maximally random jammed packings of platonic solids hyperuniform long range correlations and isostaticity we generate maximally random jammed mrj packings of the four nontiling platonic solids tetrahedra octahedra dodecahedra and icosahedra using the adaptive shrinking cell method s torquato and y jiao phys rev e 80 041104 2009 such packings can be viewed as prototypical glasses in that they are maximally disordered while simultaneously being mechanically rigid the mrj packing fractions for tetrahedra octahedra dodecahedra and icosahedra are respectively 0 763 0 005 0 697 0 005 0 716 0 002 and 0 707 0 002 we find that as the number of facets of the particles increases the translational order in the packings increases while the orientational order decreases moreover we show that the mrj packings are hyperuniform i e their infinite wavelength local number density fluctuations vanish and possess quasi long range pair correlations that decay asymptotically with scaling r 4 this provides further evidence that hyperuniform quasi long range correlations are a universal feature of mrj packings of frictionless particles of general shape however unlike mrj packings of ellipsoids superballs and superellipsoids which are hypostatic mrj packings of the nontiling platonic solids are isostatic we provide a rationale for the organizing principle that the mrj packing fractions for nonspherical particles with sufficiently small asphericities exceed the corresponding value for spheres 0 64 we also discuss how the shape and symmetry of a polyhedron particle affects its mrj packing fraction

graph theoretical clustering based on limited neighbourhood sets abstract a method for clustering data according to a visual model of clusters is proposed the method uses either of two graphs which are defined according to relative distance and based on the gabriel graph and the relative neighbourhood graph respectively the method is locally sensitive hierarchic and based on the concept of limited neighbourhood sets clusters that are either disjoint or homogeneous and separable by sharp changes in point density may be detected

equations for the modular curve and models of elliptic curves with torsion points we describe an algorithm for constructing plane models of the modular curve x 1 n and discuss the resulting equations when n 51

automatic color constancy algorithm selection and combination in this work we investigate how illuminant estimation techniques can be improved taking into account intrinsic low level properties of the images we show how these properties can be used to drive given a set of illuminant estimation algorithms the selection of the best algorithm for a given image the algorithm selection is made by a decision forest composed of several trees on the basis of the values of a set of heterogeneous features the features represent the image content in terms of low level visual properties the trees are trained to select the algorithm that minimizes the expected error in illuminant estimation we also designed a combination strategy that estimates the illuminant as a weighted sum of the different algorithms estimations experimental results on the widely used ciurea and funt dataset demonstrate the effectiveness of our approach

reformulation of the covering and quantizer problems as ground states of interacting particles it is known that the sphere packing problem and the number variance problem closely related to an optimization problem in number theory can be posed as energy minimizations associated with an infinite number of point particles in d dimensional euclidean space r d interacting via certain repulsive pair potentials we reformulate the covering and quantizer problems as the determination of the ground states of interacting particles in r d that generally involve single body two body three body and higher body interactions this is done by linking the covering and quantizer problems to certain optimization problems involving the void nearest neighbor functions that arise in the theory of random media and statistical mechanics these reformulations which again exemplify the deep interplay between geometry and physics allow one now to employ theoretical and numerical optimization techniques to analyze and solve these energy minimization problems the covering and quantizer problems have relevance in numerous applications including wireless communication network layouts the search of high dimensional data parameter spaces stereotactic radiation therapy data compression digital communications meshing of space for numerical analysis and coding and cryptography among other examples in the first three space dimensions the best known solutions of the sphere packing and number variance problems or their dual solutions are directly related to those of the covering and quantizer problems but such relationships may or may not exist for d 4 depending on the peculiarities of the dimensions involved our reformulation sheds light on the reasons for these similarities and differences we also show that disordered saturated sphere packings provide relatively thin economical coverings and may yield thinner coverings than the best known lattice coverings in sufficiently large dimensions in the case of the quantizer problem we derive improved upper bounds on the quantizer error using sphere packing solutions which are generally substantially sharper than an existing upper bound in low to moderately large dimensions we also demonstrate that disordered saturated sphere packings yield relatively good quantizers finally we remark on possible applications of our results for the detection of gravitational waves

robust algorithm to generate a diverse class of dense disordered and ordered sphere packings via linear programming we have formulated the problem of generating dense packings of nonoverlapping nontiling nonspherical particles within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem called the adaptive shrinking cell asc formulation s torquato and y jiao phys rev e 80 041104 2009 because the objective function and impenetrability constraints can be exactly linearized for sphere packings with a size distribution in d dimensional euclidean space r d it is most suitable and natural to solve the corresponding asc optimization problem using sequential linear programming slp techniques we implement an slp solution to produce robustly a wide spectrum of jammed sphere packings in r d for d 2 3 4 5 and 6 with a diversity of disorder and densities up to the respective maximal densities a novel feature of this deterministic algorithm is that it can produce a broad range of inherent structures locally maximally dense and mechanically stable packings besides the usual disordered ones such as the maximally random jammed state with very small computational cost compared to that of the best known packing algorithms by tuning the radius of the influence sphere for example in three dimensions we show that it can produce with high probability a variety of strictly jammed packings with a packing density anywhere in the wide range 0 6 0 7408 where 18 0 7408 corresponds to the density of the densest packing we also apply the algorithm to generate various disordered packings as well as the maximally dense packings for d 2 4 5 and 6 our jammed sphere packings are characterized and compared to the corresponding packings generated by the well known lubachevsky stillinger ls molecular dynamics packing algorithm compared to the ls procedure our slp protocol is able to ensure that the final packings are truly jammed produces disordered jammed packings with anomalously low densities and is appreciably more robust and computationally faster at generating maximally dense packings especially as the space dimension increases

multigrid contact detection method contact detection is a general problem of many physical simulations this work presents a o n multigrid method for general contact detection problems mgcd the multigrid idea is integrated with contact detection problems both the time complexity and memory consumption of the mgcd are o n unlike other methods whose efficiencies are influenced strongly by the object size distribution the performance of mgcd is insensitive to the object size distribution we compare the mgcd with the no binary search nbs method and the multilevel boxing method in three dimensions for both time complexity and memory consumption for objects with similar size the mgcd is as good as the nbs method both of which outperform the multilevel boxing method regarding memory consumption for objects with diverse size the mgcd outperform both the nbs method and the multilevel boxing method we use the mgcd to solve the contact detection problem for a granular simulation system based on the discrete element method from this granular simulation we get the density property of monosize packing and binary packing with size ratio equal to 10 the packing density for monosize particles is 0 636 for binary packing with size ratio equal to 10 when the number of small particles is 300 times as the number of big particles the maximal packing density 0 824 is achieved

affinity learning with diffusion on tensor product graph in many applications we are given a finite set of data points sampled from a data manifold and represented as a graph with edge weights determined by pairwise similarities of the samples often the pairwise similarities which are also called affinities are unreliable due to noise or due to intrinsic difficulties in estimating similarity values of the samples as observed in several recent approaches more reliable similarities can be obtained if the original similarities are diffused in the context of other data points where the context of each point is a set of points most similar to it compared to the existing methods our approach differs in two main aspects first instead of diffusing the similarity information on the original graph we propose to utilize the tensor product graph tpg obtained by the tensor product of the original graph with itself since tpg takes into account higher order information it is not a surprise that we obtain more reliable similarities however it comes at the price of higher order computational complexity and storage requirement the key contribution of the proposed approach is that the information propagation on tpg can be computed with the same computational complexity and the same amount of storage as the propagation on the original graph we prove that a graph diffusion process on tpg is equivalent to a novel iterative algorithm on the original graph which is guaranteed to converge after its convergence we obtain new edge weights that can be interpreted as new learned affinities we stress that the affinities are learned in an unsupervised setting we illustrate the benefits of the proposed approach for data manifolds composed of shapes images and image patches on two very different tasks of image retrieval and image segmentation with learned affinities we achieve the bull s eye retrieval score of 99 99 percent on the mpeg 7 shape dataset which is much higher than the state of the art algorithms when the data points are image patches the ncut with the learned affinities not only significantly outperforms the ncut with the original affinities but it also outperforms state of the art image segmentation methods

color constancy by category correlation finding color representations that are stable to illuminant changes is still an open problem in computer vision until now most approaches have been based on physical constraints or statistical assumptions derived from the scene whereas very little attention has been paid to the effects that selected illuminants have on the final color image representation the novelty of this paper is to propose perceptual constraints that are computed on the corrected images we define the category hypothesis which weights the set of feasible illuminants according to their ability to map the corrected image onto specific colors here we choose these colors as the universal color categories related to basic linguistic terms which have been psychophysically measured these color categories encode natural color statistics and their relevance across different cultures is indicated by the fact that they have received a common color name from this category hypothesis we propose a fast implementation that allows the sampling of a large set of illuminants experiments prove that our method rivals current state of art performance without the need for training algorithmic parameters additionally the method can be used as a framework to insert top down information from other sources thus opening further research directions in solving for color constancy

