diffusive limit of a tagged particle in asymmetric simple exclusion processes invariance principles are proved under diffusive scaling for the centered position of a tagged particle in the simple exclusion process with asymmetric nonzero drift jump probabilities in dimensions d 3 the method of proof is by martingale techniques which rely on the fact that symmetric random walks are transient in high dimensions c 2000 john wiley sons inc

multi view stereo reconstruction and scene flow estimation with a global image based matching score we present a new variational method for multi view stereovision and non rigid three dimensional motion estimation from multiple video sequences our method minimizes the prediction error of the shape and motion estimates both problems then translate into a generic image registration task the latter is entrusted to a global measure of image similarity chosen depending on imaging conditions and scene properties rather than integrating a matching measure computed independently at each surface point our approach computes a global image based matching score between the input images and the predicted images the matching process fully handles projective distortion and partial occlusions neighborhood as well as global intensity information can be exploited to improve the robustness to appearance changes due to non lambertian materials and illumination changes without any approximation of shape motion or visibility moreover our approach results in a simpler more flexible and more efficient implementation than in existing methods the computation time on large datasets does not exceed thirty minutes on a standard workstation finally our method is compliant with a hardware implementation with graphics processor units our stereovision algorithm yields very good results on a variety of datasets including specularities and translucency we have successfully tested our motion estimation algorithm on a very challenging multi view video sequence of a non rigid scene

an equivalence of h 1 norms for the simple exclusion process resolvent h 1 norms with respect to simple exclusion processes play an important role in many problems with respect to additive functionals tagged particles and hydrodynamics among other concerns here general translation invariant finite range simple exclusion processes with and without a distinguished particle are considered for the standard system of indistinguishable particles it is proved that the corresponding h 1 norms are equivalent in a sense to the h 1 norms of a nearest neighbor system the same result holds for systems with a distinguished particle in dimensions d 2 however in dimension d 1 this equivalence does not hold an application of the h 1 norm equivalence to additive functional variances is also given

shock fluctuations in asymmetric simple exclusion the one dimensional nearest neighbors asymmetric simple exclusion process in used as a microscopic approximation to the burgers equation we study the process with rates of jumpsp q to the right and left respectively and with initial product measure with densities to the left and right of the origin respectively with shock initial conditions we prove that a second class particle added to the system at the origin at time zero identifies microscopically the shock for all later times if this particle is added at another site then it describes the behavior of a characteristic of the burgers equation for vanishing left density 0 we prove in the scale t1 2 that the position of the shock at timet depends only on the initial configuration in a region depending ont the proofs are based on laws of large numbers for the second class particle

multiview stereo via volumetric graph cuts and occlusion robust photo consistency this paper presents a volumetric formulation for the multiview stereo problem which is amenable to a computationally tractable global optimization using graph cuts our approach is to seek the optimal partitioning of 3d space into two regions labeled as object and empty under a cost functional consisting of the following two terms 1 a term that forces the boundary between the two regions to pass through photo consistent locations and 2 a ballooning term that inflates the object region to take account of the effect of occlusion on the first term we use an occlusion robust photo consistency metric based on normalized cross correlation which does not assume any geometric knowledge about the reconstructed object the globally optimal 3d partitioning can be obtained as the minimum cut solution of a weighted graph

fluctuations in the occupation time of a site in the asymmetric simple exclusion process we consider the simple asymmetric exclusion process with nonzero drift under the stationary bernoulli product measure at density we prove that for dimension d 2 the occupation time of the site 0 is diffusive as soon as 1 2 for dimension d 1 if the density is equal to 1 2 we prove that the time t variance of the occupation time of the site 0 diverges in a certain sense at least as t5 4

superdiffusivity of asymmetric exclusion process in dimensions one and two we prove that the diffusion coefficient for the asymmetric exclusion process diverges at least as fast as t 1 4 in dimension d 1 and logt 1 2 in d 2 the method applies to nearest and non nearest neighbor asymmetric exclusion processes

