dealing with segmentation errors in region based stereo matching abstract graph based matching methods have been widely used in the areas of object recognition and stereo correspondence in this paper an algorithm to deal with segmentation errors in region based matching is proposed which consists of a preprocessing stage to the classical graph based matching algorithm some regions are merged and included in the matching process in order to avoid the differences in segmentation the selection of an appropriate similarity criterion to create the initial nodes in the graph and the use of approximative algorithms to find maximal cliques are important issues in order to reduce the computational burden the experimental results show that the method is robust enough in the presence of noise

metric dependence and asymptotic minimization of the expected number of critical points of random holomorphic sections we prove the main conjecture from douglas shiffman and zelditch 2006 concerning the metric dependence and asymptotic minimization of the expected number ncrit n hof critical points of random holomorphic sections of the nth tensor power of a positive line bundle the first non topological term in the asymptotic expansion of ncrit n h is the calabi functional multiplied by the constant 2 m which depends only on the dimension of the manifold we prove that 2 m is strictly positive in all dimensions showing that the expansion is non topological for all m and that the calabi extremal metric when it exists asymptotically minimizes ncrit n h

relaxation labeling in stereo image matching this paper outlines a method for solving the global stereovision matching problem using edge segments as the primitives a relaxation scheme is the technique commonly used by existing methods to solve this problem these techniques generally impose the following competing constraints similarity smoothness ordering and uniqueness and assume a bound on the disparity range the smoothness constraint is basic in the relaxation process we have verified that the smoothness and ordering constraints can be violated by objects close to the cameras and that the setting of the disparity limit is a serious problem this problem also arises when repetitive structures appear in the scene i e complex images where the existing methods produce a high number of failures we develop our approach from a relaxation labeling method 1 w j christmas j kittler m petrou structural matching in computer vision using probabilistic relaxation ieee trans pattern anal mach intell 17 8 1995 749 764 which allows us to map the above constraints the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem produced by the required fixation of a disparity limit consequently we improve the stereovision matching process a better performance of the proposed method is illustrated by comparative analysis against some recent global matching methods

scalar curvature and projective embeddings i we prove that a metric of constant scalar curvature on a polarised kahler manifold is the limit of metrics induced from a specific sequence of projective embeddings satisfying a condition introduced by h luo this gives as a corollary the uniqueness of constant scalar curvature kahler metrics in a given rational cohomology class the proof uses results in the literature on the asymptotics of the bergman kernel the arguments are presented in a general framework involving moment maps for two different group actions

relaxation by hopfield network in stereo image matching abstract this paper outlines a relaxation approach using the hopfield neural network for solving the global stereovision matching problem the primitives used are edge segments the similarity smoothness and uniqueness constraints are transformed into the form of an energy function whose minimum value corresponds to the best solution of the problem we combine two methods a optimization relaxation 1 and b relaxation merit 2 with the above three constraints mapped in an energy function the main contribution is made 1 by applying a learning strategy in the similarity constraint and 2 by introducing specific conditions to overcome the violation of the smoothness constraint and to avoid the serious problem arising from the required fixation of a disparity limit so we improve the stereovision matching process a better performance of the proposed method is illustrated with a comparative analysis against a classical relaxation method

correlations between zeros and supersymmetry in our previous work bsz2 we proved that the correlation functions for simultaneous zeros of random generalized polynomials have universal scaling limits and we gave explicit formulas for pair correlations in codimensions 1 and 2 the purpose of this paper is to compute these universal limits in all dimensions and codimensions first we use a supersymmetry method to express the n point correlations as berezin integrals then we use the wick method to give a closed formula for the limit pair correlation function for the point case in all dimensions

a sensitivity analysis algorithm for hierarchical decision models in this paper a comprehensive algorithm is developed to analyze the sensitivity of hierarchical decision models hdm including the analytic hierarchy process and its variants to single and multiple changes in the local contribution matrices at any level of the decision hierarchy the algorithm is applicable to all hdm that use an additive function to derive the overall contribution vector it is independent of pairwise comparison scales judgment quantification techniques and group opinion combining methods the allowable range region of perturbations contribution tolerance operating point sensitivity coefficient total sensitivity coefficient and the most critical decision element at a certain level are identified in the hdm sa algorithm an example is given to demonstrate the application of the algorithm and show that hdm sa can reveal information more significant and useful than simply knowing the rank order of the decision alternatives 2007 elsevier b v all rights reserved