distinctive features arising in maximally random jammed packings of superballs dense random packings of hard particles are useful models of granular media and are closely related to the structure of nonequilibrium low temperature amorphous phases of matter most work has been done for random jammed packings of spheres and it is only recently that corresponding packings of nonspherical particles e g ellipsoids have received attention here we report a study of the maximally random jammed mrj packings of binary superdisks and monodispersed superballs whose shapes are defined by x1 2p xd 2p 1 with d 2 and 3 respectively where p is the deformation parameter with values in the interval 0 a sp increases from zero one can get a family of both concave 0p0 5 and convex p0 5 particles with square symmetry d 2 or octahedral and cubic symmetry d 3 in particular for p 1 the particle is a perfect sphere circular disk and for p the particle is a perfect cube square we find that the mrj densities of such packings increase dramatically and nonanalytically as one moves away from the circular disk and sphere point p 1 moreover the disordered packings are hypostatic i e the average number of contacting neighbors is less than twice the total number of degrees of freedom per particle and yet the packings are mechanically stable as a result the local arrangements of particles are necessarily nontrivially correlated to achieve jamming we term such correlated structures nongeneric the degree of nongenericity of the packings is quantitatively characterized by determining the fraction of local coordination structures in which the central particles have fewer contacting neighbors than average we also show that such seemingly special packing configurations are counterintuitively not rare as the anisotropy of the particles increases the fraction of rattlers decreases while the minimal orientational order as measured by the tetratic and cubatic order parameters increases these characteristics result from the unique manner in which superballs break their rotational symmetry which also makes the superdisk and superball packings distinctly different from other known nonspherical hard particle packings

diversity of order and densities in jammed hard particle packings recently the conventional notion of random close packing has been supplanted by the more appropriate concept of the maximally random jammed mrj state this inevitably leads to the necessity of distinguishing the mrj state among the entire collection of jammed packings while the ideal method of addressing this question would be to enumerate and classify all possible jammed hard sphere configurations practical limitations prevent such a method from being employed instead we generate numerically a large number of representative jammed hard sphere configurations primarily relying on a slight modification of the lubachevsky stillinger algorithm to do so and evaluate several commonly employed order metrics for each of these packings our investigation shows that even in the large system limit jammed systems of hard spheres can be generated with a wide range of packing fractions from phi approximately 0 52 to the fcc limit phi approximately 0 74 moreover at a fixed packing fraction the variation in the order can be substantial indicating that the density alone does not uniquely characterize a packing interestingly each order metric evaluated yielded a relatively consistent estimate for the packing fraction of the maximally random jammed state phi mrj approximately 0 63 this estimate however is compromised by the weaknesses in the order metrics available and we propose several guiding principles for future efforts to define more broadly applicable metrics

packing ellipsoids in an optimized cylinder abstract the paper studies packing ellipsoids of revolution in a cylindrical container of minimum volume ellipsoids can be continuously rotated and translated two nonlinear mathematical programming models are introduced exact and approximated the latter uses an optimized multi spherical approximation of ellisoids for both models the phi function technique is employed to describe analytically non overlapping and containment constraints two solution approaches are proposed to solve the packing problem computational results for up to 500 ellipsoids are provided to demonstrate efficiency of the proposed approaches

dense packings of polyhedra platonic and archimedean solids understanding the nature of dense particle packings is a subject of intense research in the physical mathematical and biological sciences the preponderance of previous work has focused on spherical particles and very little is known about dense polyhedral packings we formulate the problem of generating dense packings of nonoverlapping nontiling polyhedra within an adaptive fundamental cell subject to periodic boundary conditions as an optimization problem which we call the adaptive shrinking cell asc scheme this optimization problem is solved here using a variety of multiparticle initial configurations to find the dense packings of each of the platonic solids in three dimensional euclidean space mathbb r 3 except for the cube which is the only platonic solid that tiles space we find the densest known packings of tetrahedra icosahedra dodecahedra and octahedra with densities 0 823 dots 0 836 dots 0 904 dots and 0 947 dots respectively it is noteworthy that the densest tetrahedral packing possesses no long range order unlike the densest tetrahedral packing which must not be a bravais lattice packing the densest packings of the other nontiling platonic solids that we obtain are their previously known optimal bravais lattice packings we also derive a simple upper bound on the maximal density of packings of congruent nonspherical particles and apply it to platonic solids archimedean solids superballs and ellipsoids provided that what we term the asphericity ratio of the circumradius to inradius is sufficiently small the upper bounds are relatively tight and thus close to the corresponding densities of the optimal lattice packings of the centrally symmetric platonic and archimedean solids our simulation results rigorous upper bounds and other theoretical arguments lead us to the conjecture that the densest packings of platonic and archimedean solids with central symmetry are given by their corresponding densest lattice packings this can be regarded to be the analog of kepler s sphere conjecture for these solids the truncated tetrahedron is the only non centrally symmetric archimedean solid the densest known packing of which is a non lattice packing with density at least as high as 23 24 0 958 text 333 dots we discuss the validity of our conjecture to packings of superballs prisms and antiprisms as well as to high dimensional analogs of the platonic solids in addition we conjecture that the optimal packing of any convex congruent polyhedron without central symmetry generally is not a lattice packing finally we discuss the possible applications and generalizations of the asc scheme in predicting the crystal structures of polyhedral nanoparticles and the study of random packings of hard polyhedra

an algorithm for finding a minimal weierstrass equation for an elliptic curve let e be an elliptic curve defined over an algebraic number field k and assume that some weierstrass equation for e over k is given then an algorithm is described which yields a global minimal weierstrass equation for e over k provided such a global minimal weierstrass equation does exist 1 general remarks tate s algorithm in 2 which is actually intended to give the conductor and kodaira reduction type of an elliptic curve ek defined over k where k is an algebraic number field can be used to calculate a minimal with respect to some discrete valuation of k weierstrass equation for ek once some weierstrass equation for ek is given in the following we describe an algorithm which does the same it is quite easy to write a computer program for the present algorithm whereas tate s algorithm needs greater effort and requires iteration moreover the present algorithm may be useful in conjunction with tate s algorithm for calculating the conductor because implementing tate s algorithm on a computer is much easier if one knows ahead of time that the weierstrass equation for ek is minimal in the following let k be an algebraic number field of degree n let o9k be the ring of integers of k and let w n be any integral basis for let e ek be an elliptic curve defined over k we assume that e admits a global minimal weierstrass equation over k this is always the case for example if the class number of k is prime to 6 details on elliptic curves may be found in 1 we recall here only the following facts let y2 a xy a3y x3 a2x2 a4x a6 be any weierstrass equation for e over k then y 2 ax y a y x 3 ax 2 a x a is also a weierstrass equation for e over k if and only if there is transformation of type x u2x r y u3y us2x t with r s t e k and u e k in this case the coefficients of the two equations and their quantities c4 c6 z and c c a respectively are related by the following formulas uaj al 2s u a2 a2 sa 3r s2 received march 1 1980 revised february 27 1981 1980 mathematics subject classification primary 14k07 1982 american mathematical society 0025 571 8 82 0000 0488 02 00 257 this content downloaded from 157 55 39 161 on mon 23 may 2016 05 03 29 utc all use subject to http about jstor org terms

colour constancy beyond the classical receptive field the problem of removing illuminant variations to preserve the colours of objects colour constancy has already been solved by the human brain using mechanisms that rely largely on centre surround computations of local contrast in this paper we adopt some of these biological solutions described by long known physiological findings into a simple fully automatic functional model termed adaptive surround modulation or asm in asm the size of a visual neuron s receptive field rf as well as the relationship with its surround varies according to the local contrast within the stimulus which in turn determines the nature of the centre surround normalisation of cortical neurons higher up in the processing chain we modelled colour constancy by means of two overlapping asymmetric gaussian kernels whose sizes are adapted based on the contrast of the surround pixels resembling the change of rf size we simulated the contrast dependent surround modulation by weighting the contribution of each gaussian according to the centre surround contrast in the end we obtained an estimation of the illuminant from the set of the most activated rfs outputs our results on three single illuminant and one multi illuminant benchmark datasets show that asm is highly competitive against the state of the art and it even outperforms learning based algorithms in one case moreover the robustness of our model is more tangible if we consider that our results were obtained using the same parameters for all datasets that is mimicking how the human visual system operates these results suggest a dynamical adaptation mechanisms contribute to achieving higher accuracy in computational colour constancy

neighbor list collision driven molecular dynamics simulation for nonspherical hard particles we apply the algorithm presented in the first part of this series of papers to systems of hard ellipses and ellipsoids the theoretical machinery needed to treat such particles including the overlap potentials is developed in full detail we describe an algorithm for predicting the time of collision for two moving ellipses or ellipsoids we present performance results for our implementation of the algorithm demonstrating that for dense systems of very aspherical ellipsoids the novel techniques of using neighbor lists and bounding sphere complexes offer as much as two orders of magnitude improvement in efficiency over direct adaptations of traditional event driven molecular dynamics algorithms the practical utility of the algorithm is demonstrated by presenting several interesting physical applications including the generation of jammed packings inside spherical containers the study of contact force chains in jammed packings and melting the densest known equilibrium crystals of prolate spheroids

