Local Correlation Approach Research Articles

Extracting depth information from stereo images using a fast correlation matching algorithm

ABSTRACT Stereo matching algorithms are essential for recovering depth information of objects in many computer vision applications including 3D reconstruction, robot navigation, autonomous driving and so on. Most of the stereo algorithms generally rely on two types of matching technique: global and local matching. The state-of-the-art stereo algorithms that measure disparity or depth with high accuracy are generally based on global methods. However, they are not suitable for real-time applications because of high computational costs. The local algorithms, on the other hand, are very fast but they provide less computational accuracy compared to the global methods. To make a tradeoff between computation speed and accuracy, this paper proposes an efficient local correlation approach for depth estimation using a pruning proposal. This paper also evaluates the performance of different matching cost functions/algorithms for disparity or dense estimation. Experimental evaluation confirms that our proposed pruning method for point correspondence is able to achieve a significant accuracy with high computational speed that can be very useful for real-time environments.

Cover Image, Volume 8, Issue 4

The cover image, by Denis Usvyat et al., is based on the Advanced Review Periodic and fragment models based on the local correlation approach, DOI: 10.1002/wcms.1357. image

Periodic and fragment models based on the local correlation approach

A rigorous treatment of dynamical electron correlation in crystalline solids is one of the main challenges in today's materials quantum chemistry and theoretical solid state physics. In this study, we address this problem by using the local correlation approach and exploring a variety of methods, ranging from the full periodic treatment through embedded fragments to finite clusters. Apart from the computational advantages, the direct‐space local representation for the occupied space allows one to partition the system into fragments and thus forms a natural basis for a hierarchy of embedding models. Furthermore, a subset of localized orbitals in a cluster or a fragment can be chosen to mimic the unit cell of the reference periodic system. Introduction of such subsets allows one to define a formal quantity “the correlation energy per unit cell”, which is directly related to the correlation energy per unit cell in the crystal. The orbital pairs, where neither of the two localized orbital indices belongs to the “unit cell” do not explicitly contribute to the “energy per cell”: Their role is to provide correlated embedding via the couplings in the amplitude equations. The periodic, fragment and finite‐cluster approaches can be combined in a form of high precision computational protocols, where progressively higher‐level corrections are evaluated using lower‐level embedding models. We apply these techniques to investigate the importance of Coulomb screening in dispersively interacting systems on the examples of the phosphorene bilayer and the adsorption of water on 2D silica.This article is categorized under: Structure and Mechanism > Computational Materials Science Electronic Structure Theory > Ab Initio Electronic Structure Methods Software > Quantum Chemistry

Oil and stock markets before and after financial crises: A local Gaussian correlation approach

The effect of financial shocks on the cross‐market linkages between oil prices (spot and futures) and stock markets is examined for four major crises. We employ the local Gaussian correlation approach and find that the two markets were regionalized for most of the 1990s and the early 2000s. Flights from stocks to oil occur in all crisis episodes, except the recent global financial crisis. The view that stock and oil markets behave like “a market of one” after the financialization of commodities is further supported by the presence of contagion between US stock markets and all the benchmark oil markets.

LOCAL CORRELATIONS BETWEEN PRICING DEVIATION AND MARKET PROXY OF BRAZILIAN ETFs

The Exchange Traded Funds (ETFs) have become a wide-spread investment vehicle with unique characteristics that have not been sufficiently studied yet, especially when it comes to emerging markets ETFs. Moreover, consolidated asset pricing models are not enough to analyze the dynamics of a kind of fund that adds a different dimension in relation to conventional investment funds: the variation of share prices. The difference between share prices and their net asset values (NAVs) is called pricing deviation. The goal of this paper is to verify if Brazilian ETFs pricing deviation depends on market returns and if this relationship presents differences according to market situations, before and after the European debt crisis. With the local correlation approach, our results pointed to the fact that the correlation between pricing deviation and the market return is much higher in extreme points and it becomes even higher after the beginning of the Eurozone debt crisis.

Improved cluster-in-molecule local correlation approach for electron correlation calculation of large systems.

