segmentation and classification of range images the recognition of objects in three dimensional space is a desirable capability of a computer vision system range images which directly measure 3 d surface coordinates of a scene are well suited for this task in this paper we report a procedure to detect connected planar convex and concave surfaces of 3 d objects this is accomplished in three stages the first stage segments the range image into surface patches by a square error criterion clustering algorithm using surface points and associated surface normals the second stage classifies these patches as planar convex or concave based on a non parametric statistical test for trend curvature values and eigenvalue analysis in the final stage boundaries between adjacent surface patches are classified as crease or noncrease edges and this information is used to merge compatible patches to produce reasonable faces of the object s this procedure has been successfully applied to a large number of real and synthetic images four of which we present in this paper

sign of gaussian curvature from curve orientation in photometric space we compute the sign of gaussian curvature using a purely geometric definition consider a point p on a smooth surface s and a closed curve spl gamma on s which encloses p the image of spl gamma on the unit normal gaussian sphere is a new curve spl beta the gaussian curvature at p is defined as the ratio of the area enclosed by spl gamma over the area enclosed by spl beta as spl gamma contracts to p the sign of gaussian curvature at p is determined by the relative orientations of the closed curves spl gamma and spl beta we directly compute the relative orientation of two such curves from intensity data we employ three unknown illumination conditions to create a photometric scatter plot this plot is in one to one correspondence with the subset of the unit gaussian sphere containing the mutually illuminated surface normal this permits direct computation of the sign of gaussian curvature without the recovery of surface normals our method is albedo invariant we assume diffuse reflectance but the nature of the diffuse reflectance can be general and unknown error analysis on simulated images shows the accuracy of our technique we also demonstrate the performance of this methodology on empirical data

a brief introduction to the bethe ansatz in super yang mills we give a brief introduction to the application of the bethe ansatz to the study of planar super yang mills the emphasis is on one loop integrability in the su 2 sector we use the bethe ansatz to find the anomalous dimensions for certain operators and compare these results with string theory predictions based on the ads cft correspondence

on the theory of late stage phase separation in off critically quenched binary systems the late stage of phase separation in off critically quenched binary systems is studied from an unifying viewpoint by numerically solving not only the kinetic equation for the single droplet distribution function r t but also the linear equation with the source term for the structure function s k t both of which were recently derived by the present authors to study the dynamics of phase separation the scaling behaviors r t r t 4fl r r t and s k t km t 3 l kkm t are thus recovered where r t is the average droplet radius and km t the peak position of s k t as a function of k the temporal power behavior of r and km are also shown to agree with those expected on the basis of the lifshitz slyozov wagner theory the universal features of the time independent scaling functions fl and l x are thus investigated explicitly including their volume fraction dependence and the x4 dependence of l x for small x the results are in good agreement with experiments for both scaling functions

curvature augmented tensor voting for shape inference from noisy 3d data improves the basic tensor voting formalism to infer the sign and direction of principal curvatures at each input site from noisy 3d data unlike most previous approaches no local surface fitting partial derivative computation nor oriented normal vector recovery is performed in our method these approaches are known to be noise sensitive since accurate partial derivative information is often required which is usually unavailable from real data also unlike approaches that detect signs of gaussian curvature we can handle points with zero gaussian curvature uniformly without first localizing them in a separate process the tensor voting curvature estimation is non iterative does not require initialization and is robust to a considerable amount of outlier noise as its effect is reduced by collecting a large number of tensor votes qualitative and quantitative results on synthetic and real complex data are presented

