on dividing an amount according to individual claims or liabilities a basic principle of distributive justice states that if an allocation among a group of individuals is fair then it should be perceived as fair when restricted to each subgroup of individuals this consistency principle applies in particular to methods for allocating taxes among citizens according to their ability to pay every consistent continuous taxation method optimizes an additively separable objective function optimal allocations may be computed by a simple lagrange multiplier technique similar results hold for allocating assets among creditors according to their claims the techniques are illustrated by constructing an objective function for a bankruptcy method from the babylonian talmud

solving nonlinear single facility network location problems we present a general approach to solving nonlinear single facility network location problems we assume that cost is any convex function of distances and solve this class of problem by solving convex subproblems on treelike segments into which the network is decomposed we show that only a fraction of treelike segments generally need be examined and that our method results in a reasonably efficient general purpose algorithm the algorithm is particularly effective on real world as opposed to random networks and when the cost function is nondecreasing and semiseparable as are many popular cost functions finally we describe theoretical complexity bounds and computational experience

optimal locations for a class of nonlinear single facility location problems on a network this paper investigates a class of single facility location problems on an arbitrary network necessary and sufficient conditions are obtained for characterizing locally optimal locations with respect to a certain nonlinear objective function this approach produces a number of new results for locating a facility on an arbitrary network and in addition it unifies several known results for the special case of tree networks it also suggests algorithmic procedures for obtaining such optimal locations

strategyproof approximation of the minimax on networks we consider the problem of locating a facility on a network represented by a graph a set of strategic agents have different ideal locations for the facility the cost of an agent is the distance between its ideal location and the facility a mechanism maps the locations reported by the agents to the location of the facility we wish to design mechanisms that are strategyproof sp in the sense that agents can never benefit by lying and at the same time provide a small approximation ratio with respect to the minimax measure we design a novel hybrid strategyproof randomized mechanism that provides a tight approximation ratio of 3 2 when the network is a circle known as a ring in the case of computer networks furthermore we show that no randomized sp mechanism can provide an approximation ratio better than 2 o 1 even when the network is a tree thereby matching a trivial upper bound of two

networks with condorcet solutions abstract a condorcet point on a network is a point such that thare is no other point closer to a strict majority of users which are located at the vertices of the network a complete characterization is given of those networks on which no condorcet paradox occurs in the sense that for each distribution of users there exists at least one condorcet point moreover those networks are characterized on which condorcet points and weber points always coincide a polynomial algorithm is obtained which decides whether a given network has condorcet points for all distributions of users on the network

approximately optimal mechanisms for strategyproof facility location minimizing lp norm of costs this paper is concerned with the problem of locating a facility on a line in the presence of strategic agents also located on that line each agent incurs a cost equal to her distance to the facility whereas the planner wishes to minimize the lp norm of the vector of agent costs the location of each agent is only privately known and the goal is to design a strategyproof mechanism that approximates the optimal cost well it is shown that the median mechanism provides a 21 1 p approximation ratio and that this is the optimal approximation ratio among all deterministic strategyproof mechanisms for randomized mechanisms two results are shown first for any integer p larger than 2 no mechanism from a rather large class of randomized mechanisms has an approximation ratio better than that of the median mechanism this is in contrast to the case of p 2 and p where a randomized mechanism provably helps improve the worst case approximation ratio second for the case of 2 agents the left right middle

a method for registration of 3 d shapes the authors describe a general purpose representation independent method for the accurate and computationally efficient registration of 3 d shapes including free form curves and surfaces the method handles the full six degrees of freedom and is based on the iterative closest point icp algorithm which requires only a procedure to find the closest point on a geometric entity to a given point the icp algorithm always converges monotonically to the nearest local minimum of a mean square distance metric and the rate of convergence is rapid during the first few iterations therefore given an adequate set of initial rotations and translations for a particular class of objects with a certain level of shape complexity one can globally minimize the mean square distance metric over all six degrees of freedom by testing each initial registration one important application of this method is to register sensed data from unfixtured rigid objects with an ideal geometric model prior to shape inspection experimental results show the capabilities of the registration algorithm on point sets curves and surfaces

an axiomatic characterization of some locations in trees abstract we describe axioms that uniquely characterize the absolute median and the squared median the point that minimizes the sum of squared distances of a tree a common feature of these characterizations is a consistency axiom of the type first used by h p young to characterize a voting procedure called borda s rule these results make it possible to argue in favor of or against a particular location in terms of principles satisfied or violated

new entire positive solution for the nonlinear schrodinger equation coexistence of fronts and bumps in this paper we construct new kinds of positive solutions of delta u u u p 0 quad rm on bbb r 2 when p 2 these solutions have the following asymptotic behavior u x z sim omega x f z sum i 1 infty omega 0 x z xi i vec e 1 as l rightarrow infty where omega is a unique positive homoclinic solution of omega omega omega p 0 in bbb r omega 0 is the two dimensional positive solution and vec e 1 1 0 and xi j are points such that xi j jl cal o 1 for all j geq 1 this represents a first result on the it coexistence of fronts and bumps geometrically our new solutions correspond to it triunduloid in the theory of cmc surface

shape registration in implicit spaces using information theory and free form deformations we present a novel variational and statistical approach for shape registration shapes of interest are implicitly embedded in a higher dimensional space of distance transforms in this implicit embedding space registration is formulated in a hierarchical manner the mutual information criterion supports various transformation models and is optimized to perform global registration then a b spline based incremental free form deformations iffd model is used to minimize a sum of squared differences ssd measure and further recover a dense local nonrigid registration field the key advantage of such framework is twofold 1 it naturally deals with shapes of arbitrary dimension 2d 3d or higher and arbitrary topology multiple parts closed open and 2 it preserves shape topology during local deformation and produces local registration fields that are smooth continuous and establish one to one correspondences its invariance to initial conditions is evaluated through empirical validation and various hard 2d 3d geometric shape registration examples are used to show its robustness to noise severe occlusion and missing parts we demonstrate the power of the proposed framework using two applications one for statistical modeling of anatomical structures another for 3d face scan registration and expression tracking we also compare the performance of our algorithm with that of several other well known shape registration algorithms

