smoothness prior
and non-spatial statistics in terms of the novel prior utilizing the
Wasserstein distance between probability measures. We study the combination of
the functional lifting technique with two different relaxations of the
histogram prior and derive a jointly convex variational approach. Mathematical
equivalence of both relaxations is established and cases where optimality holds
are discussed. Additionally, we present an efficient algorithmic scheme for the
numerical treatment of the presented model. Experiments using the basic
total-variation based denoising approach as a case study demonstrate our novel
regularization approach.Comment: 20 pages, 11 figure
Towards analytical model optimization in atmospheric tomography
Modern ground-based telescopes rely on a technology called adaptive optics
(AO) in order to compensate for the loss of image quality caused by atmospheric
turbulence. Next-generation AO systems designed for a wide field of view
require a stable and high-resolution reconstruction of the refractive index
fluctuations in the atmosphere. By introducing a novel Bayesian method, we
address the problem of estimating an atmospheric turbulence strength profile
and reconstructing the refractive index fluctuations simultaneously, where we
only use wavefront measurements of incoming light from guide stars. Most
importantly, we demonstrate how this method can be used for model optimization
as well. We propose two different algorithms for solving the maximum a
posteriori estimate: the first approach is based on alternating minimization
and has the advantage of integrability into existing atmospheric tomography
methods. In the second approach, we formulate a convex non-differentiable
optimization problem, which is solved by an iterative thresholding method. This
approach clearly illustrates the underlying sparsity-enforcing mechanism for
the strength profile. By introducing a tuning/regularization parameter, an
automated model reduction of the layer structure of the atmosphere is achieved.
Using numerical simulations, we demonstrate the performance of our method in
practice
Exact and Efficient Algorithm to Discover Extreme Stochastic Events in Wind Generation over Transmission Power Grids
In this manuscript we continue the thread of [M. Chertkov, F. Pan, M.
Stepanov, Predicting Failures in Power Grids: The Case of Static Overloads,
IEEE Smart Grid 2011] and suggest a new algorithm discovering most probable
extreme stochastic events in static power grids associated with intermittent
generation of wind turbines. The algorithm becomes EXACT and EFFICIENT
(polynomial) in the case of the proportional (or other low parametric) control
of standard generation, and log-concave probability distribution of the
renewable generation, assumed known from the wind forecast. We illustrate the
algorithm's ability to discover problematic extreme events on the example of
the IEEE RTS-96 model of transmission with additions of 10%, 20% and 30% of
renewable generation. We observe that the probability of failure may grow but
it may also decrease with increase in renewable penetration, if the latter is
sufficiently diversified and distributed.Comment: 7 pages, 3 figures, invited session on Smart Grid Integration of
Renewable Energy: Failure analysis, Microgrids, and Estimation at CDC/ECC
201
Hierarchical Piecewise-Constant Super-regions
Recent applications in computer vision have come to heavily rely on
superpixel over-segmentation as a pre-processing step for higher level vision
tasks, such as object recognition, image labelling or image segmentation. Here
we present a new superpixel algorithm called Hierarchical Piecewise-Constant
Super-regions (HPCS), which not only obtains superpixels comparable to the
state-of-the-art, but can also be applied hierarchically to form what we call
n-th order super-regions. In essence, a Markov Random Field (MRF)-based
anisotropic denoising formulation over the quantized feature space is adopted
to form piecewise-constant image regions, which are then combined with a
graph-based split & merge post-processing step to form superpixels. The graph
and quantized feature based formulation of the problem allows us to generalize
it hierarchically to preserve boundary adherence with fewer superpixels.
Experimental results show that, despite the simplicity of our framework, it is
able to provide high quality superpixels, and to hierarchically apply them to
form layers of over-segmentation, each with a decreasing number of superpixels,
while maintaining the same desired properties (such as adherence to strong
image edges). The algorithm is also memory efficient and has a low
computational cost
Generalized Sparse and Low-Rank Optimization for Ultra-Dense Networks
Ultra-dense network (UDN) is a promising technology to further evolve
wireless networks and meet the diverse performance requirements of 5G networks.