evaluating combinational illumination estimation methods on real world images illumination estimation is an important component of color constancy and automatic white balancing a number of methods of combining illumination estimates obtained from multiple subordinate illumination estimation methods now appear in the literature these combinational methods aim to provide better illumination estimates by fusing the information embedded in the subordinate solutions the existing combinational methods are surveyed and analyzed here with the goals of determining 1 the effectiveness of fusing illumination estimates from multiple subordinate methods 2 the best method of combination 3 the underlying factors that affect the performance of a combinational method and 4 the effectiveness of combination for illumination estimation in multiple illuminant scenes the various combinational methods are categorized in terms of whether or not they require supervised training and whether or not they rely on high level scene content cues e g indoor versus outdoor extensive tests and enhanced analyzes using three data sets of real world images are conducted for consistency in testing the images were labeled according to their high level features 3d stages indoor outdoor and this label data is made available on line the tests reveal that the trained combinational methods direct combination by support vector regression in particular clearly outperform both the non combinational methods and those combinational methods based on scene content cues

polygon based contact description for modeling arbitrary polyhedra in the discrete element method abstract many real life applications of the discrete element method dem require a particle description which accounts for irregular and arbitrary shapes in this work a novel method is presented for calculating contact force interactions between polyhedral particles a contact between two polyhedra is decomposed as a set of contacts between individual polygonal facets for each polygon polygon contact an individual contact force is obtained by integrating a linear pressure over the area of its intersection both convex as well as partially concave polyhedra can be accurately represented the proposed algorithm is validated by comparing to previously published experimental and computational gravitational particle depositions of identical cubes finally the model is demonstrated in simulations of gravitational packing of various other polyhedral shapes

a comparison of computational color constancy algorithms ii experiments with image data for pt i see ibid vol 11 no 9 p 972 84 2002 we test a number of the leading computational color constancy algorithms using a comprehensive set of images these were of 33 different scenes under 11 different sources representative of common illumination conditions the algorithms studied include two gray world methods a version of the retinex method several variants of forsyth s 1990 gamut mapping method cardei et al s 2000 neural net method and finlayson et al s color by correlation method finlayson et al 1997 2001 hubel and finlayson 2000 we discuss a number of issues in applying color constancy ideas to image data and study in depth the effect of different preprocessing strategies we compare the performance of the algorithms on image data with their performance on synthesized data all data used for this study are available online at http www cs sfu ca spl sim color data and implementations for most of the algorithms are also available http www cs sfu ca spl sim color code experiments with synthesized data part one of this paper suggested that the methods which emphasize the use of the input data statistics specifically color by correlation and the neural net algorithm are potentially the most effective at estimating the chromaticity of the scene illuminant unfortunately we were unable to realize comparable performance on real images here exploiting pixel intensity proved to be more beneficial than exploiting the details of image chromaticity statistics and the three dimensional 3 d gamut mapping algorithms gave the best performance

scale affine invariant interest point detectors in this paper we propose a novel approach for detecting interest points invariant to scale and affine transformations our scale and affine invariant detectors are based on the following recent results 1 interest points extracted with the harris detector can be adapted to affine transformations and give repeatable results geometrically stable 2 the characteristic scale of a local structure is indicated by a local extremum over scale of normalized derivatives the laplacian 3 the affine shape of a point neighborhood is estimated based on the second moment matrix our scale invariant detector computes a multi scale representation for the harris interest point detector and then selects points at which a local measure the laplacian is maximal over scales this provides a set of distinctive points which are invariant to scale rotation and translation as well as robust to illumination changes and limited changes of viewpoint the characteristic scale determines a scale invariant region for each point we extend the scale invariant detector to affine invariance by estimating the affine shape of a point neighborhood an iterative algorithm modifies location scale and neighborhood of each point and converges to affine invariant points this method can deal with significant affine transformations including large scale changes the characteristic scale and the affine shape of neighborhood determine an affine invariant region for each point we present a comparative evaluation of different detectors and show that our approach provides better results than existing methods the performance of our detector is also confirmed by excellent matching resultss the image is described by a set of scale affine invariant descriptors computed on the regions associated with our points

neighbor list collision driven molecular dynamics simulation for nonspherical hard particles i algorithmic details in this first part of a series of two papers we present in considerable detail a collision driven molecular dynamics algorithm for a system of non spherical particles within a parallelepiped simulation domain under both periodic or hard wall boundary conditions the algorithm extends previous event driven molecular dynamics algorithms for spheres and is most efficient when applied to systems of particles with relatively small aspect ratios and with small variations in size we present a novel partial update near neighbor list nnl algorithm that is superior to previous algorithms at high densities without compromising the correctness of the algorithm this efficiency of the algorithm is further increased for systems of very aspherical particles by using bounding sphere complexes bsc these techniques will be useful in any particle based simulation including monte carlo and time driven molecular dynamics additionally we allow for a non vanishing rate of deformation of the boundary which can be used to model macroscopic strain and also alleviate boundary effects for small systems in the second part of this series of papers we specialize the algorithm to systems of ellipses and ellipsoids and present performance results for our implementation demonstrating the practical utility of the algorithm

star a structure and texture aware retinex model retinex theory is developed mainly to decompose an image into the illumination and reflectance components by analyzing local image derivatives in this theory larger derivatives are attributed to the changes in reflectance while smaller derivatives are emerged in the smooth illumination in this paper we utilize exponentiated local derivatives with an exponent gamma of an observed image to generate its structure map and texture map the structure map is produced by been amplified with gamma 1 while the texture map is generated by been shrank with gamma to this end we design exponential filters for the local derivatives and present their capability on extracting accurate structure and texture maps influenced by the choices of exponents gamma the extracted structure and texture maps are employed to regularize the illumination and reflectance components in retinex decomposition a novel structure and texture aware retinex star model is further proposed for illumination and reflectance decomposition of a single image we solve the star model by an alternating optimization algorithm each sub problem is transformed into a vectorized least squares regression with closed form solutions comprehensive experiments on commonly tested datasets demonstrate that the proposed star model produce better quantitative and qualitative performance than previous competing methods on illumination and reflectance decomposition low light image enhancement and color correction the code is publicly available at https github com csjunxu star

a comparison of computational color constancy algorithms i methodology and experiments with synthesized data we introduce a context for testing computational color constancy specify our approach to the implementation of a number of the leading algorithms and report the results of three experiments using synthesized data experiments using synthesized data are important because the ground truth is known possible confounds due to camera characterization and pre processing are absent and various factors affecting color constancy can be efficiently investigated because they can be manipulated individually and precisely the algorithms chosen for close study include two gray world methods a limiting case of a version of the retinex method a number of variants of forsyth s 1990 gamut mapping method cardei et al s 2000 neural net method and finlayson et al s color by correlation method finlayson et al 1997 2001 hubel and finlayson 2000 we investigate the ability of these algorithms to make estimates of three different color constancy quantities the chromaticity of the scene illuminant the overall magnitude of that illuminant and a corrected illumination invariant image we consider algorithm performance as a function of the number of surfaces in scenes generated from reflectance spectra the relative effect on the algorithms of added specularities and the effect of subsequent clipping of the data all data is available on line at http www cs sfu ca spl sim color data and implementations for most of the algorithms are also available http www cs sfu ca spl sim color code

color constancy with spatio spectral statistics we introduce an efficient maximum likelihood approach for one part of the color constancy problem removing from an image the color cast caused by the spectral distribution of the dominating scene illuminant we do this by developing a statistical model for the spatial distribution of colors in white balanced images i e those that have no color cast and then using this model to infer illumination parameters as those being most likely under our model the key observation is that by applying spatial band pass filters to color images one unveils color distributions that are unimodal symmetric and well represented by a simple parametric form once these distributions are fit to training data they enable efficient maximum likelihood estimation of the dominant illuminant in a new image and they can be combined with statistical prior information about the illuminant in a very natural manner experimental evaluation on standard data sets suggests that the approach performs well

feedback and surround modulated boundary detection edges are key components of any visual scene to the extent that we can recognise objects merely by their silhouettes the human visual system captures edge information through neurons in the visual cortex that are sensitive to both intensity discontinuities and particular orientations the classical approach assumes that these cells are only responsive to the stimulus present within their receptive fields however recent studies demonstrate that surrounding regions and inter areal feedback connections influence their responses significantly in this work we propose a biologically inspired edge detection model in which orientation selective neurons are represented through the first derivative of a gaussian function resembling double opponent cells in the primary visual cortex v1 in our model we account for four kinds of receptive field surround i e full far iso and orthogonal orientation whose contributions are contrast dependant the output signal from v1 is pooled in its perpendicular direction by larger v2 neurons employing a contrast variant centre surround kernel we further introduce a feedback connection from higher level visual areas to the lower ones the results of our model on three benchmark datasets show a big improvement compared to the current non learning and biologically inspired state of the art algorithms while being competitive to the learning based methods