surface signatures an orientation independent free form surface representation scheme for the purpose of objects registration and matching this paper introduces anew free form surface representation scheme for the purpose of fast and accurate registration and matching accurate registration of surfaces is a common task in computer vision the proposed representation scheme captures the surface curvature information seen from certain points and produces images called surface signatures at these points matching signatures of different surfaces enables the recovery of the transformation parameters between these surfaces we propose using template matching to compare the signature images to enable partial matching another criterion the overlap ratio is used this representation scheme can be used as a global representation of the surface as well as a local one and performs near real time registration we show that the signature representation can be used to recover scaling transformation as well as matching objects in 3d scenes in the presence of clutter and occlusion applications presented include free form object matching multimodal medical volumes registration and dental teeth reconstruction from intraoral images

truthful generalized assignments via stable matching in the generalized assignment problem gap a set of jobs seek to be assigned to a set of machines for every job machine pair there are a specific value and an accommodated capacity for the assignment the objective is to find an assignment that maximizes the total sum of values given that the capacity constraint of every machine is satisfied the gap is a classic optimization problem and has been studied extensively from the algorithmic perspective dughmi and ghosh dughmi s ghosh a 2010 truthful assignment without money acm conf electronic commerce acm new york 325 334 proposed the game theoretical framework in which every job is owned by a selfish agent who aims to maximize the value of his own assignment they gave a logarithmic approximation truthful in expectation mechanism and left open the problem whether there exists a truthful mechanism with a constant approximation factor in this paper we give an affirmative answer to this question and provide a constant approximation mechanism

dynamical statistical shape priors for level set based tracking in recent years researchers have proposed introducing statistical shape knowledge into level set based segmentation methods in order to cope with insufficient low level information while these priors were shown to drastically improve the segmentation of familiar objects so far the focus has been on statistical shape priors which are static in time yet in the context of tracking deformable objects it is clear that certain silhouettes such as those of a walking person may become more or less likely over time in this paper we tackle the challenge of learning dynamical statistical models for implicitly represented shapes we show how these can be integrated as dynamical shape priors in a bayesian framework for level set based image sequence segmentation we assess the effect of such shape priors with memory on the tracking of familiar deformable objects in the presence of noise and occlusion we show comparisons between dynamical and static shape priors between models of pure deformation and joint models of deformation and transformation and we quantitatively evaluate the segmentation accuracy as a function of the noise level and of the camera frame rate our experiments demonstrate that level set based segmentation and tracking can be strongly improved by exploiting the temporal correlations among consecutive silhouettes which characterize deforming shapes

index growth of hypersurfaces with constant mean curvature in this paper we give the precise index growth for the embedded hypersurfaces of revolution with constant mean curvature cmc 1 in mathbb r n delaunay unduloids when n 3 using the asymptotics result of korevaar kusner and solomon we derive an explicit asymptotic index growth rate for finite topology cmc 1 surfaces with properly embedded ends similar results are obtained for hypersurfaces with cmc bigger than 1 in hyperbolic space

segmentation through variable order surface fitting the solution of the segmentation problem requires a mechanism for partitioning the image array into low level entities based on a model of the underlying image structure a piecewise smooth surface model for image data that possesses surface coherence properties is used to develop an algorithm that simultaneously segments a large class of images into regions of arbitrary shape and approximates image data with bivariate functions so that it is possible to compute a complete noiseless image reconstruction based on the extracted functions and regions surface curvature sign labeling provides an initial coarse image segmentation which is refined by an iterative region growing method based on variable order surface fitting experimental results show the algorithm s performance on six range images and three intensity images

a generic framework for tracking using particle filter with dynamic shape prior tracking deforming objects involves estimating the global motion of the object and its local deformations as functions of time tracking algorithms using kalman filters or particle filters pfs have been proposed for tracking such objects but these have limitations due to the lack of dynamic shape information in this paper we propose a novel method based on employing a locally linear embedding in order to incorporate dynamic shape information into the particle filtering framework for tracking highly deformable objects in the presence of noise and clutter the pf also models image statistics such as mean and variance of the given data which can be useful in obtaining proper separation of object and background

on the repeatability and quality of keypoints for local feature based 3d object retrieval from cluttered scenes 3d object recognition from local features is robust to occlusions and clutter however local features must be extracted from a small set of feature rich keypoints to avoid computational complexity and ambiguous features we present an algorithm for the detection of such keypoints on 3d models and partial views of objects the keypoints are highly repeatable between partial views of an object and its complete 3d model we also propose a quality measure to rank the keypoints and select the best ones for extracting local features keypoints are identified at locations where a unique local 3d coordinate basis can be derived from the underlying surface in order to extract invariant features we also propose an automatic scale selection technique for extracting multi scale and scale invariant features to match objects at different unknown scales features are projected to a pca subspace and matched to find correspondences between a database and query object each pair of matching features gives a transformation that aligns the query and database object these transformations are clustered and the biggest cluster is used to identify the query object experiments on a public database revealed that the proposed quality measure relates correctly to the repeatability of keypoints and the multi scale features have a recognition rate of over 95 for up to 80 occluded objects