assessing priority weights from subsets of pairwise comparisons in multiple criteria optimization problems using a set covering concept we explore the possibility and flexibility of selecting a subset of all possible pairs of comparisons to assess priority weights of the decision criteria different techniques offer different priority weights with different properties they are however interrelated when special subsets such as basic coverings elementary cycles and complete covering are considered this paper provides a framework for unifying existing assessment methods and offers some fundamental theorems which reveal the intricate relationships among the methods over the subsets

image matching using the windowed fourier phase a theoretical framework is presented in which windowed fourier phase wfp is introduced as the primary matching primitive zero crossings and peaks correspond to special values of the phase the wfp is quasi linear and dense and its spatial period and slope are controlled by the scale this framework has the following important characteristics 1 matching primitives are available almost everywhere to convey dense disparity information in every channel either coarse or fine 2 the false target problem is significantly mitigated 3 the matching is easier uniform and can be performed by a network suitable for parallel computer architecture 4 the matching is fast since very few iterations are needed in fact the wfp is so informative that the original signal can be uniquely determined up to a multiplicative constant by the wfp in any channel the use of phase as matching primitive is also supported by some existing psychophysical and neurophysiological studies an implementation of the proposed theory has shown good results from synthesized and natural images

critical points and supersymmetric vacua ii asymptotics and extremal metrics motivated by the vacuum selection problem of string m theory we study a new geometric invariant of a positive hermitian line bundle l h m over a compact kahler manifold the expected distribution k crit z of critical points dlog s z h 0 of a gaussian random holomorphic section s h 0 m l with respect to h it is a measure on m whose total mass is the average number n crit h of critical points of a random holomorphic section we are interested in the metric dependence of n crit h especially metrics h which minimize n crit h we concentrate on the asymptotic minimization problem for the sequence of tensor powers l n h n m of the line bundle and their critical point densities k critn z we prove that k critn z has a complete asymptotic expansion in n whose coefficients are curvature invariants of h the first two terms in the expansion of n crit hn are topological invariants of l m the third term is a topological invariant plus a constantm 2 depending only on the dimension m of m times the calabi functional r m 2 dv olh whereis the scalar curvature of the curvature form of h we give an integral formula form 2 and show by a computer assisted calculation thatm 2 0 for m 3 hence that n crit hn is asymptotically minimized by the calabi extremal metric when one exists we conjecture thatm 2 0 in all dimensions i e that the calabi extremal metric is always the asymptotic minimizer

distribution of zeros of random and quantum chaotic sections of positive line bundles we study the limit distribution of zeros of certain sequences of holomorphic sections of high powers m n of a positive holomorphic hermitian line bundle l over a compact complex manifold m our first result concerns random sequences of sections using the natural probability measure on the space of sequences of orthonormal bases s n j of h 0 m l n we show that for almost every sequence s n j the associated sequence of zero currents 1 n z s n j tends to the curvature form of l thus the zeros of a sequence of sections s n h 0 m l n chosen independently and at random become uniformly distributed our second result concerns the zeros of quantum ergodic eigenfunctions where the relevant orthonormal bases s n j of h 0 m l n consist of eigensections of a quantum ergodic map we show that also in this case the zeros become uniformly distributed

the geometric consistency index approximated thresholds abstract crawford and williams journal of mathematical psychology 29 1985 387 suggested for the row geometric mean method rgmm one of the most extended ahp s priorization procedure a measure of the inconsistency based on stochastic properties of a subjacent model in this paper we formalize this inconsistency measure hereafter called the geometric consistency index gci and provide the thresholds associated with it these thresholds allow us an interpretation of the inconsistency tolerance level analogous to that proposed by saaty multicriteria decision making the analytic hierarchy process new york 1980 for the consistency ratio cr used with the right eigenvector method in conventional ahp

remarks on classical invariant theory a uniform formulation applying to all classical groups simultaneously of the first fundamental theory of classical invariant theory is given in terms of the weyl algebra the formulation also allows skew symmetric as well as symmetric variables examples illustrate the scope of this formulation