statistical mechanical theory of coarsening of spherical droplets abstract a new statistical mechanical theory of diffusion controlled droplet coarsening is presented with the aid of a scaling expansion method a spatial graining is carried out in a manner consistent with an expansion in droplet volume fraction to obtain kinetic equations for a single distribution function of droplets it is shown that there two characteristic stages of coarsening depending on their space time scales an intermediate stage and a late stage in both stages new kinetic equations are systematically derived to order these equations have two terms at order a collisionless drift term and a collision term the collision term is shown to be different from the conventional encounter integral discussed by lifshitz and slyozov since the former is of order and describes distant soft collisions while the latter is of order and describes close hard collisions it is shown in both stages that the mean droplet radius increases as the cube root of the time t 1 3 a scaling behavior of the distribution function is also found in both stages in particular in the late stage this scaling behavior is shown to coincide with that obtained by lifshitz and slysov in the limit o it is also pointed out that a naive expansion in powers of breaks down due to the long range nature of interactions among droplets through diffusions fluctuations around the kinetic equations are also explicitly explored they are shown to be nonthermal fluctuations generated by the soft collision process and to be small especially in the late stage they are shown to obey a linear gaussian markov process satisfying a fluctuation dissipation relation of the second kind

elementary derivation of kinetic equations for ostwald ripening a direct and elementary derivation is presented for the kinetic equation of the single droplet distribution function and the variance equation that describe ostwald ripening the derivation is basically algebraical and the screening effects of diffusional interactions among droplets is taken into account automatically by a projection technique the results correct up to the square root of the volume fraction confirm the kinetic equations derived previously by tokuyama and kawasaki except for a correction to the variance equation

theory of morphological evolution in ostwald ripening abstract the multiple expansion theory for ostwald ripening in a three dimensional system is presented analogously to the case in two dimensional coarsening t imaeda and k kawasaki physica a 164 1990 335 the migration and the shape deformation of droplets caused by the diffusional interaction are taken into account in our kinetic equations of motion the derived equations can be solved numerically within a fairly resonable computation time the role of the mullins sekerka instability in the coarsening kinetics is examined

dynamics of fluctuations in ostwald ripening a new equation of motion for the structure function abstract a new method of finding an equation of motion for the structure function s k t from the kinetic equations recently derived for the late stage of phase separation is presented s k t is shown to be scaled by two kinds of characteristics lengths the average droplet radius r t and the screening length l t as s k t r t 3 s x q q 1 2 with x k r t and q kl t where q is the volume fraction of the minority phase and r t and l t satisfy the power laws t q 1 2 r t and r t t 1 3 the scaled structure function s x q q 1 2 is found to obey a first order differential equation with two source terms which originate from two kinds of fluctuations initial thermal fluctuations and nonthermal fluctuations generated by soft collisions among droplets the soft collision process is shown to produce a new type of narrowing of s x q q 1 2 which is different from the usual one that occurs as q increases the results are compared with other theories

yangian symmetry at two loops for the sector of sym we present the perturbative yangian symmetry at next to leading order in the sector of planar sym just like the ordinary symmetry generators the bi local yangian charges receive corrections acting on several neighbouring sites we confirm that the bi local yangian charges satisfy the necessary conditions they transform in the adjoint of they commute with the dilatation generator and they satisfy the serre relations this proves that the sector is integrable at two loops

statistics of surface curvature estimates reliable curvature estimation is an important goal in image analysis to provide viewpoint independent cues for shape classification this paper presents a model of the relationship between the variance of curvature estimates and the image noise agreement to within 10 is obtained for 3d range data a perturbation error analysis is performed on the local least square surface fitting algorithm which is commonly used to obtain partial derivative estimates in the presence of noise the theoretical results are used to implement adaptive thresholding for surface type classification this is compared with existing constant and semi adaptive thresholding schemes it is concluded that any pixel by pixel thresholding will produce poor results the theoretical relationships provide the basis for a probabilistic approach

gauss decomposition of the yangian y mathfrak gl _ m n we describe a gauss decomposition for the yangian y mathfrak gl m n of the general linear lie superalgebra this gives a connection between this yangian and the yangian of the classical lie superalgebra y a m 1 n 1 for m n defined and studied in papers by stukopin and suggests natural definitions for the yangians y mathfrak sl n n and y a n n we also show that the coefficients of the quantum berezinian generate the centre of the yangian y mathfrak gl m n this was conjectured by nazarov in 1991