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

dynamic time warping under pointwise shape context similarity measures are of fundamental importance in time series data mining dynamic time warping dtw is a quite popular measure because it handles time distortions well however dtw has an inherent shortcoming in that dtw can lead to pathological alignments between time series where a single point maps onto a large subsection of another time series to overcome this problem we propose a novel variant of dtw named sc dtw sc dtw employs shape context a rich local shape descriptor to replace the raw observed values considered by conventional dtw the main novelties of sc dtw are 1 it deeply explores both the numerical nature and shape nature of time series and 2 neighborhood information for each point is taken into account sc dtw can generate a more feature to feature alignment between time series and thus serves as a robust similarity measure we test the performance of sc dtw on ucr time series datasets using the one nearest neighbor 1nn classifier compared with other well established methods sc dtw provides better accuracy on 24 of 34 datasets

aggregation error bounds for a class of location models many location models involve distances and demand points in their objective function in urban contexts there can be millions of demand points this leads to demand point aggregation which produces error we identify a general model structure that includes most such location models and present a means of obtaining error bounds for all models with this structure the error bounds suggest how to do the demand point aggregation so as to keep the error small

elastic shape texture matching for human face recognition in this paper a novel elastic shape texture matching method namely estm for human face recognition is proposed in our approach both the shape and the texture information are used to compare two faces without establishing any precise pixel wise correspondence the edge map is used to represent the shape of an image while the texture information is characterized by both the gabor representations and the gradient direction of each pixel combining these features a shape texture hausdorff distance is devised to compute the similarity of two face images the elastic matching is robust to small local distortions of the feature points such as those caused by facial expression variations in addition the use of the edge map gabor representations and the direction of the image gradient can all alleviate the effect of illumination to a certain extent with different databases experimental results show that our algorithm can always achieve a better performance than other face recognition algorithms under different conditions except when an image is under poor and uneven illumination experiments based on the yale database ar database orl database and yaleb database show that our proposed method can achieve recognition rates of 88 7 97 7 78 3 and 89 5 respectively

shape classification using line segment statistics in this study we use straight line segment statistics for shape analysis for each contour point we consider a continuous portion with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and stardard deviation contour shape description is an important field in computer vision this is due to the fact that shape is an important low level image feature in light of this many approaches have been proposed in order to analyze it therefore this paper introduces a very simple yet efficient shape descriptor based on straight line segment statistics for each contour point we consider a continuous portion of the contour with length equal to a pre defined percentage of the contour size then we compute the length of the straight line segment between its extreme points for the set of straight line segments we compute statistical moments average and standard deviation lastly we perform this calculation for different lengths of contour portions the proposed shape descriptor is a powerful tool for shape discrimination it is robust it can characterize a huge set of different classes of shapes and is tolerant to variations in the shapes scale and orientation classification results of the proposed method overcome traditional methods found in literature proving that it is an efficient tool for shape analysis

algorithms for strategyproof classification the strategyproof classification problem deals with a setting where a decision maker must classify a set of input points with binary labels while minimizing the expected error the labels of the input points are reported by self interested agents who might lie in order to obtain a classifier that more closely matches their own labels thereby creating a bias in the data this motivates the design of truthful mechanisms that discourage false reports in this paper we give strategyproof mechanisms for the classification problem in two restricted settings i there are only two classifiers and ii all agents are interested in a shared set of input points we show that these plausible assumptions lead to strong positive results in particular we demonstrate that variations of a random dictator mechanism that are truthful can guarantee approximately optimal outcomes with respect to any family of classifiers moreover these results are tight in the sense that they match the best possible approximation ratio that can be guaranteed by any truthful mechanism we further show how our mechanisms can be used for learning classifiers from sampled data and provide pac style generalization bounds on their expected error interestingly our results can be applied to problems in the context of various fields beyond classification including facility location and judgment aggregation

the global structure of constant mean curvature surfaces in a recent ground breaking paper kapouleas constructed this century s first examples of complete finite topology properly embedded surfaces with non zero constant mean curvature ka l geometrically these surfaces are quite easy to visualize as we explain below the purpose of the present paper is to characterize the extent to which kapouleas examples are typical of all embedded constant mean curvature surfaces first and throughout this paper we scale space so that the constant mean curvature the trace of the second fundamental form of our surface l is identically one and we call such a surface an mc1 surface the only complete embedded mc1 surfaces of finite topology known before kapouleas work arise from the 1parameter family of axially symmetric and periodic examples found by delaunay in 1841 using the maximum axial radius r of such a surface as a parameter this family begins with the cylinder r 1 and evolves through embedded periodic surfaces until the family degenerates to a linear chain of touching spheres r 2 the delaunay family continues for all r 2 as periodic immersions kapouleas construction of embedded surfaces begins with a piecewise linear graph in r 3 having the property that edges are either finite segments with length a multiple of 4 or half infinite rays and with the further property that at each vertex some linear combination of their direction vectors with positive coefficients adds to zero see fig 1 he constructs an approximate solution to the problem by centering radius r 2 spheres at all vertices and connecting these smoothly by delaunay segments having r 2 but near 2 with axes along the graph edges since the periods of the delaunay surfaces are slightly longer than 4 he must assume also a flexibility condition on the graph to guarantee that such a gluing

on three dimensional surface reconstruction methods a survey is presented of some of the surface reconstruction methods that can be found in the literature the focus is on a small recent and important subset of the published reconstruction techniques the techniques are classified based on the surface representation used implicit versus explicit functions a study is made of the important aspects of the surface reconstruction techniques one aspect is the viewpoint invariance of the methods this is an important property if object recognition is the ultimate objective the robustness of the various methods is examined it is determined whether the parameter estimates are biased and the sensitivity to obscuration is addressed the latter two aspects are particularly important for fitting functions in the implicit form a detailed description is given of a parametric reconstruction method for three dimensional object surfaces that involves numeric grid generation techniques and variational principle formulations this technique is invariant to rigid motion in dimensional space