extremal bundles on calabi yau threefolds we study constructions of stable holomorphic vector bundles on calabi yau threefolds especially those with exact anomaly cancellation which we call extremal by going through the known databases we find that such examples are rare in general and can be ruled out for the spectral cover construction for all elliptic threefolds we then introduce a general hartshorne serre construction and use it to find extremal bundles of general ranks and study their stability as well as computing their chern numbers based on both existing and our new constructions we revisit the dry conjecture for the existence of stable sheaves on calabi threefolds and provide theoretical and numerical evidence for its correctness our construction can be easily generalized to bundles with no extremal conditions imposed

novel types of sensitivity analysis for additive mcdm methods three novel types of sensitivity analysis are presented they determine the following 1 the sensitivity of a ranking to specific changes in the evaluations of all alternatives on certain criteria 2 the influence of specific changes in certain criterion scores of an alternative 3 the minimum modification of the weights required to make an alternative ranked first the use of these instruments is demonstrated by the results of a simulation experiment results show that the first and second type of sensitivity analysis enable to apply multiple criteria decision making mcdm methods in dynamic circumstances the third type of sensitivity analysis is demonstrated to be a tool to analyze the total weight space

local stability intervals in the analytic hierarchy process abstract this paper provides a sensitivity analysis of the judgements used in the analytic hierarchy process ahp in relation to the rank reversal produced in two different situations the selection of the best alternative p problem and the ranking of all the alternatives p problem in both cases under the supposition that we employ the row geometric mean method rgmm to determine the local priorities we obtain in the case of a single criterion a local stability interval for each judgement for each alternative and for the paired comparisons matrix which allow us to guarantee the best alternative and the ranking of all of them the p and p problems respectively with respect to these three situations judgement alternative and matrix and two problems p and p we also calculate a local stability index to detect the critical values of the resolution process both the local stability intervals and indexes are used as management tools in the final stage of the decision making process that is to say the exploitation phase especially in the negotiation process and the search for consensus between the actors

applications of frequency dependent wavelet shrinkage to analyzing quality of image registration a fundamental problem in medical imaging is to transport an atlas associated with a template image onto new data this is sometimes achieved by registering warping the template to the data and using the induced spatial deformation field to impose an atlas on the data there are a number of alignment techniques which bring two images in register however few studies have been done to quantitatively compare various warping methods in this paper we compare different wavelet space thresholding schemes uniform spatially and frequency adaptive bayesian and develop two approaches for quantitative evaluation of the performance of three nonaffine warping techniques and one affine polynomial 12 parameter registration on groups of data the results of the affine and nonaffine warps are evaluated both on structural magnetic resonance imaging mri data and on the corresponding functional positron emission tomography pet data using a quantitative approach based on the discrete wavelet transform using i

on the lower order terms of the asymptotic expansion of tian yau zelditch we compute the first three coefficients of the asymptotic expansion of tian yau zelditch we also prove that in general the fcth coefficient is a polynomial of the curvature and its derivative of weight k

chaotic analytic zero points exact statistics for those of a random spin state a natural statistical ensemble of 2j points on the unit sphere can be associated via the majorana representation with a random quantum state of spin j and an exact expression is obtained here for the general k point correlation function in this ensemble the pair correlation in the large j limit takes the relatively simple form where and is the angular separation of the pair of points on the sphere it appears from the numerical work of others that in this limit these statistics are typical of the zero points of analytic functions associated with chaotic quantum dynamical systems

supersymmetry for systems with unitary disorder circular ensembles a generalized hubbard stratonovitch transformation relating an integral over random unitary matrices to an integral over efetov s unitary model manifold is introduced this transformation adapts the supersymmetry method to disordered and chaotic systems that are modelled not by a hamiltonian but by their scattering matrix or time evolution operator in contrast to the standard method no saddle point approximation is made and no massive modes have to be eliminated this first paper on the subject applies the generalized hubbard stratonovitch transformation to dyson s circular unitary ensemble it is shown how a supersymmetric variant of the harish chandra itzykson zuber formula can be used to compute in the large n limit the n level correlation function for any n non trivial applications to random network models quantum chaotic maps and lattice gauge theory are expected

on the weil petersson volume and the first chern class of the moduli space of calabi yau manifolds in this paper we proved that the weil petersson volume of calabi yau moduli is a rational number we also proved that the integrations of the invariants of the ricci curvature of the weli petersson metric with respect to the weil petersson volume form are all rational numbers

