Minimization Of Energy Function Research Articles

Iterative Point Matching via multi-direction geometric serialization and reliable correspondence selection

Point matching aims at finding the optimal matching between two sets of feature points. It is widely accomplished by graph matching methods which match nodes of graphs via minimizing energy functions. However, the obtained correspondences between feature points vary in their matching qualities. In this paper, we propose an innovative matching algorithm which iteratively improves the matching found by such methods. The intuition is that we may improve a given matching by identifying “reliable” correspondences, and re-matching the rest feature points without reliable correspondences. A critical issue here is how to identify reliable correspondences, which is addressed with two novel mechanisms, Multi-direction Geometric Serialization (MGS) and Reliable Correspondence Selection (RCS). Specifically, MGS provides representations of the spatial relations among feature points. With these representations, RCS determines whether a correspondence is reliable according to a reliability metric. By recursively applying MGS and RCS, and re-matching feature points without reliable correspondences, a new (intermediate) matching can be obtained. In this manner, our algorithm starts with a matching provided by a classical method, iteratively generates a number of intermediate matchings, and chooses the best one as the final matching. Experiments demonstrate that our algorithm significantly improves the matching precisions of classical graph matching methods.

Solving Unit Commitment Problem Employing Proposed Hybrid BBO-discrete Hopfield Neural Network

A novel hybrid approach is developed based on the hybridization of Biogeography Based Optimization and Discrete Hopfield Neural Network. BBO algorithm is employed to tune for the optimal weights of discrete Hopfield Neural Network leading to the minimization of energy function. The proposed hybrid BBO-DHNN is implemented for 10, 20, 40 and 60 units power system under consideration. Based on the simulation results presented, it is clearly noted that the proposed HBDHNN approach results in better solutions for the unit commitment problem considered and this in turn reduces the computational burden to a significant extent. The proposed approaches are developed in MATLAB environment version 7.8.0.347 and executed in a PC with Intel core 2 Duo processor with 2.27 GHz speed and 2 GB RAM with 64 bit operating system.

A new technique for numerical simulation of dendritic solidification using a meshfree interface finite element method

SummaryA new technique for sharp‐interface modeling of dendritic solidification is proposed using a meshfree interface finite element method such that the liquid–solid interface is represented implicitly and allowed to arbitrarily intersect the finite elements. At the interface‐embedded elements, meshfree interface points without connectivity are imposed directly at the zero level set while meshfree interpolants are constructed using radial basis functions. This ensures both the partition of unity and the Kronecker delta properties are satisfied allowing for precise and easy imposition of Dirichlet boundary conditions at the interface. The constructed meshfree interpolants are also used for solving a variational level set equation based on the Ginzburg–Landau energy functional minimization such that reinitialization is completely eliminated and fast marching algorithms for interfacial velocity extension are not necessary resulting in an efficient algorithm with excellent volume conservation. The meshfree interface finite element method is used for modeling dendritic solidification in a pure melt where it is found suitable in handling the complex interfacial dynamics often encountered in dendritic growth. Mathematical formulation and implementation followed by numerical results and analysis will be presented and discussed. Copyright © 2016 John Wiley & Sons, Ltd.

A New Approach for Robust Segmentation of the Noisy or Textured Images

Segmentation of noisy or textured images remains challenging in both accuracy and computational efficiency. In this paper, we propose a new approach for segmentation of noisy or textured images that exist widely in real life. The proposed approach finds the mean values of different pixel classes more efficiently and accurately than the benchmark expectation maximization (EM) and K-means methods. With these mean values, the segmentation is achieved by clustering the pixels to its nearest mean. When too much noise is left for the presegmentation result or when textured objects are involved, we propose transforming the density distribution of labeled pixels into grayscale distribution by down-sampling the image with a bicubic function. An optimal threshold is automatically selected from the slope difference distribution of the histogram for the final segmentation. The extracted boundary is then refined by an energy minimization function with the detected edges when enough clear edges can be obtained. A large...

Predicting RNA-RNA Interactions Using RNAstructure.