worst case and probabilistic analysis of a geometric location problem we consider the problem of choosing k medians among n points on the euclidean plane such that the sum of the distances from each of the n points to its closest median is minimized we show that this problem is np complete we also present two heuristics that produce arbitrarily good solutions with probability going to 1 one is a partition heuristic and works when k grows linearly or almost so with n the other is the honeycomb heuristic and is applicable to rates of growth of k of the form k sim n varepsilon 0 varepsilon 1

an overview of representative problems in location research we present a survey of over 50 representative problems in location research our goal is not to review all variants of different location models or to describe solution results but rather to provide a broad overview of major location problems that have been studied indicating briefly how they are formulated and how they relate to one another we review standard problems such as median center and warehouse location problems as well as less traditional location problems which have emerged in recent years our primary focus is on problems for which operations research type models have been developed most of the problems we review have been formulated as optimization problems

using spin images for efficient object recognition in cluttered 3d scenes we present a 3d shape based object recognition system for simultaneous recognition of multiple objects in scenes containing clutter and occlusion recognition is based on matching surfaces by matching points using the spin image representation the spin image is a data level shape descriptor that is used to match surfaces represented as surface meshes we present a compression scheme for spin images that results in efficient multiple object recognition which we verify with results showing the simultaneous recognition of multiple objects from a library of 20 models furthermore we demonstrate the robust performance of recognition in the presence of clutter and occlusion through analysis of recognition trials on 100 scenes

symmetry seeking models and 3d object reconstruction we propose models of 3d shape which may be viewed as deformable bodies composed of simulated elastic material in contrast to traditional purely geometric models of shape deformable models are active their shapes change in response to externally applied forces we develop a deformable model for 3d shape which has a preference for axial symmetry symmetry is represented even though the model does not belong to a parametric shape family such as generalized cylinders rather a symmetry seeking property is designed into internal forces that constrain the deformations of the model we develop a framework for 3d object reconstruction based on symmetry seeking models instances of these models are formed from monocular image data through the action of external forces derived from the data the forces proposed in this paper deform the model in space so that the shape of its projection into the image plane is consistent with the 2d silhouette of an object of interest the effectiveness of our approach is demonstrated using natural images

generalized correlation for shape alignment ordered set valued functions are introduced in this study to represent arbitrary shapes in a simple manner the arithmetic of ordered set valued functions is meaningless hence a novel concept namely generalized correlation is proposed to handle shape alignment problems generalized correlation is an extension of correlation from single valued functions to ordered set valued functions it is especially designed for shape alignment but not for a general mathematical definition moreover efficient algorithms are proposed to compute generalized correlation in 2d and 3d cases experiments indicate that the proposed alignment methods converge rapidly and globally furthermore generalized correlation is used handle registration problems to demonstrate its potential in computer vision tasks

relaxation of the condorcet and simpson conditions in voting location abstract a condorcet point in voting location is a location point such that there is no other closer to more than half of the users however such condorcet solution does not necessarily exist this concept is based on two assumptions first two locations are indifferent only if they are at the same distance of the voter second the number of voters needed to reject a location is more than half of them we relax the condorcet condition in two ways first by considering that two locations are indifferent for every user if the difference of the distances to them is within a positive threshold secondly by considering that the proportion of users needed to reject a location is not one half we consider the resulting new solution concepts that arise by applying both relaxations at the same time and develop algorithms for obtaining them in the finite case

an axiomatic approach to location on networks the problem under consideration is that of locating a facility on a tree network given data specifying the locations of the users on the network the approach taken is to formulate axioms that require consistent response of the solution to variations in the users location data it is shown that three independent axioms determine together a unique solution located at the point that minimizes the sum of the squares of the distances to the users

a visual shape descriptor using sectors and shape context of contour lines this paper describes a visual shape descriptor based on the sectors and shape context of contour lines to represent the image local features used for image matching the proposed descriptor consists of two component feature vectors first the local region is separated into sectors and their gradient magnitude and orientation values are extracted a feature vector is then constructed from these values second local shape features are obtained using the shape context of contour lines another feature vector is then constructed from these contour lines the proposed approach calculates the local shape feature without needing to consider the edges this can overcome the difficulty associated with textured images and images with ill defined edges the combination of two component feature vectors makes the proposed descriptor more robust to image scale changes illumination variations and noise the proposed visual shape descriptor outperformed other descriptors in terms of the matching accuracy 14 525 better than sift 21 better than pca sift 11 86 better than gloh and 25 66 better than the shape context

geometry and topology of some overdetermined elliptic problems we study necessary conditions on the geometry and the topology of domains in r2 that support a positive solution to a classical overdetermined elliptic problem u f u 0in u 0on u constanton the ideas and tools we use come from constant mean curvature surface theory in particular we obtain a partial answer to a question posed by h berestycki l caffarelli and l nirenberg in 1997 we investigate also some boundedness properties of the solution u some of our results generalize to higher dimensions

a structural approach to representation of curved objects abstract representation of complex curved objects is still a challenging and difficult problem in this paper we present a scheme for multi level structural qualitative representation of object surfaces the analysis begins with local face based descriptions of object surfaces surface primitive graphs and global high level structural and qualitative features are derived from these local descriptions the final descriptions global feature graphs are based on the quasi convexity concavity structures incorporating quantized directional features of closed boundaries of cross sections along several directions the global feature graphs have the following properties 1 they provide a characterization of global structural qualitative properties of the object 2 the graphs are composed of a few components nodes and edges with rich features and give compact descriptions of the objects 3 the global feature graph representations are robust and qualitative in that they are not affected by geometrical quantitative properties of the shape such as curvatures length and position 4 the representation has clear and rigorous properties furthermore we present some theoretical basis for object recognition using the global features graphs