An improved cluster-in-molecule (CIM) local correlation approach is developed to allow electron correlation calculations of large systems more accurate and faster. We have proposed a refined strategy of constructing virtual LMOs of various clusters, which is suitable for basis sets of various types. To recover medium-range electron correlation, which is important for quantitative descriptions of large systems, we find that a larger distance threshold (ξ) is necessary for highly accurate results. Our illustrative calculations show that the present CIM-MP2 (second-order Møller-Plesser perturbation theory, MP2) or CIM-CCSD (coupled cluster singles and doubles, CCSD) scheme with a suitable ξ value is capable of recovering more than 99.8% correlation energies for a wide range of systems at different basis sets. Furthermore, the present CIM-MP2 scheme can provide reliable relative energy differences as the conventional MP2 method for secondary structures of polypeptides.

Local Correlations Between Pricing Deviation and Market Proxy of Brazilian ETFs

The Exchange Traded Funds (ETFs) have become a wide-spread investment vehicle with unique characteristics that have not been sufficiently studied yet, especially when it comes to emerging markets ETFs. Moreover, consolidated asset pricing models are not enough to analyze the dynamics of a kind of fund that adds a different dimension in relation to conventional investment funds: the variation of share prices. The difference between share prices and their net asset values (NAVs) is called pricing deviation. The goal of this paper is to verify if Brazilian ETFs pricing deviation depends on market returns and if this relationship presents differences according to market situations, before and after the European debt crisis. With the local correlation approach, our results pointed to the fact that the correlation between pricing deviation and the market return is much higher in extreme points and it becomes even higher after the beginning of the Eurozone debt crisis.

A refined cluster-in-molecule local correlation approach for predicting the relative energies of large systems

A refined cluster-in-molecule (CIM) method for local correlation calculations of large molecules is presented. In the present work, two new strategies are introduced to further improve the CIM approach: (1) Some medium-range electron correlation energies, which are neglected in the previous CIM approach, are taken into account. (2) A much simpler procedure using only a distance threshold is used to construct various clusters. To cover the medium-range correlation effect as much as possible, some two-atom-centered clusters are built, in addition to one-atom-centered clusters. Our test calculations at the second order perturbation theory (MP2) level show that the refined CIM method can recover about 99.9% of the conventional MP2 correlation energy using an appropriate distance threshold. The accuracy of the present CIM method is capable of providing reliable relative energies of medium-sized systems such as polyalanines with 10 residues, and water molecules with 50 water molecules. For polyalanines with up to 30 residues, we have demonstrated that the computational cost of the CIM-MP2 calculation increases linearly with the molecular size, but the required memory and disc-space do not need to increase for large systems. The improved CIM method has been used to compute the relative energy of ice-like (H(2)O)(96) clusters (with 2400 basis functions) and to predict the dimerization energy of a double-helical foldamer (with 2330 basis functions). The present CIM method is expected to be a practical local correlation method for describing the relative energies of large systems.

PCCSD: Parameterized coupled-cluster theory with single and double excitations

The primary characteristics of single reference coupled-cluster (CC) theory are size-extensivity and size-consistency, invariance under orbital rotations of the occupied or virtual space, the exactness of CC theory for N electron systems when the cluster operator is truncated to N-tuple excitations, and the relative insensitivity of CC theory to the choice of the reference determinant. In this work, we propose a continuous class of methods which display the desirable features of the coupled-cluster approach with single and double excitations (CCSD). These methods are closely related to the CCSD method itself and are inspired by the coupled electron pair approximation (CEPA). It is demonstrated that one can systematically improve upon CCSD and obtain geometries, harmonic vibrational frequencies, and total energies from a parameterized version of CCSD or pCCSD(α,β) by selecting a specific member from this continuous family of approaches. In particular, one finds that one such approach, the pCCSD(-1,1) method, is a significant improvement over CCSD for the calculation of equilibrium structures and harmonic frequencies. Moreover, this method behaves surprisingly well in the calculation of potential energy surfaces for single bond dissociation. It appears that this methodology has significant promise for chemical applications and may be particularly useful in applications to larger molecules within the framework of a high accuracy local correlation approach.