efficient graph based image segmentation this paper addresses the problem of segmenting an image into regions we define a predicate for measuring the evidence for a boundary between two regions using a graph based representation of the image we then develop an efficient segmentation algorithm based on this predicate and show that although this algorithm makes greedy decisions it produces segmentations that satisfy global properties we apply the algorithm to image segmentation using two different kinds of local neighborhoods in constructing the graph and illustrate the results with both real and synthetic images the algorithm runs in time nearly linear in the number of graph edges and is also fast in practice an important characteristic of the method is its ability to preserve detail in low variability image regions while ignoring detail in high variability regions

color constancy using natural image statistics and scene semantics existing color constancy methods are all based on specific assumptions such as the spatial and spectral characteristics of images as a consequence no algorithm can be considered as universal however with the large variety of available methods the question is how to select the method that performs best for a specific image to achieve selection and combining of color constancy algorithms in this paper natural image statistics are used to identify the most important characteristics of color images then based on these image characteristics the proper color constancy algorithm or best combination of algorithms is selected for a specific image to capture the image characteristics the weibull parameterization e g grain size and contrast is used it is shown that the weibull parameterization is related to the image attributes to which the used color constancy methods are sensitive an mog classifier is used to learn the correlation and weighting between the weibull parameters and the image attributes number of edges amount of texture and snr the output of the classifier is the selection of the best performing color constancy method for a certain image experimental results show a large improvement over state of the art single algorithms on a data set consisting of more than 11 000 images an increase in color constancy performance up to 20 percent median angular error can be obtained compared to the best performing single algorithm further it is shown that for certain scene categories one specific color constancy algorithm can be used instead of the classifier considering several algorithms

concerning maximal packing arrangements of binary disk mixtures the determination of the maximal packing arrangements of two dimensional binary hard disks of radii rs and rl with rs 6 rl for su0ciently small rs amounts to 1nding the optimal arrangement of the small disks within a tricusp the nonconvexcavity between three close packed large disks we present a particle growth monte carlo algorithm for the generation of geometric packings of equi sized hard disks within such a tricusp the 1rst 19 members of an in1nite sequence of maximal density structures thus produced are reported in addition the monte carlo algorithm is applied to the geometric packing of disks within a 8at sided equilateral triangle and compared to published results for that packing problem we perform an analysis of geometric properties of the packings e g packing fractions and symmetries of structures con1ned to both containers interestingly we 1nd a non monotonic increase in the packing fraction with increasing number of disks packed within both the 8at sided triangle and tricusp it is important to note that for disk packings within a 8at sided equilateral triangle this non monotonic behavior of the packing fraction had not been reported in previously published works for the 8at sided equilateral triangle local maxima occur at the triangular integers ns 1 3 6 10 15 as well as ns 1 2 where ns is the number of disks in each packing however local maxima for packings within the tricusp exist at ns 1 3 6 10 18 finally we analyze the asymptotic approach to the upper bound on the packing fraction of the in1nite sequence of maximal structures of disks con1ned to the tricusp c

the reproduction angular error for evaluating the performance of illuminant estimation algorithms the angle between the rgbs of the measured illuminant and estimated illuminant colors the recovery angular error has been used to evaluate the performance of the illuminant estimation algorithms however we noticed that this metric is not in line with how the illuminant estimates are used normally the illuminant estimates are divided out from the image to hopefully provide image colors that are not confounded by the color of the light however even though the same reproduction results the same scene might have a large range of recovery errors in this work the scale of the problem with the recovery error is quantified next we propose a new metric for evaluating illuminant estimation algorithms called the reproduction angular error which is defined as the angle between the rgb of a white surface when the actual and estimated illuminations are divided out our new metric ties algorithm performance to how the illuminant estimates are used for a given algorithm adopting the new reproduction angular error leads to different optimal parameters further the ranked list of best to worst algorithms changes when the reproduction angular is used the importance of using an appropriate performance metric is established

families of elliptic curves over quartic number fields with prescribed torsion subgroups in this paper we construct infinite families of elliptic curves with given torsion group structures over cubic number fields this result provides explicit examples of the theoretical result recently developed by the first two authors and a schweizer they determined all the group structures which occur infinitely often as the torsion of elliptic curves over cubic number fields in fact this paper presents an efficient way of constructing such families of elliptic curves with prescribed torsion group structures over cubic number fields

exactly solvable disordered sphere packing model in arbitrary dimensional euclidean spaces we introduce a generalization of the well known random sequential addition rsa process for hard spheres in d dimensional euclidean space mathbb r d we show that all of the n particle correlation functions of this nonequilibrium model in a certain limit called the ghost rsa packing can be obtained analytically for all allowable densities and in any dimension this represents the first exactly solvable disordered sphere packing model in an arbitrary dimension the fact that the maximal density ensuremath phi ensuremath infty 1 2 d of the ghost rsa packing implies that there may be disordered sphere packings in sufficiently high d whose density exceeds minkowski s lower bound for bravais lattices the dominant asymptotic term of which is 1 2 d indeed we report on a conjectural lower bound on the density whose asymptotic behavior is controlled by 2 ensuremath 0 778 65 dots d thus providing the putative exponential improvement on minkowski s 100 year old bound our results suggest that the densest packings in sufficiently high dimensions may be disordered rather than periodic implying the existence of disordered classical ground states for some continuous potentials

new family of tilings of three dimensional euclidean space by tetrahedra and octahedra abstract it is well known that two regular tetrahedra can be combined with a single regular octahedron to tile complete fill three dimensional euclidean space this structure was called the octet truss by buckminster fuller it was believed that such a tiling which is the delaunay tessellation of the face centered cubic fcc lattice and its closely related stacking variants are the only tessellations of that involve two different regular polyhedra here we identify and analyze a unique family comprised of a noncountably infinite number of periodic tilings of whose smallest repeat tiling unit consists of one regular octahedron and six smaller regular tetrahedra we first derive an extreme member of this unique tiling family by showing that the holes in the optimal lattice packing of octahedra obtained by minkowski over a century ago are congruent tetrahedra this tiling has 694 distinct concave i e nonconvex repeat units 24 of which possess central symmetry and hence is distinctly different and combinatorically richer than the fcc tetrahedra octahedra tiling which only has two distinct tiling units then we construct a one parameter family of octahedron packings that continuously spans from the fcc to the optimal lattice packing of octahedra we show that the holes in these packings except for the two extreme cases are tetrahedra of two sizes leading to a family of periodic tilings with units composed four small tetrahedra and two large tetrahedra that contact an octahedron these tilings generally possess 2 068 distinct concave tiling units 62 of which are centrally symmetric

underconstrained jammed packings of nonspherical hard particles ellipses and ellipsoids continuing on recent computational and experimental work on jammed packings of hard ellipsoids donev et al science 303 990 2004 we consider jamming in packings of smooth strictly convex nonspherical hard particles we explain why an isocounting conjecture which states that for large disordered jammed packings the average contact number per particle is twice the number of degrees of freedom per particle overline z 2 d f does not apply to nonspherical particles we develop first and second order conditions for jamming and demonstrate that packings of nonspherical particles can be jammed even though they are underconstrained hypoconstrained overline z l2 d f we apply an algorithm using these conditions to computer generated hypoconstrained ellipsoid and ellipse packings and demonstrate that our algorithm does produce jammed packings even close to the sphere point we also consider packings that are nearly jammed and draw connections to packings of deformable but stiff particles finally we consider the jamming conditions for nearly spherical particles and explain quantitatively the behavior we observe in the vicinity of the sphere point

defining equations of modular curves we obtain defining equations of modular curves x0 n x1 n and x n by explicitly constructing modular functions using generalized dedekind eta functions as applications we describe a method of obtaining a basis for the space of cusp forms of weight 2 on a congruence subgroup we also use our model of x0 37 to find explicit modular parameterization of rational elliptic curves of conductor 37

the tractability of segmentation and scene analysis one of the fundamental problems in computer vision is the segmentation of an image into semantically meaningful regions based only on image characteristics a single segmentation can be determined using a linear number of evaluations of a uniformity predicate however minimising the number of regions is shown to be an np complete problem we also show that the variational approach to segmentation based on minimising a criterion combining the overall variance of regions and the number of regions also gives rise to an np complete problem when a library of object models is available segmenting the image becomes a problem of scene analysis a sufficient condition for the reconstruction of a 3d scene from a 2d image to be solvable in polynomial time is that the scene contains no cycles of mutually occluding objects and that no range information can be deduced from the image it is known that relaxing the no cycles condition renders the problem np complete we show that relaxing the no range information condition also produces an np complete problem