large scale simulations of the two dimensional cahn hilliard model abstract we review some recent numerical studies of the cahn hilliard model in two dimensions for phase separation with different values of the minority area fraction we find that dynamical scaling is satisfied at sufficiently late times for the pair correlation function the structure factor and the droplet distribution function we study how the shape of these scaling functions change with the area fractions and compare these results with available theoretical predictions the time dependence of the characteristics length is consistent with an asymptotic growth law exponent 1 3 for all area fractions

curvature based algorithms for nonrigid motion and correspondence estimation we present a novel technique for utilizing the gaussian curvature information in 3d nonrigid motion estimation in the absence of known correspondence differential geometric constraints derived in the paper allow one to estimate parameters of the local affine motion model given the values of gaussian curvature before and after motion these constraints can be further combined with the previously known constraints based on the unit normals before and after motion our experiments demonstrate that the resulting hybrid algorithm is more accurate than each of its constituents and more accurate than the classical icp algorithm we also present a technique for curvilinear orthogonalization of quadratic monge patches that is essential in our derivation and useful in other applications

isogeometric analysis of the cahn hilliard phase field model abstract the cahn hilliard equation involves fourth order spatial derivatives finite element solutions are not common because primal variational formulations of fourth order operators are only well defined and integrable if the finite element basis functions are piecewise smooth and globally c 1 continuous there are a very limited number of two dimensional finite elements possessing c 1 continuity applicable to complex geometries but none in three dimensions we propose isogeometric analysis as a technology that possesses a unique combination of attributes for complex problems involving higher order differential operators namely higher order accuracy robustness two and three dimensional geometric flexibility compact support and most importantly the possibility of c 1 and higher order continuity a nurbs based variational formulation for the cahn hilliard equation was tested on two and three dimensional problems we present steady state solutions in two dimensions and for the first time in three dimensions to achieve these results an adaptive time stepping method is introduced we also present a technique for desensitizing calculations to dependence on mesh refinement this enables the calculation of topologically correct solutions on coarse meshes opening the way to practical engineering applications of phase field methodology

parabolic presentations of the yangian we introduce some new presentations for the yangian associated to the lie algebra open image in new window these presentations are parametrized by tuples of positive integers summing to n at one extreme for the tuple n the presentation is the usual rtt presentation of y n at the other extreme for the tuple 1 n the presentation is closely related to drinfeld s presentation in general the presentations are useful for understanding the structure of the standard parabolic subalgebras of y n

fluctuation effects in coagulation processes abstract we study diffusion controlled coagulation processes in the system with a finite density of droplets using the fock space formalism we find that the effective reaction rate has a correction to smoluchowski s classical rate constant for three dimensional systems we also predict the scaling form of the scattering function and find that our results qualitatively agree with experimental results

encounter effects on the dynamics of fluctuations in phase separations of off critically quenched binary systems abstract the encounter effect on the dynamics of fluctuations in phase separations of off critically quenched binary systems is studied by performing three dimensional computer simulations of the droplet growth model proposed recently by the authors the dynamical behavior of the scattering structure function including the dynamical scaling the temporal power laws and the crossovers have been investigated at higher volume fractions the encounter effect is shown to strongly influence not only the dynamics of the single droplet size distribution function leading to flattening and broadening of the distribution function but also the dynamics of fluctuations in phase separating systems leading to sharpening and narrowing the structure function