Non-covalent interactions using local correlation methods: energy partitioning, geometry optimisation and harmonic frequency calculations

The performance of density fitting, local correlation methods (DF-LMP2 and DF-LCCSD) in studies of non-covalent interactions is tested against literature data for a standard set of 22 inter-molecular complexes. Partitioning of interaction energy in the local correlation approach, based on the classes of occupied and virtual orbital involved in the interaction, clearly distinguishes the three types of interaction present in the set of complexes, in agreement with previous classifications. Geometry optimisation is found to be straightforward with DF-LMP2 without the need for counterpoise correction, resulting in geometries very close to previous, counterpoise-corrected structures. Spin-component scaling of gradients to correct for the known shortcomings of conventional MP2 has only a small effect on geometries in most cases, but significantly alters the distance between aromatic rings in stacked complexes. Harmonic frequency calculation is made possible by efficient use of parallel computing resources, and confirms all structures to be true minima, unlike previous estimates using density functional theory. Corrections for the change in zero-point vibrational energy are determined from this data, and typically constitute between 10 and 50% of the overall binding energy of the complex.

Local correlation calculations using standard and renormalized coupled-cluster approaches

The linear scaling local correlation approach, termed "cluster-in-molecule" (CIM), is extended to the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and noniterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the system size, (ii) the use of orthonormal orbitals in the CC subsystem calculations, (iii) the natural parallelism, (iv) the high computational efficiency, enabling calculations for much larger systems and at higher levels of CC theory than previously possible, and (v) the purely noniterative character of local triples corrections. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is shown that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches accurately reproduce the corresponding canonical CC correlation and relative energies, while offering savings in the computer effort by orders of magnitude.

A local-MP2 approach to the ab initio study of electron correlation in crystals and to the simulation of vibrational spectra: the case of Ice XI

Wave-function-based computational techniques for describing electron correlation effects in periodic systems have a long history. Among early attempts, the method proposed by Colle and Salvetti (Theor Chim Acta 37:329, 1975) more than 30 years ago is noteworthy for its simplicity, power, and far-reaching consequences. The renewed interest in this topic is due to the well-known failure of techniques based on Density Functional Theory when it comes to obtaining very accurate estimates of some important quantities. Here we present the essential features of an ab initio code, (CRYSCOR) recently implemented (Phys Rev B 76: 075101, 075102, 2007), which solves the MP2 equations for crystals by adopting a local-correlation approach and using as a reference the Hartree-Fock solution provided by the CRYSTAL program. As an example of application, we discuss the MP2 corrections to the frequency of some vibrational modes in a proton-ordered structure of water ice (Ice XI).

Periodic density functional theory and local-MP2 study of the librational modes of Ice XI

Two periodic codes, CRYSTAL and CRYSCOR, are here used to simulate and characterize the librational modes of the nu(R) band of Ice XI: this band has been found experimentally to be the region of the vibrational spectrum of ordinary ice most affected by the transition from the proton-disordered (Ice Ih) to the proton-ordered (Ice XI) phase. With CRYSTAL, the problem is solved using Hartree-Fock (HF), pure Kohn-Sham (PW91) or hybrid (B3LYP) one-electron Hamiltonians: the harmonic approximation is employed to obtain the vibrational spectrum after optimizing the geometry. The B3LYP results are those in best agreement with the experiment. For a given crystalline geometry, CRYSCOR computes the energy per cell in an ab initio HF+MP2 approximation using a local-correlation approach; this technique is employed for recalculating the frequencies of the different modes identified by the B3LYP approach, by fully accounting for long range dispersive interactions. The effect of anharmonicity is evaluated separately for each mode both in the B3LYP and HF+MP2 case. The two approaches accurately reproduce the four-peak structure of the librational band. The harmonic B3LYP nu(R) bandwidth of 70 meV is lowered to 60 meV by anharmonic corrections, and becomes 57 meV in the HF+MP2 anharmonic calculation, in excellent agreement with the experimental IINS data (56-59 meV). The assignment of the librational modes is discussed.

DFT and Local-MP2 Periodic Study of the Structure and Stability of Two Proton-Ordered Polymorphs of Ice

The equilibrium geometry and the formation energy of two periodic polymorphs of Ice have been theoretically studied: the former (Ice XI, crystal group Cmc2(1)) is experimentally observed as the most stable structure at low temperature and pressure; the latter (crystal group Pna2(1)) is the simplest proton-ordered model of ordinary ice. With the Crystal code, the problem is solved using Hartree-Fock (HF), pure Kohn-Sham (PW91), or hybrid (B3LYP) one-electron Hamiltonians. The B3LYP results are those in best agreement with the experiment. Using the B3LYP-optimized geometry and starting from the corresponding HF Crystal solution, the energetics of the two polymorphs have been investigated at an ab initio MP2 level using the Cryscor code, based on a local-correlation approach: these calculations have allowed us not only to confirm the excellent B3LYP results as concerns the formation energy and the relative stability of the two structures but also to analyze the role in this respect of the intra- and intermolecular contributions to the correlation energy. Since both Crystal and Cryscor adopt a basis set of localized Gaussian-type functions and since very small energy differences are involved, utter attention has been paid to correcting for the basis set superposition error in the calculation of formation energies.