With abundant access points, each with communication, computation and storage
resources, UDN brings unprecedented benefits, including significant improvement
in network spectral efficiency and energy efficiency, greatly reduced latency
to enable novel mobile applications, and the capability of providing massive
access for Internet of Things (IoT) devices. However, such great promises come
with formidable research challenges. To design and operate such complex
networks with various types of resources, efficient and innovative
methodologies will be needed. This motivates the recent introduction of highly
structured and generalizable models for network optimization. In this article,
we present some recently proposed large-scale sparse and low-rank frameworks
for optimizing UDNs, supported by various motivating applications. A special
attention is paid on algorithmic approaches to deal with nonconvex objective
functions and constraints, as well as computational scalability.Comment: This paper has been accepted by IEEE Communication Magazine, Special
Issue on Heterogeneous Ultra Dense Network
Constrained Optimization for Liquid Crystal Equilibria: Extended Results
This paper investigates energy-minimization finite-element approaches for the
computation of nematic liquid crystal equilibrium configurations. We compare
the performance of these methods when the necessary unit-length constraint is
enforced by either continuous Lagrange multipliers or a penalty functional.
Building on previous work in [1,2], the penalty method is derived and the
linearizations within the nonlinear iteration are shown to be well-posed under
certain assumptions. In addition, the paper discusses the effects of tailored
trust-region methods and nested iteration for both formulations. Such methods
are aimed at increasing the efficiency and robustness of each algorithms'
nonlinear iterations. Three representative, free-elastic, equilibrium problems
are considered to examine each method's performance. The first two
configurations have analytical solutions and, therefore, convergence to the
true solution is considered. The third problem considers more complicated
boundary conditions, relevant in ongoing research, simulating surface
nano-patterning. A multigrid approach is introduced and tested for a
flexoelectrically coupled model to establish scalability for highly complicated
applications. The Lagrange multiplier method is found to outperform the penalty
method in a number of measures, trust regions are shown to improve robustness,
and nested iteration proves highly effective at reducing computational costs.Comment: 28 Pages, 8 Figures, 15 Tables, 5 Procedures. Added and removed
references, as well as some minor figure rearrangemen
Algorithms for the Markov Entropy Decomposition
The Markov entropy decomposition (MED) is a recently-proposed, cluster-based
simulation method for finite temperature quantum systems with arbitrary
geometry. In this paper, we detail numerical algorithms for performing the
required steps of the MED, principally solving a minimization problem with a
preconditioned Newton's algorithm, as well as how to extract global
susceptibilities and thermal responses. We demonstrate the power of the method
with the spin-1/2 XXZ model on the 2D square lattice, including the extraction
of critical points and details of each phase. Although the method shares some
qualitative similarities with exact-diagonalization, we show the MED is both
more accurate and significantly more flexible.Comment: 12 pages, 9 figure
Higher-order Segmentation via Multicuts
Multicuts enable to conveniently represent discrete graphical models for
unsupervised and supervised image segmentation, in the case of local energy
functions that exhibit symmetries. The basic Potts model and natural extensions
thereof to higher-order models provide a prominent class of such objectives,
that cover a broad range of segmentation problems relevant to image analysis
and computer vision. We exhibit a way to systematically take into account such
higher-order terms for computational inference. Furthermore, we present results
of a comprehensive and competitive numerical evaluation of a variety of
dedicated cutting-plane algorithms. Our approach enables the globally optimal
evaluation of a significant subset of these models, without compromising
runtime. Polynomially solvable relaxations are studied as well, along with
advanced rounding schemes for post-processing
Making Sense of Hidden Layer Information in Deep Networks by Learning Hierarchical Targets
This paper proposes an architecture for deep neural networks with hidden
layer branches that learn targets of lower hierarchy than final layer targets.
The branches provide a channel for enforcing useful information in hidden layer
which helps in attaining better accuracy, both for the final layer and hidden
layers. The shared layers modify their weights using the gradients of all cost
functions higher than the branching layer. This model provides a flexible
inference system with many levels of targets which is modular and can be used
efficiently in situations requiring different levels of results according to
complexity. This paper applies the idea to a text classification task on 20
Newsgroups data set with two level of hierarchical targets and a comparison is
made with training without the use of hidden layer branches.Comment: Updated to add a note with commentary on original (v1) submissio
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