a note on ahp group consistency for the row geometric mean priorization procedure abstract this work analyses the consistency in group decision making for the analytic hierarchy process ahp when using the weighted geometric mean method wgmm as the aggregation procedure the row geometric mean method rgmm as the priorization procedure and the geometric consistency index as the inconsistency measure the paper proves that the inconsistency of the group is smaller than the largest individual inconsistency this result complements that obtained by xu eur j oper res 126 2000 683 for the eigenvector priorization method em and its associated consistency index saaty multicriteria decision making the analytic hierarchy process mcgraw hill 1980 moreover our result guarantees that by using the rgmm priorization procedure the group priorities obtained through the aggregation of the individual priorities verify the requirement of consistency proposed in ahp methodology if the individual priorities also verify this requirement

dense features for semi dense stereo correspondence we present a new feature based algorithm for stereo correspondence most of the previous feature based methods match sparse features like edge pixels producing only sparse disparity maps our algorithm detects and matches dense features between the left and right images of a stereo pair producing a semi dense disparity map our dense feature is defined with respect to both images of a stereo pair and it is computed during the stereo matching process not a preprocessing step in essence a dense feature is a connected set of pixels in the left image and a corresponding set of pixels in the right image such that the intensity edges on the boundary of these sets are stronger than their matching error which is the difference in intensities between corresponding boundary pixels our algorithm produces accurate semi dense disparity maps leaving featureless regions in the scene unmatched it is robust requires little parameter tuning can handle brightness differences between images nonlinear errors and is fast linear complexity

a new methodology for sensitivity and stability analysis of analytic network models abstract in this paper we develop a methodology to study the sensitivity and the stability of models built using the analytic network process we study two types of stability core and solution stability the former deals with finding the region of the perturbation space in which the initial solution i e the alternative that is ranked first obtained from the anp model remains most preferred the latter deals with finding the regions of the perturbation space in which the solutions that were not initially most preferred i e alternatives that were not ranked first become most preferred i e they are ranked first the methodology consists of three stages generation of the perturbation space finding the boundaries of the regions in the perturbation space in which the different alternatives are ranked first and finding the stability regions

a new learning strategy for stereo matching derived from a fuzzy clustering method this paper presents an approach to the local stereo correspondence problem the primitives or features used are groups of collinear connected edge points called segments each segment has several associated attributes or properties we have verified that the differences of the attributes for the true matches cluster in a cloud around a center then for each current pair of primitives we compute a distance between the difference of its attributes and the cluster center the correspondence is established in the basis of the minimum distance criterion similarity constraint we have designed an image understanding system to learn the best representative cluster center for such purpose a new learning method is derived from the fuzzy c means fcm algorithm where the dispersion of the true samples in the cluster is taken into account through the mahalanobis distance this is the main contribution of this paper a better performance of the proposed local stereo matching learning method is illustrated with a comparative analysis between classical local methods without learning

stereo correspondence through feature grouping and maximal cliques the authors propose a method for solving the stereo correspondence problem the method consists of extracting local image structures and matching similar such structures between two images linear edge segments are extracted from both the left and right images each segment is characterized by its position and orientation in the image as well as its relationships with the nearby segments a relational graph is thus built from each image for each segment in one image as set of potential assignments is represented as a set of nodes in a correspondence graph arcs in the graph represent compatible assignments established on the basis of segment relationships stereo matching becomes equivalent to searching for sets of mutually compatible nodes in this graph sets are found by looking for maximal cliques the maximal clique best suited to represent a stereo correspondence is selected using a benefit function numerous results obtained with this method are shown

reliable and efficient pattern matching using an affine invariant metric we present a new pattern similarity measure that behaves well under affine transformations our similarity measure is useful for pattern matching since it is defined on patterns with multiple components satisfies the metric properties is invariant under affine transformations and is robust with respect to perturbation and occlusion we give an algorithm based on hierarchical subdivision of transformation space which minimises our measure under the group of affine transformations given two patterns in addition we present results obtained using an implementation of this algorithm