a novel algorithm for color constancy color constancy is the skill by which it is possible to tell the color of an object even under a colored light i interpret the color of an object as its color under a fixed canonical light rather than as a surface reflectance function this leads to an analysis that shows two distinct sets of circumstances under which color constancy is possible in this framework color constancy requires estimating the illuminant under which the image was taken the estimate is then used to choose one of a set of linear maps which is applied to the image to yield a color descriptor at each point this set of maps is computed in advance the illuminant can be estimated using image measurements alone because given a number of weak assumptions detailed in the text the color of the illuminant is constrained by the colors observed in the image this constraint arises from the fact that surfaces can reflect no more light than is cast on them for example if one observes a patch that excites the red receptor strongly the illuminant cannot have been deep blue two algorithms are possible using this constraint corresponding to different assumptions about the world the first algorithm crule will work for any surface reflectance crule corresponds to a form of coefficient rule but obtains the coefficients by using constraints on illuminant color the set of illuminants for which crule will be successful depends strongly on the choice of photoreceptors for narrowband photoreceptors crule will work in an unrestricted world the second algorithm mwext requires that both surface reflectances and illuminants be chosen from finite dimensional spaces but under these restrictive conditions it can recover a large number of parameters in the illuminant and is not an attractive model of human color constancy crule has been tested on real images of mondriaans and works well i show results for crule and for the retinex algorithm of land land 1971 land 1983 land 1985 operating on a number of real images the experimental work shows that for good constancy a color constancy system will need to adjust the gain of the receptors it employs in a fashion analagous to adaptation in humans

color based object recognition abstract the purpose is to arrive at recognition of multicolored objects invariant to a substantial change in viewpoint object geometry and illumination assuming dichromatic reflectance and white illumination it is shown that normalized color rgb saturation s and hue h and the newly proposed color models c 1 c 2 c 3 and l 1 l 2 l 3 are all invariant to a change in viewing direction object geometry and illumination further it is shown that hue h and l1l2l3 are also invariant to highlights finally a change in spectral power distribution of the illumination is considered to propose a new color constant color model m1m2m3 to evaluate the recognition accuracy differentiated for the various color models experiments have been carried out on a database consisting of 500 images taken from 3 d multicolored man made objects the experimental results show that highest object recognition accuracy is achieved by l1l2l3 and hue h followed by c1c2c3 normalized color rgb and m1m2m3 under the constraint of white illumination also it is demonstrated that recognition accuracy degrades substantially for all color features other than m1m2m3 with a change in illumination color the recognition scheme and images are available within the pictoseek and pic2seek systems on line at http www wins uva nl research isis zomax

finding suitable curves for the elliptic curve method of factorization using the parametrizations of kubert we show how to produce in nite families of elliptic curves which have prescribed nontrivial torsion over q and rank at least one these curves can be used to speed up the ecm factorization algorithm of lenstra we also brie y discuss curves with complex multiplication in this context

sequences of rational torsions on abelian varieties we address the question of how fast the available rational torsion on abelian varieties over increases with dimension the emphasis will be on the derivation of sequences of torsion divisors on hyperelliptic curves work of hellegouarch and lozach and klein may be made explicit to provide sequences of curves with rational torsion divisors of orders increasing linearly with respect to genus the main results in 2 are applications of a new technique which provide sequences of hyperelliptic curves for all torsions in an interval a g a g b g wherea g is quadratic ing andb g is linear ing as well as providing an improvement from linear to quadratic these results provide a wide selection of torsion orders for potential use by those involved in computer integration we conclude by considering possible techniques for divisors of non hyperelliptic curves and for general abelian varieties

cumulative attribute space regression for head pose estimation and color constancy abstract two stage cumulative attribute ca regression has been found effective in regression problems of computer vision such as facial age and crowd density estimation the first stage regression maps input features to cumulative attributes that encode correlations between target values the previous works have dealt with single output regression in this work we propose cumulative attribute spaces for 2 and 3 output multivariate regression we show how the original ca space can be generalized to multiple output by the cartesian product cartca however for target spaces with more than two outputs the cartca becomes computationally infeasible and therefore we propose an approximate solution multi view ca mvca where cartca is applied to output pairs we experimentally verify improved performance of the cartca and mvca spaces in 2d and 3d face pose estimation and three output rgb illuminant estimation for color constancy

efficient linear programming algorithm to generate the densest lattice sphere packings finding the densest sphere packing in d dimensional euclidean space r d is an outstanding fundamental problem with relevance in many fields including the ground states of molecular systems colloidal crystal structures coding theory discrete geometry number theory and biological systems numerically generating the densest sphere packings becomes very challenging in high dimensions due to an exponentially increasing number of possible sphere contacts and sphere configurations even for the restricted problem of finding the densest lattice sphere packings in this paper we apply the torquato jiao packing algorithm which is a method based on solving a sequence of linear programs to robustly reproduce the densest known lattice sphere packings for dimensions 2 through 19 we show that the tj algorithm is appreciably more efficient at solving these problems than previously published methods indeed in some dimensions the former procedure can be as much as three orders of magnitude faster at finding the optimal solutions than earlier ones we also study the suboptimal local density maxima solutions inherent structures or extreme lattices to gain insight about the nature of the topography of the density landscape

on the translative packing densities of tetrahedra and cuboctahedra abstract in 1900 as a part of his 18th problem hilbert asked the question to determine the density of the densest tetrahedron packings however up to now no mathematician knows the density t t of the densest translative tetrahedron packings and the density c t of the densest congruent tetrahedron packings this paper presents a local method to estimate the density of the densest translative packings of a general convex solid as an application we obtain the upper bound in 0 3673469 t t 0 3840610 where the lower bound was established by groemer in 1962 which corrected a mistake of minkowski for the density t c of the densest translative cuboctahedron packings we obtain the upper bound in 0 9183673 t c 0 9601527 in both cases we conjecture the lower bounds to be the correct answer

an optimal graph theoretic approach to data clustering theory and its application to image segmentation a novel graph theoretic approach for data clustering is presented and its application to the image segmentation problem is demonstrated the data to be clustered are represented by an undirected adjacency graph g with arc capacities assigned to reflect the similarity between the linked vertices clustering is achieved by removing arcs of g to form mutually exclusive subgraphs such that the largest inter subgraph maximum flow is minimized for graphs of moderate size approximately 2000 vertices the optimal solution is obtained through partitioning a flow and cut equivalent tree of g which can be efficiently constructed using the gomory hu algorithm 1961 however for larger graphs this approach is impractical new theorems for subgraph condensation are derived and are then used to develop a fast algorithm which hierarchically constructs and partitions a partially equivalent tree of much reduced size this algorithm results in an optimal solution equivalent to that obtained by partitioning the complete equivalent tree and is able to handle very large graphs with several hundred thousand vertices the new clustering algorithm is applied to the image segmentation problem the segmentation is achieved by effectively searching for closed contours of edge elements equivalent to minimum cuts in g which consist mostly of strong edges while rejecting contours containing isolated strong edges this method is able to accurately locate region boundaries and at the same time guarantees the formation of closed edge contours

multi cue illumination estimation via a tree structured group joint sparse representation a multi cue illumination estimation method based on tree structured group joint sparse representation is proposed tests show that the proposed method works better than existing methods most of which are based on using only a single cue type for example a binarized color histogram or simple image statistic such as the mean rgb most existing illumination estimation methods make their estimates using only one of three kinds of cues they differ in which cue type they use but the chosen cue is either based on 1 properties of the low level rgb color distribution 2 mid level initial illuminant estimates provided by subordinate methods or 3 high level knowledge of scene content e g indoor versus outdoor scene the proposed multi cue method combines the information provided by cues of all three of these types within the framework of a tree structured group joint sparse representation tgjsr in tgjsr the training data is grouped into a tree of subgroups a test image under an unknown illuminant has its features reconstructed in terms of a joint sparse representation model derived from the grouped training data the test image s illumination is then estimated based on the weights involved in the joint sparse representation model as a general framework the proposed tgjsr framework can also easily be extended to incorporate any new features or cues that might be discovered in the future for illumination estimation

packing tiling and covering with tetrahedra it is well known that three dimensional euclidean space cannot be tiled by regular tetrahedra but how well can we do in this work we give several constructions that may answer the various senses of this question in so doing we provide some solutions to packing tiling and covering problems of tetrahedra our results suggest that the regular tetrahedron may not be able to pack as densely as the sphere which would contradict a conjecture of ulam the regular tetrahedron might even be the convex body having the smallest possible packing density

learning invariant color features for person reidentification matching people across multiple camera views known as person reidentification is a challenging problem due to the change in visual appearance caused by varying lighting conditions the perceived color of the subject appears to be different under different illuminations previous works use color as it is or address these challenges by designing color spaces focusing on a specific cue in this paper we propose an approach for learning color patterns from pixels sampled from images across two camera views the intuition behind this work is that even though varying lighting conditions across views affect the pixel values of the same color the final representation of a particular color should be stable and invariant to these variations i e they should be encoded with the same values we model color feature generation as a learning problem by jointly learning a linear transformation and a dictionary to encode pixel values we also analyze different photometric invariant color spaces as well as popular color constancy algorithm for person reidentification using color as the only cue we compare our approach with all the photometric invariant color spaces and show superior performance over all of them combining with other learned low level and high level features we obtain promising results in viper person re id 2011 and caviar4reid data sets