constant mean curvature surfaces with three ends abstract we announce the classification of complete almost embedded surfaces of constant mean curvature with three ends and genus zero they are classified by triples of points on the sphere whose distances are the asymptotic necksizes of the three ends

invariant descriptors for 3d object recognition and pose invariant descriptors are shape descriptors that are unaffected by object pose by perspective projection or by the intrinsic parameters of the camera these descriptors can be constructed using the methods of invariant theory which are briefly surveyed a range of applications of invariant descriptors in 3d model based vision is demonstrated first a model based vision system that recognizes curved plane objects irrespective of their pose is demonstrated curves are not reduced to polyhedral approximations but are handled as objects in their own right models are generated directly from image data once objects have been recognized their pose can be computed invariant descriptors for 3d objects with plane faces are described all these ideas are demonstrated using images of real scenes the stability of a range of invariant descriptors to measurement error is treated in detail

3d face recognition with sparse spherical representations this paper addresses the problem of 3d face recognition using simultaneous sparse approximations on the sphere the 3d face point clouds are first aligned with a fully automated registration process they are then represented as signals on the 2 sphere in order to preserve depth and geometry information next we implement a dimensionality reduction process with simultaneous sparse approximations and subspace projection it permits to represent each 3d face by only a few spherical functions that are able to capture the salient facial characteristics and hence to preserve the discriminant facial information we eventually perform recognition by effective matching in the reduced space where linear discriminant analysis can be further activated for improved recognition performance the 3d face recognition algorithm is evaluated on the frgc v 1 0 data set where it is shown to outperform classical state of the art solutions that work with depth images

centers in connected undirected graphs an axiomatic approach a center is a function that associates with every finite connected and undirected graph a nonempty subset of its vertices these functions play an important role in networks such as social or interorganizational networks centers capture notions like being a focal point of communication being strategically located ability and willingness to participate in strategic alliances and the like we focus on the conceptual issue of what makes a position in a graph a central one and investigate some possible concepts of centrality in relation to various properties characterizations of the uncovered center the median and degree center are presented where each of these centers is defined for arbitrary connected undirected simple and possibly cyclic graphs

a fast and robust local descriptor for 3d point cloud registration this paper proposes a novel local feature descriptor called a local feature statistics histogram lfsh for efficient 3d point cloud registration an lfsh forms a comprehensive description of local shape geometries by encoding their statistical properties on local depth point density and angles between normals the sub features in the lfsh descriptor are low dimensional and quite efficient to compute in addition an optimized sample consensus osac algorithm is developed to iteratively estimate the optimum transformation from point correspondences osac can handle the challenging cases of matching highly self similar models based on the proposed lfsh and osac a coarse to fine algorithm can be formed for 3d point cloud registration experiments and comparisons with the state of the art descriptors demonstrate that lfsh is highly discriminative robust and significantly faster than other descriptors meanwhile the proposed coarse to fine registration algorithm is demonstrated to be robust to common nuisances including noise and varying point cloud resolutions and can achieve high accuracy on both model data and scene data

localizing overlapping parts by searching the interpretation tree this paper discusses how local measurements of positions and surface normals may be used to identify and locate overlapping objects the objects are modeled as polyhedra or polygons having up to six degrees of positional freedom relative to the sensors the approach operates by examining all hypotheses about pairings between sensed data and object surfaces and efficiently discarding inconsistent ones by using local constraints on distances between faces angles between face normals and angles relative to the surface normals of vectors between sensed points the method described here is an extension of a method for recognition and localization of nonoverlapping parts previously described in 18 and 15

on maximal entries in the principal eigenvector of graphs abstract for an undirected connected graph it is well known that an eigenvector belonging to the principal eigenvalue of g can be given such that all entries are positive we ask whether this vector carries information on the structure of the graph and approach this question by investigating the values that can occur in its maximal entry

registration of partially overlapping surfaces by rejection of false point correspondences we present a new algorithm for the registration of three dimensional partially overlapping surfaces it is based on an efficient scheme for the rejection of false point correspondences correspondence outliers and does not require initial pose estimation or feature extraction an initial list of corresponding points is first derived using the regional properties of vertices on both surfaces from these point correspondences pairs of corresponding rigid triplets are formed the normal vectors at the vertices of each corresponding triplet are used to compute the candidate rotations by clustering the candidate rotation axes and candidate rotation angles separately a large number of false correspondences are eliminated and an approximate rotation is decided from which an approximate translation is also obtained finally the optimal transformation parameters are determined by further refining the estimated parameters in an iterative manner mathematical analysis and experimental results show that the registration process is fast and accurate even when the objects are regularly shaped and contain many regionally similar surface patches

distance weighted voting and a single facility location problem abstract we generalize the notion of a condorcet point of a network by allowing an individual s vote to be weighted by an integral power of his her distance from a facility to be sited we show that on a tree network this generalized condorcet point coincides with the solution of a certain nonlinear single facility location problem this result may be viewed as a generalization of an earlier result due to hansen and thisse 1985 we also give a polynomial algorithm for solving this nonlinear location problem

