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Moment-based approaches in imaging part 3: computational considerations [A Look at...]

Huazhong Shu, Limin Luo, J.-L. Coatrieux
2008 IEEE Engineering in Medicine and Biology Magazine  
This issue is also of concern for moments in particular when high orders have to be computed. Special attention must therefore be paid to fast computation.  ...  The problem of accurate computation of moments should thus be addressed. These two aspects are examined in this third paper.  ...  Because the problem of fast computation of the geometric moments has been extensively investigated, one way for efficiently computing other kinds of moments such as Legendre and Zernike moments is to express  ... 
doi:10.1109/memb.2008.918690 pmid:18519189 pmcid:PMC2527213 fatcat:6tkun5m3ybeo7ibyctyoua5kzm

Toward affine recognition of handwritten mathematical characters

Oleg Golubitsky, Vadim Mazalov, Stephen M. Watt
2010 Proceedings of the 8th IAPR International Workshop on Document Analysis Systems - DAS '10  
We present a distance-based classification method, in which feature vectors are constructed from Legendre-Sobolev expansions of the coordinate functions and of the affine integral invariants of the curves  ...  We address the problem of handwritten symbol classification in the presence of distortions modeled by affine transformations.  ...  Out of an infinite family of such invariants, a subfamily was chosen that is fast to compute, numerically stable and sufficiently discriminating.  ... 
doi:10.1145/1815330.1815335 dblp:conf/das/GolubitskyMW10 fatcat:q552jkxlr5eytbdhesubzxq2wu

Efficient isoparametric integration over arbitrary space-filling Voronoi polyhedra for electronic structure calculations

Aftab Alam, S. N. Khan, Brian G. Wilson, D. D. Johnson
2011 Physical Review B  
We combine a weighted Voronoi tessellation with isoparametric integration via Gauss-Legendre quadratures to provide rapidly convergent VP integrals for a variety of integrands, including those with a Coulomb  ...  A numerically efficient, accurate, and easily implemented integration scheme over convex Voronoi polyhedra (VP) is presented for use in ab-initio electronic-structure calculations.  ...  Department of Energy BES/Materials Science and Engineering Division from contracts with Illinois (DEFG02-03ER46026), Ames Laboratory (DE-AC02-07CH11358), operated by Iowa State University, and Lawrence  ... 
doi:10.1103/physrevb.84.045105 fatcat:uxq7wkaujvftlh2rshqlvhxqde

Product Gauss cubature over polygons based on Green's integration formula

A. Sommariva, M. Vianello
2007 BIT Numerical Mathematics  
It does not need any preprocessing like triangulation of the domain, but relies directly on univariate Gauss-Legendre quadrature via Green's integral formula.  ...  The formula is exact for polynomials of degree at most 2n − 1 using N ∼ mn 2 nodes, m being the number of sides that are not orthogonal to a given line, and not lying on it.  ...  The literature on cubature over polygons is not very wide, despite the fact that polygons (and polyhedra) are at the core of computational geometry.  ... 
doi:10.1007/s10543-007-0131-2 fatcat:kdwfwrllyzewfp2z3auyy2m2by

The influence of a protein on water dynamics in its vicinity investigated by molecular dynamics simulation

Roger Abseher, Hellfried Schreiber, Othmar Steinhauser
1996 Proteins: Structure, Function, and Bioinformatics  
Using Voronoi polyhedra, the solvent has been divided into three subsets, i.e., the first and second hydration shell, and the remaining bulk, which is hardly affected by the protein.  ...  In other words, the functional form of the distributions of singlemolecule rotational correlation times is not subject to a temperature effect.  ...  The first Legendre polynomial of the dipole moment of the water molecule is the essential quantity of infrared spectroscopy.  ... 
doi:10.1002/(sici)1097-0134(199607)25:3<366::aid-prot8>3.0.co;2-d pmid:8844871 fatcat:q2tgqsuawbby5iu5frqf4ezyhy

Polarizability of a dielectric hemisphere

Henrik Kettunen, Henrik Wallén, Ari Sihvola
2007 Journal of Applied Physics  
The polarizability of a hemisphere depends on the direction of the exciting electric field.  ...  object as a function of its relative electric permittivity.  ...  It is defined as the ratio of the dipole moment and the magnitude of the incident field, p = ␣E e , ͑1͒ where E e is the uniform external field and p is the induced dipole moment.  ... 
doi:10.1063/1.2769288 fatcat:jusu2qg43nfozbqamtok6z6oom

Polynomial approximation in handwriting recognition

Stephen M. Watt
2011 Proceedings of the 2011 International Workshop on Symbolic-Numeric Computation - SNC '11  
Many useful properties are obtained in this representation, allowing fast recognition based on small training sets.  ...  The beauty of this framework is that a single, coherent view leads to highly efficient methods with a high recognition rate.  ...  It was then shown that a Legendre polynomial basis allowed the coefficients to be calculated instantly on pen-up from moments of x(λ) and y(λ) integrated as the curve is written [4] .  ... 
doi:10.1145/2331684.2331687 dblp:conf/snc/Watt11 fatcat:yrnnivrt3jf3bfm5rmgyqqngjm