a 3 d discrete element method for dry granular flows of ellipsoidal particles abstract we use 3 d discrete element method dem to simulate dry granular flows of non spherical particles in our simulation code non spherical particles are represented by clusters of spheres for contact detection and for contact force calculation for particles in contact the normal force displacement nfd model is simulated by a partially latching spring system whereas the tangential force displacement tfd model is simulated by an incremental relation that corresponds to a simplification of the mindlin and deresiewicz r d mindlin h deresiewicz asme j appl mech 20 1953 327 344 contact mechanics theory to establish the validity of the simulation procedure benchmark tests such as superball and superbean simulations were carried out we present various results obtained from the simulation of ellipsoidal particles flowing down a chute having a bumpy bottom these ellipsoidal particles had their physical properties obtained from experiments

multiple illuminant color estimation via statistical inference on factor graphs this paper presents a method to recover a spatially varying illuminant color estimate from scenes lit by multiple light sources starting with the image formation process we formulate the illuminant recovery problem in a statistically data driven setting to do this we use a factor graph defined across the scale space of the input image in the graph we utilize a set of illuminant prototypes computed using a data driven approach as a result our method delivers a pixelwise illuminant color estimate being devoid of libraries or user input the use of a factor graph also allows for the illuminant estimates to be recovered making use of a maximum a posteriori inference process moreover we compute the probability marginals by performing a delaunay triangulation on our factor graph we illustrate the utility of our method for pixelwise illuminant color recovery on widely available data sets and compare against a number of alternatives we also show sample color correction results on real world images

maximally dense packings of two dimensional convex and concave noncircular particles dense packings of hard particles have important applications in many fields including condensed matter physics discrete geometry and cell biology in this paper we employ a stochastic search implementation of the torquato jiao adaptive shrinking cell asc optimization scheme nature london 460 876 2009 to find maximally dense particle packings in d dimensional euclidean space mathbb r d while the original implementation was designed to study spheres and convex polyhedra in d ensuremath ge 3 our implementation focuses on d 2 and extends the algorithm to include both concave polygons and certain complex convex or concave nonpolygonal particle shapes we verify the robustness of this packing protocol by successfully reproducing the known putative optimal packings of congruent copies of regular pentagons and octagons then employ it to suggest dense packing arrangements of congruent copies of certain families of concave crosses convex and concave curved triangles incorporating shapes resembling the mercedes benz logo and moonlike shapes analytical constructions are determined subsequently to obtain the densest known packings of these particle shapes for the examples considered we find that the densest packings of both convex and concave particles with central symmetry are achieved by their corresponding optimal bravais lattice packings for particles lacking central symmetry the densest packings obtained are nonlattice periodic packings which are consistent with recently proposed general organizing principles for hard particles moreover we find that the densest known packings of certain curved triangles are periodic with a four particle basis and we find that the densest known periodic packings of certain moonlike shapes possess no inherent symmetries our work adds to the growing evidence that particle shape can be used as a tuning parameter to achieve a diversity of packing structures

explicit determination of nontrivial torsion structures of elliptic curves over quadratic number fields we determine equations of the modular curves x1 n for n 11 13 14 15 16 17 and 18 except for n 17 these are the only existing elliptic or hyperelliptic x1 n applying these x1 n we calculate tables of elliptic curves e over quadratic fields k with torsion groups of one of the following isomorphism types etor k z mz m 11 13 14 15 16 and 18

globally optimal regions and boundaries as minimum ratio weight cycles we describe a new form of energy functional for the modeling and identification of regions in images the energy is defined on the space of boundaries in the image domain and can incorporate very general combinations of modeling information both from the boundary intensity gradients etc and from the interior of the region texture homogeneity etc we describe two polynomial time digraph algorithms for finding the global minima of this energy one of the algorithms is completely general minimizing the functional for any choice of modeling information it runs in a few seconds on a 256 spl times 256 image the other algorithm applies to a subclass of functionals but has the advantage of being extremely parallelizable neither algorithm requires initialization

exact constructions of a family of dense periodic packings of tetrahedra the determination of the densest packings of regular tetrahedra one of the five platonic solids is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures that have emerged here we provide the most general analytical formulation to date to construct dense periodic packings of tetrahedra with four particles per fundamental cell this analysis results in six parameter family of dense tetrahedron packings that includes as special cases recently discovered dimer packings of tetrahedra including the densest known packings with density ensuremath phi frac 4000 4671 0 856347 dots this study strongly suggests that the latter set of packings are the densest among all packings with a four particle basis whether they are the densest packings of tetrahedra among all packings is an open question but we offer remarks about this issue moreover we describe a procedure that provides estimates of upper bounds on the maximal density of tetrahedron packings which could aid in assessing the packing efficiency of candidate dense packings

random sequential addition of hard spheres in high euclidean dimensions sphere packings in high dimensions have been the subject of recent theoretical interest employing numerical and theoretical methods we investigate the structural characteristics of random sequential addition rsa of congruent spheres in d dimensional euclidean space mathbb r d in the infinite time or saturation limit for the first six space dimensions 1 ensuremath le d ensuremath le 6 specifically we determine the saturation density pair correlation function cumulative coordination number and the structure factor in each of these dimensions we find that for 2 ensuremath le d ensuremath le 6 the saturation density ensuremath phi s scales with dimension as ensuremath phi s c 1 2 d c 2 d 2 d where c 1 0 202 phantom rule 0 2em 0ex 048 and c 2 0 973 phantom rule 0 2em 0ex 872 we also show analytically that the same density scaling is expected to persist in the high dimensional limit albeit with different coefficients a byproduct of this high dimensional analysis is a relatively sharp lower bound on the saturation density for any d given by ensuremath phi s ensuremath ge d 2 1 ensuremath s 0 2 d 1 where s 0 0 1 is the structure factor at k 0 i e infinite wavelength number variance in the high dimensional limit we demonstrate that a pal asti type conjecture the saturation density in mathbb r d is equal to that of the one dimensional problem raised to the d th power cannot be true for rsa hyperspheres we show that the structure factor s k must be analytic at k 0 and that rsa packings for 1 ensuremath le d ensuremath le 6 are nearly hyperuniform consistent with the recent decorrelation principle we find that pair correlations markedly diminish as the space dimension increases up to six we also obtain kissing contact number statistics for saturated rsa configurations on the surface of a d dimensional sphere for dimensions 2 ensuremath le d ensuremath le 5 and compare to the maximal kissing numbers in these dimensions we determine the structure factor exactly for the related ghost rsa packing in mathbb r d and demonstrate that its distance from hyperuniformity increases as the space dimension increases approaching a constant asymptotic value of 1 2 our work has implications for the possible existence of disordered classical ground states for some continuous potentials in sufficiently high dimensions

color constancy using 3d scene geometry derived from a single image the aim of color constancy is to remove the effect of the color of the light source as color constancy is inherently an ill posed problem most of the existing color constancy algorithms are based on specific imaging assumptions e g gray world and white patch assumption in this paper 3d geometry models are used to determine which color constancy method to use for the different geometrical regions depth layer found in images the aim is to classify images into stages rough 3d geometry models according to stage models images are divided into stage regions using hard and soft segmentation after that the best color constancy methods are selected for each geometry depth to this end we propose a method to combine color constancy algorithms by investigating the relation between depth local image statistics and color constancy image statistics are then exploited per depth to select the proper color constancy method our approach opens the possibility to estimate multiple illuminations by distinguishing nearby light source from distant illuminations experiments on state of the art data sets show that the proposed algorithm outperforms state of the art single color constancy algorithms with an improvement of almost 50 of median angular error when using a perfect classifier i e all of the test images are correctly classified into stages the performance of the proposed method achieves an improvement of 52 of the median angular error compared with the best performing single color constancy algorithm

stationary state volume fluctuations in a granular medium a statistical description of static granular material requires ergodic sampling of the phase space spanned by the different configurations of the particles we periodically fluidize a column of glass beads and find that the sequence of volume fractions ensuremath phi of postfluidized states is history independent and gaussian distributed about a stationary state the standard deviation of ensuremath phi exhibits as a function of ensuremath phi a minimum corresponding to a maximum in the number of statistically independent regions measurements of the fluctuations enable us to determine the compactivity x a temperaturelike state variable introduced in the statistical theory of edwards and oakeshott physica a 157 1080 1989

breakdown of elasticity theory for jammed hard particle packings conical nonlinear constitutive theory abstract hard particle packings have provided a rich source of outstanding theoretical problems and served as useful starting points to model the structure of granular media liquids living cells glasses and random media the nature of jammed hard particle packings is a current subject of keen interest we demonstrate that the response of jammed hard particle packings to global deformations cannot be described by linear elasticity even for small particle displacements but involves a conical nonlinear constitutive theory it is the singular nature of the hard particle potential that leads to the breakdown of linear elasticity interestingly a nonlinear theory arises because the feasible particle displacements leading to unjamming depend critically on the local spatial arrangement of the particles implying a directionality in the feasible strains that is absent in particle systems with soft potentials mathematically the set of feasible strains has a conical structure i e components of the imposed strain tensor generally obey linear inequalities the nature of the nonlinear behavior is illustrated by analyzing several specific packings finally we examine the conditions under which a packing can be considered to incompressible in the traditional sense