a double annealing algorithm for discrete location allocation problems abstract many algorithms inspired by the simulated annealing paradigm for approximately solving combinatorial optimization problems have been presented and tested in the last years the aim of this paper is to present a double annealing algorithm a new idea for the application of annealing based algorithms to discrete location allocation problems with two mutuallu dependent sets of binary variables the double annealing algorithm consists of two annealing processes synchronized with each other each process is executed on a different subset of variables and with a different annealing parameter temperature and the synchronization depends on the saturation of the two variable subsets in order to improve such synchronization deannealing steps are also performed the double annealing algorithm is quite robust and easy to tune it is rather insensitive to the initial values of the annealing parameters and to the initialization and it is able to achieve good approximate solutions the experiments were done on the p median problem

winner imposing strategyproof mechanisms for multiple facility location games we study facility location games where a number of facilities are placed in a metric space based on locations reported by strategic agents a mechanism maps the agents locations to a set of facilities the agents seek to minimize their connection cost namely the distance of their true location to the nearest facility and may even misreport their location we are interested in mechanisms that are strategyproof i e ensure that no agent can benefit from misreporting her location do not resort to monetary transfers and approximate the optimal social cost we focus on the closely related problems of k facility location and facility location with a uniform facility opening cost instead of a bound of k on the number of facilities in the former the social cost is the agents total connection cost while in the latter the social cost is the sum of the total connection cost and the total facility opening cost we mostly study mechanisms that are winner imposing in the sense that they allocate facilities to agents and require that each agent allocated a facility should connect to it we prove that the winner imposing version of the proportional mechanism proposed by lu et al 2010 18 is stategyproof for the k facility location game and achieves an approximation ratio of at most 4k for any k 1 for the facility location game we show that the winner imposing version of the randomized online algorithm of meyerson 2001 21 which has an approximation ratio of 8 is strategyproof furthermore we present a deterministic non imposing group strategyproof o logn approximate mechanism for the facility location game on the line we also consider oblivious winner imposing mechanisms for location games on continuous metric spaces and show that they are strategyproof iff they are locally strategyproof i e no agent can benefit by reporting a location arbitrarily close to her true location

an axiomatic characterization of a class of locations in tree networks in this paper we describe four axioms that uniquely characterize the class of locations in tree networks that are obtained by minimizing an additively separable nonnegative nondecreasing differentiable and strictly convex function of distances this result is analogous to results that have been obtained in the theory of bargaining social choice and fair resource allocation

characterizations of the 3 cycle count and backward length of a tournament measures of inconsistency or difference between a set of pairwise comparisons and the final ranking of alternatives give valuable and useful information in this paper we present characterizations of two such measures the 3 cycle count and the backward length the characterizations provide insight into what exactly is measured and how measures differ in processing adjustments in a tournament

shape classification by manifold learning in multiple observation spaces manifold learning is a non linear method with the aim of finding a constructive way to embed the data from a high dimensional space into a low dimensional one the improvement of shape classification is the major approach in this paper which is based on the continuity in feature space in accordance with the continuity in semantic one in this regard a non linear approach is employed to map the shape feature vectors to a new space while their semantics become similar with human opinion the euclidean distance between two feature vectors would be closed shapes are described by four contour based and region based techniques by the proposed method in other word they are described in four observation spaces furthermore a parameter space is learnt from multiple observation spaces based on fusion of dissimilarities in a supervised manner experimental results show the validity and efficiency of the proposed approach for shape classification over a variety of standard shape datasets

a spherical representation for recognition of free form surfaces introduces a new surface representation for recognizing curved objects the authors approach begins by representing an object by a discrete mesh of points built from range data or from a geometric model of the object the mesh is computed from the data by deforming a standard shaped mesh for example an ellipsoid until it fits the surface of the object the authors define local regularity constraints that the mesh must satisfy the authors then define a canonical mapping between the mesh describing the object and a standard spherical mesh a surface curvature index that is pose invariant is stored at every node of the mesh the authors use this object representation for recognition by comparing the spherical model of a reference object with the model extracted from a new observed scene the authors show how the similarity between reference model and observed data can be evaluated and they show how the pose of the reference object in the observed scene can be easily computed using this representation the authors present results on real range images which show that this approach to modelling and recognizing 3d objects has three main advantages 1 it is applicable to complex curved surfaces that cannot be handled by conventional techniques 2 it reduces the recognition problem to the computation of similarity between spherical distributions in particular the recognition algorithm does not require any combinatorial search and 3 even though it is based on a spherical mapping the approach can handle occlusions and partial views

global shape invariants a solution for 3d free form object discrimination identification problem abstract a method for solving the 3d object recognition problem is described in this paper the method uses a new set of global features as discriminant parameters the general purpose of our approach is to achieve simplicity speed and efficiency by using global invariants for this two new global parameters are introduced which are invariant to rotation translation and scaling canonical length cl which provides an indirect measurement of object surface and weighted principal directions wpds corresponding to the meaningful normal directions of the object surface abundant experimentation has been conducted with a real world system in order to validate the method

mechanism design for one facility location game with obnoxious effects on a line abstract in this paper we introduce obnoxious effects into obnoxious facility location games on a line where each agent i has a private location x i on a closed interval 0 1 and one facility will be built on a location y in the interval according to the bids of all the agents in addition there are two thresholds d 1 and d 2 in the utility function of each agent where 0 d 1 d 2 1 denote d y x i y x i to be the distance between agent i and the facility on the location y the utility function of agent i is 0 if d y x i is at most d 1 1 if d y x i is at least d 2 otherwise a linear increasing function between 0 and 1 each agent attempts to get the largest utility while the social welfare is to maximize the sum of all the agents utilities the classic obnoxious facility game 4 11 is a special case of our problem when d 1 0 and d 2 1 in this work we first study the hardness of approximate mechanism design on this generalized problem which states that our problem cannot admit any deterministic strategy proof mechanism with bounded approximation ratio if d 1 1 2 then we limit the thresholds to some ranges both deterministic and randomized strategy proof mechanisms are studied and the approximation ratios vary with the specific values of d 1 and d 2