the geometry and matching of lines and curves over multiple views this paper describes the geometry of imaged curves in two and three views multi view relationships are developed for lines conics and non algebraic curves the new relationships focus on determining the plane of the curve in a projective reconstruction and in particular using the homography induced by this plane for transfer from one image to another it is shown that given the fundamental matrix between two views and images of the curve in each view then the plane of a conic may be determined up to a two fold ambiguity but local curvature of a curve uniquely determines the plane it is then shown that given the trifocal tensor between three views this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third simple expressions are developed for the plane and homography in each case a set of algorithms are then described for automatically matching individual line segments and curves between images the algorithms use both photometric information and the multiple view geometric relationships for image pairs the homography facilitates the computation of a neighbourhood cross correlation based matching score for putative line curve correspondences for image triplets cross correlation matching scores are used in conjunction with line curve transfer based on the trifocal geometry to disambiguate matches algorithms are developed for both short and wide baselines the algorithms are robust to deficiencies in the segment extraction and partial occlusion experimental results are given for image pairs and triplets for varying motions between views and for different scene types the methods are applicable to line curve matching in stereo and trinocular rigs and as a starting point for line curve matching through monocular image sequences

critical points and supersymmetric vacua i supersymmetric vacua universes of string m theory may be identified with certain critical points of a holomorphic section the superpotential of a hermitian holomorphic line bundle over a complex manifold an important physical problem is to determine how many vacua there are and how they are distributed as the superpotential varies over physically relevant ensembles in several papers over the last few years m r douglas and co workers have studied such vacuum statistics problems for a variety of physical models at the physics level of rigor do ad dd the present paper is the first of a series by the present authors giving a rigorous mathematical foundation for the vacuum statistics problem it sets down basic results on the statistics of critical points s 0 of random holomorphic sections of hermitian holomorphic line bundles with respect to a metric connection when the sections are endowed with a gaussian measure the principal results give formulas for the expected density and number of critical points of fixed morse index of gaussian random sections relative to they are particularly concrete for riemann surfaces in our subsequent work the results will be applied to the vacuum statistics problem and to the purely geometric problem of studying metrics which minimize the expected number of critical points

consistency stability intervals for a judgement in ahp decision support systems abstract this paper focuses on the need to evaluate the consistency of human judgements in decision support systems dss in this sense and in the context of one of the most applied multicriteria methodologies the analytic hierarchy process ahp we obtain the consistency stability interval csi associated with each judgement that is to say the interval in which this can oscillate without exceeding a value of the consistency measure fixed in advance to calculate these csis we consider the row geometric mean method as the priorisation procedure the geometric consistency index as the consistency measure and a local situation with one criterion the proposed procedure has been implemented in a module that is easily adaptable to any decision support system based on ahp

psychophysical and computational studies towards a theory of human stereopsis psychophysical studies are described which pose a strong challenge to models of human stereopsis based on the processing of disparity information within independent spatial frequency tuned binocular channels these studies support instead the proposal that the processes of human binocular combination integrally relate the extraction of disparity information with the construction of raw primal sketch assertions this proposal implies global binocular combination rules using principles of figural continuity and cross channel correspondence to disambiguate local matches found independently within spatial frequency channels exploratory small scale computational experiments with stereo algorithms based on these rules are described and found to be successful in dealing with a variety of stereo inputs the constraints presented by objects which are exploited by these algorithms are discussed

universality and scaling of correlations between zeros on complex manifolds we study the limit as n of the correlations between simultaneous zeros of random sections of the powers l n of a positive holomorphic line bundle l over a compact complex manifold m when distances are rescaled so that the average density of zeros is independent of n we show that the limit correlation is independent of the line bundle and depends only on the dimension of m and the codimension of the zero sets we also provide some explicit formulas for pair correlations in particular we prove that hannay s limit pair correlation function for su 2 polynomials holds for all compact riemann surfaces