packing of concave polyhedra with continuous rotations using nonlinear optimisation we study the problem of packing a given collection of arbitrary in general concave polyhedra into a cuboid of minimal volume continuous rotations and translations of polyhedra are allowed in addition minimal allowable distances between polyhedra are taken into account we derive an exact mathematical model using adjusted radical free quasi phi functions for concave polyhedra to describe non overlapping and distance constraints the model is a nonlinear programming formulation we develop an efficient solution algorithm which employs a fast starting point algorithm and a new compaction procedure the procedure reduces our problem to a sequence of nonlinear programming subproblems of considerably smaller dimension and a smaller number of nonlinear inequalities the benefit of this approach is borne out by the computational results which include a comparison with previously published instances and new instances

modeling contact interactions between triangulated rounded bodies for the discrete element method calculating contact forces between complex shapes for performing discrete element method dem simulations is a long standing problem with no unique ideal solution in this work a new method to calculate interactions between arbitrary rounded bodies is presented each body is represented by a triangulated surface mesh in which each triangle is associated with a unique radius of curvature then normal contact forces are calculated by numerically integrating a hertz contact pressure formulation over the contact area between two contacting particles this results in a mechanistic contact description that is converging with refinement of a given triangulation and directly uses physical material properties as parameters of the contact model after showing convergence upon mesh refinement towards the hertzian solution the error for non spherical curvatures is investigated and the new model is compared with an indentation experiment of a pear shaped object finally the method is demonstrated in a simulation of gravitational packing by simulating packing of spheres pear shaped as well as gummy bear shaped objects

arithmetic of elliptic curves upon quadratic extension this paper is a study of variations in the rank of the mordell weil group of an elliptic curve e defined over a number field f as one passes to quadratic extensions k of f let s k be the selmer group for multiplication by 2 on e k in analogy with genus theory we describe s k in terms of various objects defined over f and the local norm indices dimf2 ft norm ah for each completion fv of f in particular we show that dim s k dim e k 2 has the same parity as zi we compute i when e has good or multiplicative reduction modulo v assuming that the 2 primary component of the tate shafare vitch group u1 k is finite as conjectured we obtain the parity of rank e k for semistable elliptic curves defined over q and parametrized by modular functions our parity results agree with those predicted analytically by the conjectures of birch and swinnerton dyer 1 introduction let e be an elliptic curve defined over a number field f our motivating question is this what can be said about variations in the rank of the mordell weil group e k over quadratic extensions k f dl 2 1 let e d denote the twist of e which becomes isomorphic to e over k but not over f concretely if we choose for e a model over f of the form y2 f x then a model for d is given by dy2 f x if a denotes the generator of gal k f then e f can be identified with the l eigenspace and e d f with the l eigenspace of a acting on e k it follows that rank e k rank e f rank e d f an equiv alent question therefore is to describe changes in the rank of e d f as d varies for certain specific curves defined over q this question has been discussed for

a two scale model of granular materials a concurrent two scale and two method approach for modeling the mechanical behavior of dry frictional non cohesive granular materials is presented in domains of large eventually discontinuous deformation the material is modeled on the grain scale using a three dimensional discrete element method in the remaining domain the material is considered continuous and modeled by the finite element method using an elasto plastic constitutive equation whose parameters are fit to the particle model via a homogenization scheme the discrete and finite element models are coupled at the interface by the arlequin method an overlapping domain is introduced where the overall virtual work is interpolated between both models and compatibility is assured by kinematic constraints for this purpose the discrete particle displacements are split into a fine and coarse scale part and equality of the coarse scale part and the continuum solution is enforced through the penalty method

new upper bounds on sphere packings i we continue the study of the linear programming bounds for sphere packing introduced by cohn and elkies we use theta series to give another proof of the principal theorem and present some related results and conjectures this article is in the arxiv as arxiv math mg 0110010

order metrics and order maps of octahedron packings abstract we apply the ideal octahedron model and the relaxation algorithm in generating octahedron packings the cubatic order parameter p 4 1 bond orientational order metric q 6 and local cubatic order parameter p 4 l o c a l of the packings are calculated and their correlations with the packing density are investigated in the order maps the border curve of packing density separates the geometrically feasible and infeasible regions in the order maps observing the transition phenomenon on the border curve we propose the concept of the maximally dense random packing mdrp as the densest packing in the random state in which the particle positions and orientations are randomly distributed and there is no nontrivial spatial correlations among particles the mdrp characterizes the onset of nontrivial spatial correlations among particles a special packing with a density about 0 7 is found in the order maps and considered to be the mdrp of octahedra the p 4 l o c a l is proposed as a new order parameter for octahedron packings which measures the average order degree in the neighborhoods of particles the p 4 1 q 6 and p 4 l o c a l evaluate the order degree of orientation bond orientation and local structures respectively and are applied simultaneously to measure the order degree of the octahedron packings their thresholds in the random state are determined by monte carlo simulations

approaching the computational color constancy as a classification problem through deep learning abstract computational color constancy refers to the problem of computing the illuminant color so that the images of a scene under varying illumination can be normalized to an image under the canonical illumination in this paper we adopt a deep learning framework for the illumination estimation problem the proposed method works under the assumption of uniform illumination over the scene and aims for the accurate illuminant color computation specifically we trained the convolutional neural network to solve the problem by casting the color constancy problem as an illumination classification problem we designed the deep learning architecture so that the output of the network can be directly used for computing the color of the illumination experimental results show that our deep network is able to extract useful features for the illumination estimation and our method outperforms all previous color constancy methods on multiple test datasets

optimal packings of superballs dense hard particle packings are intimately related to the structure of low temperature phases of matter and are useful models of heterogeneous materials and granular media most studies of the densest packings in three dimensions have considered spherical shapes and it is only more recently that nonspherical shapes e g ellipsoids have been investigated superballs whose shapes are defined by x1 2p x2 2p x3 2p 1 provide a versatile family of convex particles p0 5 with both cubic like and octahedral like shapes as well as concave particles 0p0 5 with octahedral like shapes in this paper we provide analytical constructions for the densest known superball packings for all convex and concave cases the candidate maximally dense packings are certain families of bravais lattice packings in which each particle has 12 contacting neighbors possessing the global symmetries that are consistent with certain symmetries of a superball we also provide strong evidence that our packings for convex superballs p0 5 are most likely the optimal ones the maximal packing density as a function of p is nonanalytic at the sphere point p 1 and increases dramatically as p moves away from unity two more nontrivial nonanalytic behaviors occur at p c 1 150 9 and p o ln 3 ln 4 0 792 4 for cubic and octahedral superballs respectively where different bravais lattice packings possess the same densities the packing characteristics determined by the broken rotational symmetry of superballs are similar to but richer than their two dimensional superdisk counterparts y jiao et al phys rev lett 100 245504 2008 and are distinctly different from that of ellipsoid packings our candidate optimal superball packings provide a starting point to quantify the equilibrium phase behavior of superball systems which should deepen our understanding of the statistical thermodynamics of nonspherical particle systems

edge based color constancy color constancy is the ability to measure colors of objects independent of the color of the light source a well known color constancy method is based on the gray world assumption which assumes that the average reflectance of surfaces in the world is achromatic in this paper we propose a new hypothesis for color constancy namely the gray edge hypothesis which assumes that the average edge difference in a scene is achromatic based on this hypothesis we propose an algorithm for color constancy contrary to existing color constancy algorithms which are computed from the zero order structure of images our method is based on the derivative structure of images furthermore we propose a framework which unifies a variety of known gray world max rgb minkowski norm and the newly proposed gray edge and higher order gray edge algorithms the quality of the various instantiations of the framework is tested and compared to the state of the art color constancy methods on two large data sets of images recording objects under a large number of different light sources the experiments show that the proposed color constancy algorithms obtain comparable results as the state of the art color constancy methods with the merit of being computationally more efficient

mr linear contact detection algorithm large scale discrete element simulations as well as a whole range of related problems involve contact of a large number of separate bodies and an efficient and robust contact detection algorithm is necessary there has been a number of contact detection algorithms with total detection time proportional to n ln n where n is the total number of separate bodies reported in the past in more recent years algorithms with total cpu time proportional to n have been developed in this work a novel contact detection algorithm with total detection time proportional to n is proposed the performance of the algorithm is not influenced by packing density while memory requirements are insignificant the algorithm is applicable to systems comprising bodies of a similar size the algorithm is named mr munjiza rougier munjiza devised the algorithm rougier implemented it in the second part of the paper the algorithm is extended to particles of different sizes the new algorithm is called mmr multi step mr algorithm copyright 2005 john wiley sons ltd