fast approximate energy minimization via graph cuts many tasks in computer vision involve assigning a label such as disparity to every pixel a common constraint is that the labels should vary smoothly almost everywhere while preserving sharp discontinuities that may exist e g at object boundaries these tasks are naturally stated in terms of energy minimization the authors consider a wide class of energies with various smoothness constraints global minimization of these energy functions is np hard even in the simplest discontinuity preserving case therefore our focus is on efficient approximation algorithms we present two algorithms based on graph cuts that efficiently find a local minimum with respect to two types of large moves namely expansion moves and swap moves these moves can simultaneously change the labels of arbitrarily large sets of pixels in contrast many standard algorithms including simulated annealing use small moves where only one pixel changes its label at a time our expansion algorithm finds a labeling within a known factor of the global minimum while our swap algorithm handles more general energy functions both of these algorithms allow important cases of discontinuity preserving energies we experimentally demonstrate the effectiveness of our approach for image restoration stereo and motion on real data with ground truth we achieve 98 percent accuracy

approximating tensor product bezier surfaces with tangent plane continuity we present a simple method for degree reduction of tensor product bezier surfaces with tangent plane continuity in l 2 norm continuity constraints at the four corners of surfaces are considered so that the boundary curves preserve endpoints continuity of any order a we obtain matrix representations for the control points of the degree reduced surfaces by the least squares method a simple optimization scheme that minimizes the perturbations of some related control points is proposed and the surface patches after adjustment are c continuous in the interior and g 1 continuous at the common boundaries we show that this scheme is applicable to surface patches defined on chessboard like domains

superdiffusivity of occupation time variance in 2 dimensional asymmetric exclusion processes with density ρ 1 2 we compute that the growth of the occupation time variance at the origin up to time t in dimension d 2 with respect to asymmetric simple exclusion in equilibrium with density 1 2 is in a certain sense at least tlog log t for general rates and at least t log t 1 2 for rates which are asymmetric only in the direction of one of the axes these estimates give a complement to bounds in the literature when d 1 and are consistent with an important conjecture with respect to the transition function and variance of second class particles

variational principles surface evolution pdes level set methods and the stereo problem we present a novel geometric approach for solving the stereo problem for an arbitrary number of images spl ges 2 it is based upon the definition of a variational principle that must be satisfied by the surfaces of the objects in the scene and their images the euler lagrange equations that are deduced from the variational principle provide a set of partial differential equations pdes that are used to deform an initial set of surfaces which then move toward the objects to be detected the level set implementation of these pdes potentially provides an efficient and robust way of achieving the surface evolution and to deal automatically with changes in the surface topology during the deformations i e to deal with multiple objects results of an implementation of our theory also dealing with occlusion and visibility are presented on synthetic and real images

explicit g2 constrained degree reduction of bezier curves by quadratic optimization in this paper we revisit g 2 constrained degree reduction of bezier curves which has been solved in our previous work by using iterative methods we propose an explicit and effective method for g 1 constrained degree reduction and c 1g 2 constrained degree reduction our main idea is to express the distance function defined in the l 2 norm as a strictly convex quadratic function of two variables which becomes a quadratic optimization problem we can explicitly obtain the unique solution by solving two linear equations such that the distance function is minimized the existence of the unique solution is also proved

best one sided approximation of polynomials under l 1 norm in this paper we develop an analytic solution for the best one sided approximation of polynomials under l1 norm that is we find two polynomials with lower degree which bound the given polynomial such that the areas between the bounding polynomials and the given polynomial attain minimum the key ingredient of our technique is a characterization for one sided approximations based on orthogonal polynomials this result is applied in the degree reduction of interval polynomial bezier curves in computer aided design

application of chebyshev ii bernstein basis transformations to degree reduction of bezier curves a polynomial curve on 0 1 can be expressed in terms of bernstein polynomials and chebyshev polynomials of the second kind we derive the transformation matrices that map the bernstein and chebyshev coefficients into each other and examine the stability of this linear map in the p 1 and norms the condition number of the chebyshev bernstein transformation matrix grows at a significantly slower rate with n than in the power bernstein case and the rate is very close somewhat faster to the legendre bernstein case using the transformation matrices we present a method for the best multi degree reduction with respect to the t t 2 weighted square norm for the unconstrained case which is further developed to provide a good approximation to the best multi degree reduction with constraints of endpoints continuity of orders r s r s 0 this method has a quadratic complexity and may be ill conditioned when it is applied to the curves of high degree we estimate the posterior l 1 error bounds for degree reduction