multi view face identification and pose estimation using b spline interpolation the available face views in the training set are mostly limited in this paper we present a view interpolation method using nonlinear b spline on face manifolds two models the inner outer ellipse model and the moment of inertia model are developed to estimate the pose orientation we use the limited view pose face images to form the pose eigen space then based on these nonlinear manifolds we form a b spline for each individual identification is to compute the shortest euclidean distance from a given test view to the nearest point within one of these b splines once the test view is classified as a familiar individual in the training set not only can the individual be identified but also the pose angle can be estimated experimental results show that b spline interpolation can achieve a recognition rate of 95

a unified family of single server queueing location models in this paper we introduce a general class of single server network location models which includes the median center stochastic queue median stochastic queue center lp norm and other location problems in a single parametric framework the model incorporates both queueing effects and a cost function similar to a disutility function which is nonlinear in response time we develop a number of properties of this class of models and present a method for evaluating a range of different objective functions for any given problem the robustness of the median and center objectives as solution concepts is highlighted

robust point set registration using gaussian mixture models in this paper we present a unified framework for the rigid and nonrigid point set registration problem in the presence of significant amounts of noise and outliers the key idea of this registration framework is to represent the input point sets using gaussian mixture models then the problem of point set registration is reformulated as the problem of aligning two gaussian mixtures such that a statistical discrepancy measure between the two corresponding mixtures is minimized we show that the popular iterative closest point icp method and several existing point set registration methods in the field are closely related and can be reinterpreted meaningfully in our general framework our instantiation of this general framework is based on the the l2 distance between two gaussian mixtures which has the closed form expression and in turn leads to a computationally efficient registration algorithm the resulting registration algorithm exhibits inherent statistical robustness has an intuitive interpretation and is simple to implement we also provide theoretical and experimental comparisons with other robust methods for point set registration

structural indexing efficient 3 d object recognition the authors present an approach for the recognition of multiple 3 d object models from three 3 d scene data the approach uses two different types of primitives for matching small surface patches where differential properties can be reliably computed and lines corresponding to depth or orientation discontinuities these are represented by splashes and 3 d curves respectively it is shown how both of these primitives can be encoded by a set of super segments consisting of connected linear segments these super segments are entered into a table and provide the essential mechanism for fast retrieval and matching the issues of robustness and stability of the features are addressed in detail the acquisition of the 3 d models is performed automatically by computing splashes in highly structured areas of the objects and by using boundary and surface edges for the generation of 3 d curves the authors present results with the current system 3 d object recognition based on super segments and discuss further extensions

heterogeneous facility location without money the study of the facility location problem in the presence of self interested agents has recently emerged as the benchmark problem in the research on mechanism design without money in the setting studied in the literature so far agents are single parameter in that their type is a single number encoding their position on a real line we here initiate a more realistic model for several real life scenarios specifically we propose and analyze heterogeneous facility location without money a novel model wherein i we have multiple heterogeneous i e serving different purposes facilities ii agents locations are disclosed to the mechanism and iii agents bid for the set of facilities they are interested in as opposed to bidding for their position on the network we study the heterogeneous facility location problem under two different objective functions namely social cost i e sum of all agents costs and maximum cost for either objective function we study the approximation ratio of both deterministic and randomized truthful algorithms under the simplifying assumption that the underlying network topology is a line for the social cost objective function we devise an n 1 approximate deterministic truthful mechanism and prove a constant approximation lower bound furthermore we devise an optimal and truthful in expectation randomized algorithm as regards the maximum cost objective function we propose a 3 approximate deterministic strategyproof algorithm and prove a 3 2 approximation lower bound for deterministic strategyproof mechanisms furthermore we propose a 3 2 approximate randomized strategyproof algorithm and prove a 4 3 approximation lower bound for randomized strategyproof algorithms

continuous generalized procrustes analysis two dimensional shape models have been successfully applied to solve many problems in computer vision such as object tracking recognition and segmentation typically 2d shape models are learned from a discrete set of image landmarks corresponding to projection of 3d points of an object after applying generalized procustes analysis gpa to remove 2d rigid transformations however the standard gpa process suffers from three main limitations firstly the 2d training samples do not necessarily cover a uniform sampling of all the 3d transformations of an object this can bias the estimate of the shape model secondly it can be computationally expensive to learn the shape model by sampling 3d transformations thirdly standard gpa methods use only one reference shape which can might be insufficient to capture large structural variability of some objects to address these drawbacks this paper proposes continuous generalized procrustes analysis cgpa cgpa uses a continuous formulation that avoids the need to generate 2d projections from all the rigid 3d transformations it builds an efficient in space and time non biased 2d shape model from a set of 3d model of objects a major challenge in cgpa is the need to integrate over the space of 3d rotations especially when the rotations are parameterized with euler angles to address this problem we introduce the use of the haar measure finally we extended cgpa to incorporate several reference shapes experimental results on synthetic and real experiments show the benefits of cgpa over gpa highlightscontinuous formulation of the generalized procrustes analysis cgpa avoids the need to generate 2d projections from all 3d rigid transformations cgpa builds an efficient non biased 2d shape model from 3d objects cgpa uses the haar measure to integrate over the space of 3d rotations experimental results building 2d shape models for different public datasets