Periodic local-MP2 computational study of crystalline neon

Face-centered-cubic crystalline Neon is taken as a test system to explore the influence of computational parameters on the quality of the MP2 solution provided by the Cryscor program using a local-correlation approach. The effect of the various approximations adopted is analyzed: basis set limitations, finite size of excitation domains, truncation of the tails of the local functions, approximate evaluation of two-electron integrals, estimate (by extrapolation) of long-range contributions are shown to play roles of different importance. The Ne2 dimer is used as an auxiliary test case in order to allow comparison with recent and accurate literature data.

Periodic local MP2 method for the study of electronic correlation in crystals: Theory and preliminary applications

A computational technique for solving the MP2 equations for periodic systems using a local-correlation approach and implemented in the CRYSCOR code is presented. The Hartree-Fock solution provided by the CRYSTAL program is used as a reference. The motivations for the implementation of the new code are discussed, and the techniques adopted are briefly recalled. With respect to the original formulation (Pisani et al., J Chem Phys 2005, 122, 094113), many new features have been introduced in CRYSCOR to improve its efficiency and robustness. In particular, an adaptation of the density fitting scheme to translationally periodic systems is described, based on Fourier transformation techniques. Three examples of application are provided, concerning the CO(2) crystal, proton transfer in ice XI, and the adsorption of methane on MgO (001). The results obtained with the periodic LMP2 method for these systems appear more reliable than the ones obtained using density functional theory.

Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms

When solving the M\o{}ller-Plesset second order perturbation theory (MP2) equations for periodic systems using a local-correlation approach [J. Chem. Phys. 122 (2005) 094113], the computational bottleneck is represented by the evaluation of the two-electron Coulomb interaction integrals between product distributions, each involving a Wannier function and a projected atomic orbital. While for distant product distributions a multipolar approximation performs very efficiently, the four index transformation for close-by distributions, which by far constitutes the bottleneck of correlated electronic structure calculations of crystals, can be avoided through the use of density fitting techniques. An adaptation of that scheme to translationally periodic systems is described, based on Fourier transformation techniques. The formulas and algorithms adopted allow the point symmetry of the crystal to be exploited. Problems related to the possible divergency of lattice sums of integrals involving fitting functions are identified and eliminated through the use of Poisson transformed fitting functions and of dipole-corrected product distributions. The iterative scheme for solving the linear local MP2 (LMP2) equations is revisited. Prescreening in the evaluation of the residual matrix is introduced, which significantly lowers the scaling of the LMP2 equations.

On the Prospective Use of the One-Electron Density Matrix as a Test of the Quality of Post-Hartree–Fock Schemes for Crystals

It is argued that experimental determinations of the one-electron density matrix of crystalline systems, γ 1 (r,r'), based on directional Compton profiles and X-ray structure factors could be useful to assess the quality of computational techniques which take electron correlation effects into account. A scheme is here outlined for evaluating the correlation correction to the Hartree-Fock one-electron density, starting from the solution obtained for the periodic system at a perturbative MPn level. The case of crystalline lithium hydride is discussed. Preliminary MP2 results for that system are presented, obtained using a local-correlation approach.

Divide-and-conquer local correlation approach to the correlation energy of large molecules.

A divide-and-conquer local correlation approach for correlation energy calculations on large molecules is proposed for any post-Hartree-Fock correlation method. The main idea of this approach is to decompose a large system into various fragments capped by their local environments. The total correlation energy of the whole system can be approximately obtained as the summation of correlation energies from all capped fragments, from which correlation energies from all adjacent caps are removed. This approach computationally achieves linear scaling even for medium-sized systems. Our test calculations for a wide range of molecules using the 6-31G or 6-31G( * *) basis set demonstrate that this simple approach recovers more than 99.0% of the conventional second-order Moller-Plesset perturbation theory and coupled cluster with single and double excitations correlation energies.

Linear scaling local correlation approach for solving the coupled cluster equations of large systems.

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.