color by correlation a simple unifying framework for color constancy the paper considers the problem of illuminant estimation how given an image of a scene recorded under an unknown light we can recover an estimate of that light obtaining such an estimate is a central part of solving the color constancy problem thus the work presented will have applications in fields such as color based object recognition and digital photography rather than attempting to recover a single estimate of the illuminant we instead set out to recover a measure of the likelihood that each of a set of possible illuminants was the scene illuminant we begin by determining which image colors can occur and how these colors are distributed under each of a set of possible lights we discuss how for a given camera we can obtain this knowledge we then correlate this information with the colors in a particular image to obtain a measure of the likelihood that each of the possible lights was the scene illuminant finally we use this likelihood information to choose a single light as an estimate of the scene illuminant computation is expressed and performed in a generic correlation framework which we develop we propose a new probabilistic instantiation of this correlation framework and show that it delivers very good color constancy on both synthetic and real images we further show that the proposed framework is rich enough to allow many existing algorithms to be expressed within it the gray world and gamut mapping algorithms are presented in this framework and we also explore the relationship of these algorithms to other probabilistic and neural network approaches to color constancy

noise reduction based on partial reference dual tree complex wavelet transform shrinkage this paper presents a novel way to reduce noise introduced or exacerbated by image enhancement methods in particular algorithms based on the random spray sampling technique but not only according to the nature of sprays output images of spray based methods tend to exhibit noise with unknown statistical distribution to avoid inappropriate assumptions on the statistical characteristics of noise a different one is made in fact the non enhanced image is considered to be either free of noise or affected by non perceivable levels of noise taking advantage of the higher sensitivity of the human visual system to changes in brightness the analysis can be limited to the luma channel of both the non enhanced and enhanced image also given the importance of directional content in human vision the analysis is performed through the dual tree complex wavelet transform dtwct unlike the discrete wavelet transform the dtwct allows for distinction of data directionality in the transform space for each level of the transform the standard deviation of the non enhanced image coefficients is computed across the six orientations of the dtwct then it is normalized the result is a map of the directional structures present in the non enhanced image said map is then used to shrink the coefficients of the enhanced image the shrunk coefficients and the coefficients from the non enhanced image are then mixed according to data directionality finally a noise reduced version of the enhanced image is computed via the inverse transforms a thorough numerical analysis of the results has been performed in order to confirm the validity of the proposed approach

estimates of the optimal density of sphere packings in high dimensions the problem of finding the asymptotic behavior of the maximal density max of sphere packings in high euclidean dimensions is one of the most fascinating and challenging problems in discrete geometry one century ago minkowski obtained a rigorous lower bound on max that is controlled asymptotically by 1 2d where d is the euclidean space dimension an indication of the difficulty of the problem can be garnered from the fact that exponential improvement of minkowski s bound has proved to be elusive even though existing upper bounds suggest that such improvement should be possible using a statistical mechanical procedure to optimize the density associated with a test pair correlation function and a conjecture concerning the existence of disordered sphere packings s torquato and f h stillinger exp math 15 307 2006 the putative exponential improvement on max was found with an asymptotic behavior controlled by 1 2 0 77865 d using the same methods we investigate whether this exponential im

improving color constancy by photometric edge weighting edge based color constancy methods make use of image derivatives to estimate the illuminant however different edge types exist in real world images such as material shadow and highlight edges these different edge types may have a distinctive influence on the performance of the illuminant estimation therefore in this paper an extensive analysis is provided of different edge types on the performance of edge based color constancy methods first an edge based taxonomy is presented classifying edge types based on their photometric properties e g material shadow geometry and highlights then a performance evaluation of edge based color constancy is provided using these different edge types from this performance evaluation it is derived that specular and shadow edge types are more valuable than material edges for the estimation of the illuminant to this end the iterative weighted gray edge algorithm is proposed in which these edge types are more emphasized for the estimation of the illuminant images that are recorded under controlled circumstances demonstrate that the proposed iterative weighted gray edge algorithm based on highlights reduces the median angular error with approximately 25 percent in an uncontrolled environment improvements in angular error up to 11 percent are obtained with respect to regular edge based color constancy

color constancy for multiple light sources color constancy algorithms are generally based on the simplifying assumption that the spectral distribution of a light source is uniform across scenes however in reality this assumption is often violated due to the presence of multiple light sources in this paper we will address more realistic scenarios where the uniform light source assumption is too restrictive first a methodology is proposed to extend existing algorithms by applying color constancy locally to image patches rather than globally to the entire image after local patch based illuminant estimation these estimates are combined into more robust estimations and a local correction is applied based on a modified diagonal model quantitative and qualitative experiments on spectral and real images show that the proposed methodology reduces the influence of two light sources simultaneously present in one scene if the chromatic difference between these two illuminants is more than 1 the proposed framework outperforms algorithms based on the uniform light source assumption with error reduction up to approximately 30 otherwise when the chromatic difference is less than 1 and the scene can be considered to contain one approximately uniform light source the performance of the proposed method framework is similar to global color constancy methods

energy conserving contact interaction models for arbitrarily shaped discrete elements abstract this work aims to establish a unified theoretical framework for normal contact of arbitrarily shaped discrete elements in discrete element modelling solely based on the energy conservation principle for elastic contact it will show that the normal force must be a potential field vector associated with a potential with the construction of an appropriate potential function a complete normal contact model including the magnitude and direction of the normal force and the normal contact line can be unambiguously derived for a pair of any shaped bodies the model in its final form is simple and has a clear geometric perspective for 2d bodies it can also recover some well known models for bodies with simple geometric shapes

densest binary sphere packings the densest binary sphere packings in the x plane of small to large sphere radius ratio and small sphere relative concentration x have historically been very difficult to determine previous research had led to the prediction that these packings were composed of a few known alloy phases including for example the alb2 hexagonal hgbr2 a nd aute2 structures and to xyn structures composed of close packed large spheres with small spheres in a number ratio of n to 1 in the interstices e g the nacl packing for n 1 however utilizing an implementation of the torquato jiao sphere packing algorithm torquato and jiao phys rev e 82 061302 2010 we have discovered that many more structures appear in the densest packings for example while all previously known densest structures were composed of spheres in small to large number ratios of one to one two to one and very recently three to one we have identified densest structures with number ratios of seven to three and five to two in a recent work hopkins et al phys rev lett 107 125501 2011 we summarized these findings in this work we present the structures of the densest known packings and provide details about their characteristics our findings demonstrate that a broad array of different densest mechanically stable structures consisting of only two types of components can form without any consideration of attractive or anisotropic interactions in addition the structures that we have identified may correspond to currently unidentified stable phases of certain binary atomic and molecular systems particularly at high temperatures and pressures

phase behavior of colloidal superballs shape interpolation from spheres to cubes the phase behavior of hard superballs is examined using molecular dynamics within a deformable periodic simulation box a superball s interior is defined by the inequality x 2q y 2q z 2q ensuremath le 1 which provides a versatile family of convex particles q ensuremath ge 0 5 with cubelike and octahedronlike shapes as well as concave particles ql0 5 with octahedronlike shapes here we consider the convex case with a deformation parameter q between the sphere point q 1 and the cube q ensuremath infty we find that the asphericity plays a significant role in the extent of cubatic ordering of both the liquid and crystal phases calculation of the first few virial coefficients shows that superballs that are visually similar to cubes can have low density equations of state closer to spheres than to cubes dense liquids of superballs display cubatic orientational order that extends over several particle lengths only for large q along the ordered high density equation of state superballs with 1lql3 exhibit clear evidence of a phase transition from a crystal state to a state with reduced long ranged orientational order upon the reduction of density for q ensuremath ge 3 long ranged orientational order persists until the melting transition the width of the apparent coexistence region between the liquid and ordered high density phase decreases with q up to q 4 0 the structures of the high density phases are examined using certain order parameters distribution functions and orientational correlation functions we also find that a fixed simulation cell induces artificial phase transitions that are out of equilibrium current fabrication techniques allow for the synthesis of colloidal superballs and thus the phase behavior of such systems can be investigated experimentally

a novel image representation via local frequency analysis for illumination invariant stereo matching in this paper we propose a novel image representation approach to tackle illumination variations in stereo matching problems images are mapped using their fourier transforms which are convolved with a set of monogenic filters frequency analysis is carried out at different scales to account for most image content the phase congruency and the local weighted mean phase angle are then computed over all the scales the original image is transformed into a new representation using these two mappings this representation is invariant to illumination and contrast variations more importantly it is generic and can be used with most sparse as well as dense stereo matching algorithms in addition sequential feature matching or tracking can also benefit from our approach in varying radiometric conditions we demonstrate the improvements introduced with our image mappings on well established data sets in the literature as well as on our own experimental scenarios that include high dynamic range imagery the experiments include both dense and sparse stereo and sequential matching algorithms where the latter is considered in the very challenging visual odometry framework