the topology and geometry of embedded surfaces of constant mean curvature si m est une surface proprement plongee dans r 3 avec une courbure moyenne constante non nulle alors m n est pas homeomorphe a une surface fermee avec un seul point elimine soit m une surface proprement plongee dans r 3 a courbure moyenne constante non nulle si m est homeomorphe a une surface fermee avec 2 points elimines alors m est une distance bornee a partir d une ligne droite soit m une surface proprement plongee de courbure moyenne non nulle qui est homeomorphe a une surface fermee avec 3 points elimines alors m reste une distance bornee a partir d un plan

three dimensional model based object recognition and segmentation in cluttered scenes viewpoint independent recognition of free form objects and their segmentation in the presence of clutter and occlusions is a challenging task we present a novel 3d model based algorithm which performs this task automatically and efficiently a 3d model of an object is automatically constructed offline from its multiple unordered range images views these views are converted into multidimensional table representations which we refer to as tensors correspondences are automatically established between these views by simultaneously matching the tensors of a view with those of the remaining views using a hash table based voting scheme this results in a graph of relative transformations used to register the views before they are integrated into a seamless 3d model these models and their tensor representations constitute the model library during online recognition a tensor from the scene is simultaneously matched with those in the library by casting votes similarity measures are calculated for the model tensors which receive the most votes the model with the highest similarity is transformed to the scene and if it aligns accurately with an object in the scene that object is declared as recognized and is segmented this process is repeated until the scene is completely segmented experiments were performed on real and synthetic data comprised of 55 models and 610 scenes and an overall recognition rate of 95 percent was achieved comparison with the spin images revealed that our algorithm is superior in terms of recognition rate and efficiency

approximately global optimization for robust alignment of generalized shapes in this paper we introduce a novel method to solve shape alignment problems we use gray scale images to represent source shapes and propose a novel two component gaussian mixture gm distance map representation for target shapes this asymmetric representation is a flexible image based representation which is able to represent different kinds of shape data including continuous contours unstructured sparse point sets edge maps and even gray scale gradient maps using this representation a new energy function based on a novel two component gaussian mixture distance model is proposed the new energy function was empirically evaluated to be a more robust shape dissimilarity metric that can be computed efficiently such high efficiency is essential for global optimization methods we adopt and modify one of them the particle swarm optimization pso to effectively estimate the global optimum of the new energy function differently from the original pso several new strategies were employed to make the optimization more robust and prevent it from converging prematurely the overall performance of the proposed framework as well as the properties of each algorithmic component were evaluated and compared with those of some state of the art methods extensive experiments and comparison performed on generalized 2d and 3d shape data demonstrate the robustness and effectiveness of the method

stable network topologies using the notion of covering abstract an alternative perspective to evaluate networks and network evolution is introduced based on the notion of covering for a particular node in a network covering captures the idea of being outperformed by another node in terms of for example visibility and possibility of information gathering in this paper we focus on networks where these subdued network positions do not exist we call these networks stable within this set we identify the minimal stable networks which frequently have a bubble like structure severing a link in such a network results in at least one of the nodes being covered in a minimal stable network therefore all nodes cooperate to avoid that one of the nodes ends up in a subdued position our results can be applied to for example the design of covert communication networks and the dynamics of social and information networks

similarity measures for convex polyhedra based on minkowski addition abstract in this paper we introduce and investigate similarity measures for convex polyhedra based on minkowski addition and inequalities for the mixed volume and volume related to the brunn minkowski theory all measures considered are invariant under translations furthermore some of them are also invariant under subgroups of the affine transformation group for the case of rotation and scale invariance we prove that to obtain the measures based on mixed volume it is sufficient to compute certain functionals only for a finite number of critical rotations the paper presents a theoretical framework for comparing convex shapes and contains a complexity analysis of the solution numerical implementations of the proposed approach are not discussed

automatic registration for 3d shapes using hybrid dimensionality reduction shape descriptions automatic registration for 3d shapes is an attractive problem in computer vision various registration algorithms based on different surface representations have been developed for this topic however most of the existing algorithms suffer from some limitations mainly related to discriminating similarity metric partially overlapping data and the robustness to resolution noise and occlusion in this research hybrid dimensionality reduction shape descriptions drsd are proposed for pair wise registration which aims to overcome these limitations based on recently emerging angle preserving parameterization techniques such as harmonic maps and abf 3d shapes are described in low dimension space with both local and global considerations therefore searching for correspondences verifying overlapping regions and calculating registration error all can be implemented in low dimension space moreover a large number of experiments using both real and synthetic images have been carried out to show the accuracy efficiency and robustness of the hybrid drsd algorithm

point set registration via particle filtering and stochastic dynamics in this paper we propose a particle filtering approach for the problem of registering two point sets that differ by a rigid body transformation typically registration algorithms compute the transformation parameters by maximizing a metric given an estimate of the correspondence between points across the two sets of interest this can be viewed as a posterior estimation problem in which the corresponding distribution can naturally be estimated using a particle filter in this work we treat motion as a local variation in pose parameters obtained by running a few iterations of a certain local optimizer employing this idea we introduce stochastic motion dynamics to widen the narrow band of convergence often found in local optimizer approaches for registration thus the novelty of our method is threefold first we employ a particle filtering scheme to drive the point set registration process second we present a local optimizer that is motivated by the correlation measure third we increase the robustness of the registration performance by introducing a dynamic model of uncertainty for the transformation parameters in contrast with other techniques our approach requires no annealing schedule which results in a reduction in computational complexity with respect to particle size as well as maintains the temporal coherency of the state no loss of information also unlike some alternative approaches for point set registration we make no geometric assumptions on the two data sets experimental results are provided that demonstrate the robustness of the algorithm to initialization noise missing structures and or differing point densities in each set on several challenging 2d and 3d registration scenarios