What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

Yves Lucet
2010 SIAM Review  
the equivalent of the Fast Fourier Transform), multi-fractal analysis, etc.  ...  To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis.  ...  The paper was initially announced as a companion paper of [163] under the title Fast Moreau Envelope Computation II: Applications.  ... 
doi:10.1137/100788458 fatcat:es26qkvsebh5lkiafnnqkb3h34

What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

Yves Lucet
2009 SIAM Journal on Optimization  
the equivalent of the Fast Fourier Transform), multi-fractal analysis, etc.  ...  To further communications between practitioners, we review the field of Computational Convex Analysis, which focuses on the numerical computation of fundamental transforms arising from convex analysis.  ...  The paper was initially announced as a companion paper of [163] under the title Fast Moreau Envelope Computation II: Applications.  ... 
doi:10.1137/080719613 fatcat:htdlaubydjf3xez3s7h2ovbko4

Fourier, Legendre and Jacobi

Jean-Pierre Kahane
2011 Journal of the Egyptian Mathematical Society  
It was not for long, as we shall see in a moment. The second episode took place in 1815.  ...  Nowadays his name is everywhere in the scientific literature, in the form of Fourier series, Fourier integrals, Fast Fourier transforms, Fourier analysis, that is, the part of his work that was considered  ... 
doi:10.1016/j.joems.2011.08.001 fatcat:ndmephb3i5fvtnbdx3wxyqdomu

Smoothed corners and scattered waves [article]

Charles L. Epstein, Michael O'Neil
2016 arXiv   pre-print
We introduce an arbitrary order, computationally efficient method to smooth corners on curves in the plane, as well as edges and vertices on surfaces in R^3.  ...  We observe that significant reductions in computational cost can be obtained if merely approximate solutions are desired in the near- or far-field.  ...  As this class of polyhedra can be smoothed by smoothing only edges, we take a moment to describe the procedure.  ... 
arXiv:1506.08449v2 fatcat:yexlwec3grg4fl457ybm74xnf4

Polyhedra in loop quantum gravity

Eugenio Bianchi, Pietro Doná, Simone Speziale
2011 Physical Review D  
In particular, coherent spin-network states with nodes of arbitrary valence represent a collection of semiclassical polyhedra.  ...  Moreover, coherent intertwiners result to be peaked on the classical geometry of polyhedra. We discuss the relevance of this result for loop quantum gravity.  ...  The work of S.S. is partially supported by the ANR "Programme Blanc" grant LQG-09.  ... 
doi:10.1103/physrevd.83.044035 fatcat:gko3mkkb7bhuzpbkfkuoa646rm

On the uncertainty quantification of the unsteady aerodynamics of 2D free falling plates

N. Zorzi, J. M. C. Pereira, J. C. F. Pereira
2015 Theoretical and Computational Fluid Dynamics  
The free fall of two-dimensional cards immersed in a fluid was studied using a deterministic and stochastic numerical approach.  ...  The analysis was focused on finding the ensemble mean trajectory and error bar for a confidence interval of 95% for both tumbling and fluttering regimes.  ...  the resultant moment acting on the body (due to fluid forces) and I is the tensor of the moments of inertia.  ... 
doi:10.1007/s00162-015-0360-y fatcat:x35fnb2knvevnktzcrmtpv3jge

Adaptively Weighted Numerical Integration in the Finite Cell Method

Vaidyanathan Thiagarajan, Vadim Shapiro
2016 Computer Methods in Applied Mechanics and Engineering  
With Adaptively Weighted (AW) numerical integration, for a given set of quadrature nodes, order and domain of integration, the quadrature weights are obtained by solving a system of suitable moment fitting  ...  The moments in the moment equations are approximated over a simplified domain that is homeomorphic to the original domain, and then are corrected for the deviation from the original domain using shape  ...  Acknowledgments This research was supported by the National Science Foundation grants CMMI-1344205 and CMMI-1361862 and the National Institute of Standards and Technology.  ... 
doi:10.1016/j.cma.2016.08.021 fatcat:ewbv6fjufze6notunlourpuzbq

Density functional theory and simulations of colloidal triangular prisms

Matthieu Marechal, Simone Dussi, Marjolein Dijkstra
2017 Journal of Chemical Physics  
Additionally, we perform Monte Carlo computer simulations and we employ a simpler Onsager theory with a Parsons-Lee correction.  ...  Here we consider rod-like triangular prisms to gauge the effect of the cross section of the rods on liquid crystal phase behavior.  ...  Subsequently, particle-resolved computer simulations improve on these predictions at the cost of a greater computational effort.  ... 
doi:10.1063/1.4978502 pmid:28388166 fatcat:riop2w22ojgvfdwwhaacmtipom
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