RNA-RNA binding is a required step for many regulatory and catalytic processes in the cell. Identifying RNA-RNA hybridization sites is challenging because of the competition between intramolecular and intermolecular structure formation. A complete picture of RNA-RNA binding includes an understanding of single-stranded folding and binding site accessibility, and is strongly concentration-dependent. This chapter provides guidance for using RNAstructure to predict RNA-RNA binding sites and RNA-RNA structures, utilizing free energy minimization and partition function calculations. RNAstructure is freely available at http://rna.urmc.rochester.edu/RNAstructure.html .

Multi-Target Tracking by Discrete-Continuous Energy Minimization.

The task of tracking multiple targets is often addressed with the so-called tracking-by-detection paradigm, where the first step is to obtain a set of target hypotheses for each frame independently. Tracking can then be regarded as solving two separate, but tightly coupled problems. The first is to carry out data association, i.e., to determine the origin of each of the available observations. The second problem is to reconstruct the actual trajectories that describe the spatio-temporal motion pattern of each individual target. The former is inherently a discrete problem, while the latter should intuitively be modeled in continuous space. Having to deal with an unknown number of targets, complex dependencies, and physical constraints, both are challenging tasks on their own and thus most previous work focuses on one of these subproblems. Here, we present a multi-target tracking approach that explicitly models both tasks as minimization of a unified discrete-continuous energy function. Trajectory properties are captured through global label costs, a recent concept from multi-model fitting, which we introduce to tracking. Specifically, label costs describe physical properties of individual tracks, e.g., linear and angular dynamics, or entry and exit points. We further introduce pairwise label costs to describe mutual interactions between targets in order to avoid collisions. By choosing appropriate forms for the individual energy components, powerful discrete optimization techniques can be leveraged to address data association, while the shapes of individual trajectories are updated by gradient-based continuous energy minimization. The proposed method achieves state-of-the-art results on diverse benchmark sequences.

New Real-Coded Genetic Algorithm Operators for Minimization of Molecular Potential Energy Function

The global minimum of the potential energy of a molecule corresponds to its most stable conformation and it dictates most of its properties. Due to the extensive search space and the massive number of local minima that propagate exponentially with molecular size, determining the global minimum of a potential energy function could prove to be significantly challenging. This study demonstrates the application of newly designed real-coded genetic algorithm (RCGA) called RX-STPM, which incorporates the use of Rayleigh crossover (RX) and scale-truncated Pareto mutator (STPM) as defined earlier for minimizing molecular potential energy functions. Computational results for problems with up to 100 degrees of freedom are compared with five other existing methods from the literature. The numerical results indicate the underlying reliability (robustness) and efficiency of the proposed approach compared to other existing algorithms with low computational costs.

Variational contrast enhancement guided by global and local contrast measurements for single-image defogging

The visibility of images captured in foggy conditions is impaired severely by a decrease in the contrasts of objects and veiling with a characteristic gray hue, which may limit the performance of visual applications out of doors. Contrast enhancement together with color restoration is a challenging mission for conventional fog-removal methods, as the degrading effect of fog is largely dependent on scene depth information. Nowadays, people change their minds by establishing a variational framework for contrast enhancement based on a physically based analytical model, unexpectedly resulting in color distortion, dark-patch distortion, or fuzzy features of local regions. Unlike previous work, our method treats an atmospheric veil as a scattering disturbance and formulates a foggy image as an energy functional minimization to estimate direct attenuation, originating from the work of image denoising. In addition to a global contrast measurement based on a total variation norm, an additional local measurement is designed in that optimal problem for the purpose of digging out more local details as well as suppressing dark-patch distortion. Moreover, we estimate the airlight precisely by maximization with a geometric constraint and a natural image prior in order to protect the faithfulness of the scene color. With the estimated direct attenuation and airlight, the fog-free image can be restored. Finally, our method is tested on several benchmark and realistic images evaluated by two assessment approaches. The experimental results imply that our proposed method works well compared with the state-of-the-art defogging methods.