geometric constraints and stereo disparity computation most stereo techniques compute disparity assuming that it varies slowly along surfaces we quantify and justify this assumption using weak assumptions about surface orientation distributions in the world to derive the density of disparity surface orientations the small disparity change assumption is justified by the orientation density s heavy bias toward disparity surfaces that are nearly parallel to the image plane in addition the bias strengthens with smaller baselines larger focal lengths and as surfaces move farther from the cameras to analyze current stereo techniques we derive three densities from the first density those of the disparity gradient magnitude the directional derivative of disparity and the difference in disparity between neighboring surface points the latter may be used in bayesian algorithms computing dense disparity fields the directional derivative density and the disparity difference density both show that feature based algorithms should strongly favor small disparity changes contrary to several well known algorithms finally we use our original surface orientation density and the gradient magnitude density to derive two new surfaces from stereo techniques techniques combining feature based matching and surface reconstruction the first uses the densities to severely restrict the search range for the optimum fit the second incorporates the surface orientation density into the optimization criteria producing a bayesian formulation both algorithms are shown to be efficient and effective

representing stereo data with the delaunay triangulation abstract this article proposes a coherent way of interpolating three dimensional data obtained by stereo for example with a simplicial polyhedral surface the proposed method is based on the use of the constrained delaunay triangulation the polyhedral surface is obtained by using a simple visibility property to mark tetrahedra likely to be empty the method is intrinsically discontinuity preserving works for multiple viewpoints and yields both a surface representation of objects and a volume representation of free space which may be useful in robotics algorithms to implement the method are described and their complexity analyzed in the worst case and average case situations where tools of probabilistic geometry are used

intensity and gradient based stereo matching using hierarchical gaussian basis functions we propose a stereo correspondence method by minimizing intensity and gradient errors simultaneously in contrast to conventional use of image gradients the gradients are applied in the deformed image space although a uniform smoothness constraint is imposed it is applied only to nonfeature regions to avoid local minima in the function minimization we propose to parameterize the disparity function by hierarchical gaussians both the uniqueness and the ordering constraints can be easily imposed in our minimization framework besides we propose a method to estimate the disparity map and the camera response difference parameters simultaneously experiments with various real stereo images show robust performances of our algorithm

multicriteria procedural rationality on sisdema abstract this paper considers the application under the multicriteria procedural rationality paradigm mprp of two environmental selection tools included in the priorization module prior of the sisdema decisional system preference structures and stability intervals these tools apart from being used in analysing the robustness of the model allow us to obtain some critical points of the environmental decision making process dmp which will be employed in the negotiation and consensus building process between the actors involved in the resolution of the problem

a new look at independence the concentration of measure phenomenon in product spaces is a farreaching abstract generalization of the classical exponential inequalities for sums of independent random variables we attempt to explain in the simplest possible terms the basic concepts underlying this phenomenon the basic method to prove concentration inequalities and the meaning of several of the most useful inequalities

critical points and supersymmetric vacua iii string m models a fundamental problem in contemporary string m theory is to count the number of inequivalent vacua satisfying constraints in a string theory model this article contains the first rigorous results on the number and distribution of supersymmetric vacua of type iib string theories compactified on a calabi yau 3 fold x with flux in particular complete proofs of the counting formulas in ashok douglas ad and denef douglas dd1 are given together with van der corput style remainder estimates

hierarchical stereo and motion correspondence using feature groupings hierarchical feature based stereo matching and motion correspondence algorithms are presented the hierarchy consists of lines vertices edges and surfaces matching starts at the highest level of the hierarchy surfaces and proceeds to the lowest lines higher level features are easier to match because they are fewer in number and more distinct in form these matches then constrain the matches at lower levels perceptual and structural relations are used to group matches into islands of certainty a truth maintenance system tms is used to enforce grouping constraints and eliminate inconsistent match groupings the tms is also used to carry out belief revisions necessitiated by additions deletions and confirmations of feature and match hypotheses

asymptotics and dimensional dependence of the number of critical points of random holomorphic sections we prove two conjectures from dsz2 dsz3 concerning the expected number of critical points of random holomorphic sections of a positive line bundle we show that on average the critical points of minimal morse index are the most plentiful for holomorphic sections of mathcal o n to mathbb cp m and in an asymptotic sense for those of line bundles over general kahler manifolds we calculate the expected number of these critical points for the respective cases and use these to obtain growth rates and asymptotic bounds for the total expected number of critical points in these cases this line of research was motivated by landscape problems in string theory and spin glasses

scaled correlations of critical points of random sections on riemann surfaces in this paper we prove that as n goes to infinity the scaling limit of the correlation between critical points z1 and z2 of random holomorphic sections of the n th power of a positive line bundle over a compact riemann surface tends to 2 3 2 for small sqrt n z 1 nobreak z 2 the scaling limit is directly calculated using a general form of the kac rice formula and formulas and theorems of pavel bleher bernard shiffman and steve zelditch

