3,061 research outputs found
Robust Feature-Preserving Mesh Denoising Based on Consistent Sub-Neighborhoods
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Advances in Graph-Cut Optimization: Multi-Surface Models, Label Costs, and Hierarchical Costs
Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of low-level inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing better energies and better algorithms for energies. This dissertation presents work along the same line, specifically new energies and algorithms based on graph cuts.
We present three distinct contributions. First we consider biomedical segmentation where the object of interest comprises multiple distinct regions of uncertain shape (e.g. blood vessels, airways, bone tissue). We show that this common yet difficult scenario can be modeled as an energy over multiple interacting surfaces, and can be globally optimized by a single graph cut. Second, we introduce multi-label energies with label costs and provide algorithms to minimize them. We show how label costs are useful for clustering and robust estimation problems in vision. Third, we characterize a class of energies with hierarchical costs and propose a novel hierarchical fusion algorithm with improved approximation guarantees. Hierarchical costs are natural for modeling an array of difficult problems, e.g. segmentation with hierarchical context, simultaneous estimation of motions and homographies, or detecting hierarchies of patterns
Hyperspectral Unmixing Overview: Geometrical, Statistical, and Sparse Regression-Based Approaches
Imaging spectrometers measure electromagnetic energy scattered in their
instantaneous field view in hundreds or thousands of spectral channels with
higher spectral resolution than multispectral cameras. Imaging spectrometers
are therefore often referred to as hyperspectral cameras (HSCs). Higher
spectral resolution enables material identification via spectroscopic analysis,
which facilitates countless applications that require identifying materials in
scenarios unsuitable for classical spectroscopic analysis. Due to low spatial
resolution of HSCs, microscopic material mixing, and multiple scattering,
spectra measured by HSCs are mixtures of spectra of materials in a scene. Thus,
accurate estimation requires unmixing. Pixels are assumed to be mixtures of a
few materials, called endmembers. Unmixing involves estimating all or some of:
the number of endmembers, their spectral signatures, and their abundances at
each pixel. Unmixing is a challenging, ill-posed inverse problem because of
model inaccuracies, observation noise, environmental conditions, endmember
variability, and data set size. Researchers have devised and investigated many
models searching for robust, stable, tractable, and accurate unmixing
algorithms. This paper presents an overview of unmixing methods from the time
of Keshava and Mustard's unmixing tutorial [1] to the present. Mixing models
are first discussed. Signal-subspace, geometrical, statistical, sparsity-based,
and spatial-contextual unmixing algorithms are described. Mathematical problems
and potential solutions are described. Algorithm characteristics are
illustrated experimentally.Comment: This work has been accepted for publication in IEEE Journal of
Selected Topics in Applied Earth Observations and Remote Sensin
Combinatorial Mesh Optimization
International audienceA new mesh optimization framework for 3D triangular surface meshes is presented, which formulates the task as an energy minimization problem in the same spirit as in Hoppe et al. (SIGGRAPH’93: Proceedings of the 20th Annual Conference on Computer Graphics and Interactive Techniques, 1993). The desired mesh properties are controlled through a global energy function including data attached terms measuring the fidelity to the original mesh, shape potentials favoring high quality triangles, and connectivity as well as budget terms controlling the sampling density. The optimization algorithm modifies mesh connectivity as well as the vertex positions. Solutions for the vertex repositioning step are obtained by a discrete graph cut algorithm examining global combinations of local candidates.Results on various 3D meshes compare favorably to recent state-of-the-art algorithms. Applications consist in optimizing triangular meshes and in simplifying meshes, while maintaining high mesh quality. Targeted areas are the improvement of the accuracy of numerical simulations, the convergence of numerical schemes, improvements of mesh rendering (normal field smoothness) or improvements of the geometric prediction in mesh compression technique
Rapid Computation of Thermodynamic Properties Over Multidimensional Nonbonded Parameter Spaces using Adaptive Multistate Reweighting
We show how thermodynamic properties of molecular models can be computed over
a large, multidimensional parameter space by combining multistate reweighting
analysis with a linear basis function approach. This approach reduces the
computational cost to estimate thermodynamic properties from molecular
simulations for over 130,000 tested parameter combinations from over a thousand
CPU years to tens of CPU days. This speed increase is achieved primarily by
computing the potential energy as a linear combination of basis functions,
computed from either modified simulation code or as the difference of energy
between two reference states, which can be done without any simulation code
modification. The thermodynamic properties are then estimated with the
Multistate Bennett Acceptance Ratio (MBAR) as a function of multiple model
parameters without the need to define a priori how the states are connected by
a pathway. Instead, we adaptively sample a set of points in parameter space to
create mutual configuration space overlap. The existence of regions of poor
configuration space overlap are detected by analyzing the eigenvalues of the
sampled states' overlap matrix. The configuration space overlap to sampled
states is monitored alongside the mean and maximum uncertainty to determine
convergence, as neither the uncertainty or the configuration space overlap
alone is a sufficient metric of convergence.
This adaptive sampling scheme is demonstrated by estimating with high
precision the solvation free energies of charged particles of Lennard-Jones
plus Coulomb functional form. We also compute entropy, enthalpy, and radial
distribution functions of unsampled parameter combinations using only the data
from these sampled states and use the free energies estimates to examine the
deviation of simulations from the Born approximation to the solvation free
energy
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