Partial regularity for minimizers of singular energy functionals, with application to liquid crystal models

where F is quasiconvex in the gradient variables and the convex function f blows up to infinity at the boundary of a given bounded open set K ⊂ R . As we will explain later in Section 5, this sort of energy functional arises in some recently proposed models in nematic liquid crystal theory. We assume hereafter that U ⊂ R is bounded smooth domain and that K is a bounded, open convex subset of R. Our assumptions are these: (H1) Hypotheses on f : The given function f : R → [0,∞] is nonnegative, convex and smooth on K ⊂ R. We will write f = f(z). We further require that

A strongly convergent primal–dual method for nonoverlapping domain decomposition

We propose a primal---dual parallel proximal splitting method for solving domain decomposition problems for partial differential equations. The problem is formulated via minimization of energy functions on the subdomains with coupling constraints which model various properties of the solution at the interfaces. The proposed method can handle a wide range of linear and nonlinear problems, with flexible, possibly nonlinear, transmission conditions across the interfaces. Strong convergence in the energy spaces is established in this general setting, and without any additional assumption on the energy functions or the geometry of the problem. Several examples are presented.

Constraint minimizers of mass critical Hartree energy functionals: Existence and mass concentration

We consider L2-constraint minimizers of mass critical Hartree energy functionals in ℝN with N ≥ 3. We prove that minimizers exist if and only if the parameter a > 0 satisfies a<a∗=Q22, where Q is a positive radially symmetric ground state of Δu−u+∫RNu(y)2x−y2dyu=0 in ℝN. The blow-up behavior of minimizers as a approaches a∗ is also analyzed, for which all the mass concentrates at a global minimum point x0 of the external potential V(x).

Study of capacity region and minimum energy of delay-tolerant unicast mobile ad hoc networks using cell-partitioned model

Capacity region and minimum energy function for a variety of delay-tolerant mobile unicast ad hoc networks are studied by using a cell-partitioned model. First, theorems about analytical expressions of network capacity and upper bound of minimum energy function are proposed and proved. Algorithm aiming at maximizing capacity and minimizing energy cost is presented and analyzed by Lyapunov drift method. Second, these two theorems are applied to several types of ad hoc networks. Expressions of network capacity and minimum energy function are obtained. Third, capacity property of a type of hybrid ad hoc networks is analyzed in detail. Relationship among limitation of capacity, node density, and coverage of base stations are investigated. Numerical analysis and simulation are carried out. Copyright © 2015 John Wiley & Sons, Ltd.

Depth-based computational photography

A depth-based computational photography model is proposed for all-in-focus image capture. A decomposition function, a defocus matrix, and a depth matrix are introduced to construct the photography model. The original image acquired from a camera can be decomposed into several sub-images on the basis of depth information. The defocus matrix can be deduced from the depth matrix according to the sensor defocus geometry for a thin lens model. And the depth matrix is reconstructed using the axial binocular stereo vision algorithm. This photography model adopts an energy functional minimization method to acquire the sharpest image pieces separately. The implementation of the photography method is described in detail. Experimental results for an actual scene demonstrate that our model is effective.

Modeling of Concrete Behavior under Compression

Formulation of the model suitable for the description of the full material deformation diagram is considered, with axial compression applied, and a loosening component added to elastic and plastic deformation. The materials involved are initially heterogeneous environments like rocks and artificial construction materials, like concrete. Such materials, being in a stationary state, stable for small disturbances, can be interpreted as dissipative structures after the limit of elasticity is reached. The deformation and destruction processes are analysed as instability hierarchy, resulting from self-organization. Methods of mathematical catastrophe theory are applied for the model construction. The energy state function is presented as the sum of the potential function, responsible for reversible deformations and disturbances. The latter involves an imperfection parameter (a controlling one), connected with damageability and responsible for the structurization process. The state equation is obtained by energy function minimization on the order parameter and is supplemented with the kinetic equation for the imperfection parameter. The synergetic methods are shown to be advantageous for the problems of formulating physically well-grounded nonlinear defining equations.

Assessment and Reduction of the Seismic Vulnerability of a Stone Masonry Vault

A numerical approach is presented to assess the seismic vulnerability of barrel masonry vaults and evaluate the eectiveness of a traditional retrofitting intervention consisting in the reinforcement of the extrados. A linear elastic no–tension model is adopted to cope with the negligible strength in tension of ancient brick and stone masonry and perform a two–dimensional finite element analysis of arch–like sections. Instead of implementing conventional load history analysis or limit load analysis, the minimization of the relevant strain energy function is implemented to solve the non–linear equilibrium under the effect of dierent load scenarios. A segmental barrel vault made of stone masonry is investigated in an ancient building under static and seismic loads. The collapse load of the structural element is computed before and after the intervention and the reduction achieved in terms of seismic vulnerability is evaluated as prescribed by technical codes.