silhouette coherence for camera calibration under circular motion we present a new approach to camera calibration as a part of a complete and practical system to recover digital copies of sculpture from uncalibrated image sequences taken under turntable motion in this paper we introduce the concept of the silhouette coherence of a set of silhouettes generated by a 3d object we show how the maximization of the silhouette coherence can be exploited to recover the camera poses and focal length silhouette coherence can be considered as a generalization of the well known epipolar tangency constraint for calculating motion from silhouettes or outlines alone further silhouette coherence exploits all the geometric information encoded in the silhouette not just at epipolar tangency points and can be used in many practical situations where point correspondences or outer epipolar tangents are unavailable we present an algorithm for exploiting silhouette coherence to efficiently and reliably estimate camera motion we use this algorithm to reconstruct very high quality 3d models from uncalibrated circular motion sequences even when epipolar tangency points are not available or the silhouettes are truncated the algorithm has been integrated into a practical system and has been tested on more than 50 uncalibrated sequences to produce high quality photo realistic models three illustrative examples are included in this paper the algorithm is also evaluated quantitatively by comparing it to a state of the art system that exploits only epipolar tangents

transience of second class particles and diffusive bounds for additive functionals in one dimensional asymmetric exclusion processes consider a one dimensional exclusion process with finite range translation invariant jump rates with nonzero drift let the process be stationary with product bernoulli invariant distribution at density place a second class particle initially at the origin for the case 1 2 we show that the time spent by the second class particle at the origin has finite expectation this strong transience is then used to prove that variances of additive functionals of local mean zero functions are diffusive when 1 2 as a corollary to previous work we deduce the invariance principle for these functionals the main arguments are comparisons of h 1 norms a large deviation estimate for second class particles and a relation between occupation times of second class particles and additive functional variances

log t 2 3 law of the two dimensional asymmetric simple exclusion process we prove that the diffusion coefficient for the two dimensional asymmetric simple exclusion process with nearest neighbor jumps diverges as log t 2 3 to the leading order the method applies to nearest and non nearest neighbor asymmetric simple exclusion processes

central limit theorems for additive functionals of the simple exclusion process definition 2 1 in the above paper is incorrectly stated in the proof of theo rem 2 1 which gives an invariance principle for certain processes satisfying defi nition 2 1 conditions in definition 2 1 are sufficient to deduce finite dimensional convergence but not enough to apply a maximal inequality for demimartingales to obtain tightness the problem is definition 2 1 as stated only considers pair increment associations and not more general associations needed for the demi martingale property we slightly strengthen the definition here in this correction so that the proof of tightness in theorem 2 1 holds details of how this is accom plished are given below by substituting the corrected definition 2 1 for the previous one all results in the article hold as written in particular proposition 2 1 which is the link between theorem 2 1 and the main results and which states certain additive processes sat isfy definition 2 1 holds with the same argument

scaling limits of additive functionals of interacting particle systems using the renormalization method introduced in 17 we prove what we call the local boltzmann gibbs principle for conservative stationary interacting particle systems in dimension d 1 as applications of this result we obtain various scaling limits of additive functionals of particle systems like the occupation time of a given site or extensive additive fields of the dynamics as a by product of these results we also construct a novel process related to the stationary solution of the stochastic burgers equation

occupation times of long range exclusion and connections to kpz class exponents with respect to a class of long range exclusion processes on mathbb z d with single particle transition rates of order cdot d alpha starting under bernoulli invariant measure nu rho with density rho we consider the fluctuation behavior of occupation times at a vertex and more general additive functionals part of our motivation is to investigate the dependence on alpha d and rho with respect to the variance of these functionals and associated scaling limits in the case the rates are symmetric among other results we find the scaling limits exhaust a range of fractional brownian motions with hurst parameter h in 1 2 3 4 however in the asymmetric case we study the asymptotics of the variances which when d 1 and rho 1 2 points to a curious dichotomy between long range strength parameters 0 alpha le 3 2 and alpha 3 2 in the former case the order of the occupation time variance is the same as under the process with symmetrized transition rates which are calculated exactly in the latter situation we provide consistent lower and upper bounds and other motivations that this variance order is the same as under the asymmetric short range model which is connected to kpz class scalings of the space time bulk mass density fluctuations