theory of phase separation dynamics in quenched binary mixtures a systematic theory of the dynamics of phase separation of quenched binary systems into metastable states is presented not only the kinetic equation for the single droplet size distribution function f r t but also the linear equation for the structure function s k t which are valid over the entire time region after the nucleation stage are derived from a unified point of view the functions f r t and s k t are shown to satisfy the dynamical scaling relations f r t n t r t f r r t and s k t mathit k mathit m t mathrm ensuremath mathit d ensuremath phi t mathrm ensuremath delta ensuremath psi k mathit k mathit m t with mathit k mathit m mathrm ensuremath 1 t ensuremath propto r mathrm ensuremath phi 1 mathit d where n is the number density of the minority phase r the average droplet radius ensuremath phi the volume fraction of the minority phase mathit k mathit m the peak position of s k t and d 3 here three characteristic stages are then shown to exist after the nucleation stage the growth stage with ensuremath delta 2 where the power laws are given by r ensuremath propto mathit t 1 2 n ensuremath propto mathit t 0 mathit k mathit m ensuremath propto mathit t 0 and ensuremath phi ensuremath propto mathit t 3 2 the intermediate stage with ensuremath delta 1 d where r ensuremath propto mathit t 1 4 n ensuremath propto mathit t mathrm ensuremath 2 3 mathit k mathit m ensuremath propto mathit t mathrm ensuremath 2 9 and ensuremath phi ensuremath propto mathit t 1 12 and the coarsening stage with ensuremath delta 1 d where r ensuremath propto mathit t 1 3 n ensuremath propto mathit t mathrm ensuremath 1 mathit k mathit m ensuremath propto mathit t mathrm ensuremath 1 3 and ensuremath phi ensuremath propto mathit t 0 two crossovers are then observed in the time exponents the time evolution of the scaling functions f ensuremath rho t and ensuremath psi x t are thus studied explicitly including their asymptotic behavior and their dependence on ensuremath phi

multipole expansion in the ostwald ripening theory abstract a multipole expansion theory for ostwald ripening is presented the theory takes into account morphological deformation as well as migration of coarsening droplets numerical computation are performed for the two dimensional ripening process even in a few mode truncation our results reproduce well the direct numerical solution of the laplace equation at a small spatial separation between droplets the importance of these degrees of freedom in the coarsening kinetics is discussed

many body effects in two dimensional ostwald ripening abstract a theory for ostwald ripening in two dimensions is presented using a many body approach we show the existence of a screening length which had been previously assumed by marqusee j chem phys 81 1984 976 in two dimensional diffusion controlled growth processes we also confirm that the growth law of the critical droplet radius in our model is given by r c t t 1 3

parallel kinetic monte carlo simulations of two dimensional island coarsening the results of parallel kinetic monte carlo kmc simulations of island coarsening based on a bond counting model are presented our simulations were carried out both as a test of and as an application of the recently developed semirigorous synchronous sublattice sl algorithm by carrying out simulations over long times and for large system sizes the asymptotic coarsening behavior and scaled island size distribution isd were determined our results indicate that while cluster diffusion and coalescence play a role at early and intermediate times at late times the coarsening proceeds via ostwald ripening in addition we find that the asymptotic scaled isd is significantly narrower and more sharply peaked than the mean field theory prediction the dependence of the scaled isd on coverage is also studied our results demonstrate that parallel kmc simulations can be used to effectively extend the time scale over which realistic coarsening simulations can be carried out in particular for simulations of the late stages of coarsening with system size l 1600 and eight processors a parallel efficiency larger than 80 was obtained these results suggest that the sl algorithm is likely to be useful in the future in parallel kmc simulations of more complicated models of coarsening

on first order corrections to the lsw theory ii finite systems we consider first order corrections to the classical theory by lifshitz slyozov and wagner lsw for systems with a finite number of particles numerical simulations in v e fradkov etal phys rev e 53 3925 3932 1996 show a cross over in the scaling of the correction term from 1 3 to 1 2 is the volume fraction of particles when the system size becomes larger than the screening length we rigorously derive this cross over for the rate of change of the energy starting from the monopole approximation the proof exploits the fact that the rate of change of energy has a variational characterization

structure of the string r matrix by requiring invariance directly under the yangian symmetry we rederive beisert s quantum r matrix in a form that carries explicit dependence on the representation labels the braiding factors and the spectral parameters ui in this way we demonstrate that there exists rewriting of its entries such that the dependence on the spectral parameters is purely of a difference form namely the latter enter only in the combination u1 u2 as indicated by the shift automorphism of the yangian when recasted in this fashion the entries exhibit a cleaner structure which allows us to spot new interesting relations among them this permits us to package them into a practical tensorial expression where the nondiagonal entries are taken care of by explicit combinations of symmetry algebra generators