gauss bonnet chern theorem on moduli space in this paper we prove a gauss bonnet chern type theorem in full generality for the chern weil forms of hodge bundles that is the chern weil forms compute the corresponding chern classes this settles a long standing problem second we apply the result to calabi yau moduli and proved the corresponding gauss bonnet chern type theorem in the setting of weil petersson geometry as an application of our results in string theory we prove that the number of flux vacua of type ii string compactified on a calabi yau manifold is finite and their number is bounded by an intrinsic geometric quantity

a model for the relative importance of the criteria in the multiplicative ahp and smart abstract we define the relative importance of any pair of criteria as the substitution rate between the relative gains and losses of the alternatives when we move along an indifference curve under the geometric mean aggregation rule in the multiplicative ahp and under the arithmetic mean aggregation rule in smart the relative not the marginal substitution rate depends neither on the performance of the alternatives under the remaining criteria nor on the units of performance measurement hence it provides a sound argument for distributed decision making processes where those who judge the criteria are not the same actors as those who assess the performance of the alternatives the definition has a plausible basis in the psycho physical research on the relationship between physical stimuli and sensory responses which shows that human beings are sensitive not to marginal but to relative changes of the stimulus intensities

image based rendering using parameterized image varieties this paper addresses the problem of characterizing the set of all images of a rigid set of m points and n lines observed by a weak perspective or paraperspective camera by taking explicitly into account the euclidean constraints associated with calibrated cameras we show that the corresponding image space can be represented by a six dimensional variety embedded in cal r 2 m n and parameterized by the image positions of three reference points the coefficients defining this parameterized image variety or piv for short can be estimated from a sample of images of a scene via linear and non linear least squares the piv provides an integrated framework for using both point and line features to synthesize new images from a set of pre recorded pictures image based rendering the proposed technique does not perform any explicit three dimensional scene reconstruction but it supports hidden surface elimination texture mapping and interactive image synthesis at frame rate on ordinary pcs it has been implemented and extensively tested on real data sets

new measurements and corner guidance for curve matching with probabilistic relaxation reliable curve matching is a difficult yet important problem in many vision based applications including image based modeling we describe in this paper two aspects of our research in this area a new algorithm for curve matching including lines within a probabilistic relaxation framework and an approach of incorporating previously matched points corners to guide curve matching we propose similarity invariant unary and binary measurements suitable for curves and introduce an additional measurement to model the uncertainty of the binary measurements the uncertainty measure is proven to be very important in computing the matching support from neighboring matches we also show how to use a set of previously matched points corners to guide the curve matching the role of the corner guidance is explicitly modeled by a set of unary measurements and a similarity function under the same relaxation framework preprocessing techniques contributing to the success of our curve matching techniques are also developed and discussed experiments with complex real scenes show that the rate of correct matching is higher than 98

uncertainty propagation and the matching of junctions as feature groupings the interpretation of the 3d world from image sequences requires the identification and correspondences of key features in the scene we describe a robust algorithm for matching groupings of features related to the objects in the scene we consider the propagation of uncertainty from the feature detection stage through the grouping stage to provide a measure of uncertainty at the matching stage we focus upon indoor scenes and match junctions which are groupings of line segments that meet at a single point a model of the uncertainty in junction detection is described and the junction uncertainty under the epipolar constraint is determined junction correspondence is achieved through matching of each line segment associated with the junction a match likelihood is then derived based upon the detection uncertainties and then combined with information on junction topology to create a similarity measure a robust matching algorithm is proposed and used to match junctions between pairs of images the presented experimental results on real images show that the matching algorithm produces sufficiently reliable results for applications such as structure from motion

efficient registration of stereo images by matching graph descriptions of edge segments we present a new approach to the stereo matching problem images are individually described by aneighborhood graph of line segments coming from a polygonal approximation of the contours the matching process is defined as the exploration of the largest components of adisparity graph built from the descriptions of the two images and is performed by an efficient prediction and propagation technique this approach was tested on a variety of man made environments and it appears to be fast and robust enough for mobile robot navigation and three dimensional part positioning applications