Weld Inspection Based on Radiography Image Segmentation with Level Set Active Contour Guided Off-Center Saliency Map

Radiography is one of the most used techniques in weld defect inspection. Weld defect detection becomes a complex task when uneven illumination and low contrast characterize radiographic images. In this paper we propose a new active contour based level set method for weld defect detection in radiography images. An off-center saliency map exploited as a feature to represent image pixels is embedded into a region energy minimization function to guide the level set active contour to defects boundaries. The aim behind using salient feature is that a small defect can frequently attract attention of human eyes which permits enhancing defects in low contrasted image. Experiment results on different weld radiographic images with various kinds of defects show robustness and good performance of the proposed approach comparing with other segmentation methods.

An active contour model based on fused texture features for image segmentation

Texture image segmentation plays an important role in various computer vision tasks. In this paper, a convex texture image segmentation model is proposed. First, the texture features of Gabor and GLCM (gray level co-occurrence matrix) are extracted for original image. Then, the two kinds of texture features are fused together to effectively construct a discriminative feature space by concatenating with each other. In the image segmentation step, a convex energy function is defined by taking the non-convex vector-valued model of Active Contour without Edges (ACWE) into a global minimization framework (GMAC). The proposed global minimization energy function with fused textures (GMFT) can avoid the existence of local minima in the minimization of the vector-valued ACWE model. In addition, a fast dual formulation is adopted to achieve the efficient contour evolution. The experimental results on synthetic and natural animal images demonstrate that the proposed GMFT model obtains more satisfactory segmentation results compared to two state-of-the-art methods in terms of segmentation accuracy and efficiency.

Model-based graph-cut method for automatic flower segmentation with spatial constraints

In this paper, we present an accelerated system for segmenting flower images based on graph-cut technique which formulates the segmentation problem as an energy function minimization. The contribution of this paper consists to propose an improvement of the classical used energy function, which is composed of a data-consistent term and a boundary term. For this, we integrate an additional data-consistent term based on the spatial prior and we add gradient information in the boundary term. Then, we propose an automated coarse-to-fine segmentation method composed mainly of two levels: coarse segmentation and fine segmentation. First, the coarse segmentation level is based on minimizing the proposed energy function. Then, the fine segmentation is done by optimizing the energy function through the standard graph-cut technique. Experiments were performed on a subset of Oxford flower database and the obtained results are compared to the reimplemented method of Nilsback et al. [1]. The evaluation shows that our method consumes less CPU time and it has a satisfactory accuracy compared with the mentioned method above [1].

Multi-classification of cell deformation based on object alignment and run length statistic.

Cellular morphology is widely applied in digital pathology and is essential for improving our understanding of the basic physiological processes of organisms. One of the main issues of application is to develop efficient methods for cell deformation measurement. We propose an innovative indirect approach to analyze dynamic cell morphology in image sequences. The proposed approach considers both the cellular shape change and cytoplasm variation, and takes each frame in the image sequence into account. The cell deformation is measured by the minimum energy function of object alignment, which is invariant to object pose. Then an indirect analysis strategy is employed to overcome the limitation of gradual deformation by run length statistic. We demonstrate the power of the proposed approach with one application: multi-classification of cell deformation. Experimental results show that the proposed method is sensitive to the morphology variation and performs better than standard shape representation methods.

Incremental variational approach for time dependent deformation in clayey rock

An extension of Lahellec (2007) incremental variational approach to geomaterials is proposed. By using an implicit time-discretization scheme, the evolution equations describing the small strains constitutive behavior of the phases can be reduced to the minimization of an incremental energy function. This minimization problem is rigorously equivalent to a nonlinear thermoelastic problem with a transformation strain that is a heterogeneous field. The new approach proposed is for Callovo-Oxfordian argillites and considers the specific properties of geomaterials such as compressibility-dilatancy transition and influence of confining pressure. An isotropic, kinematic hardening effect is also considered for the more general cases. The accuracy of the model is assessed by comparison with FE and experimental results.