a fuzzy and bipolar approach to preference modeling with application to need and desire fuzziness and bipolarity allow representing human knowledge taking into account the gradual and the dialectic properties of language focusing on the meaning of concepts under this cognitive and linguistic approach we explore preference relations examining their semantic decomposition through fuzzy preference structures and the specification of meaningful opposites in particular we introduce the preference aversion p a model which allows analyzing under an independent aggregation methodology the possible gains and losses like pros and cons towards a given set of alternatives as an attractive feature of this proposal we show that the p a model allows distinguishing between need and desire contrary to common preference models where both notions are indistinguishable

reasoning about actions with imprecise and incomplete state descriptions this article is a first step in the direction of extending possibilistic planning to account for incomplete and imprecise knowledge of the world state fundamental definitions are given and the possibilistic planning problem is recast in this new setting finally it is shown that under certain conditions possibilistic planning with imprecise and incomplete state descriptions is no harder than possibilistic planning with crisp and complete information

an axiomatic approach to fuzzy preference modelling abstract we propose an axiomatic approach to the definition of fuzzy strict preference p indifference i and incomparability j associated with a fuzzy preference relation r expression for p i and j are given via solving two systems of functional equations

estimating the fundamental matrix via constrained least squares a convex approach in this paper a new method for the estimation of the fundamental matrix from point correspondences in stereo vision is presented the minimization of the algebraic error is performed while taking explicitly into account the rank two constraint on the fundamental matrix it is shown how this nonconvex optimization problem can be solved avoiding local minima by using recently developed convexification techniques the obtained estimate of the fundamental matrix turns out to be more accurate than the one provided by the linear criterion where the rank constraint of the matrix is imposed after its computation by setting the smallest singular value to zero this suggests that the proposed estimate can be used to initialize nonlinear criteria such as the distance to epipolar lines and the gradient criterion in order to obtain a more accurate estimate of the fundamental matrix

coherent continuous systems and the generalized functional equation of associativity a theory of coherent continuous systems is outlined systems are to be decomposed hierarchically into modules for this purpose some results on the structure of continuous functions are adapted to generalize the classic 3 modules theorem of binary systems consideration of the modular structure of coherent continuous systems leads naturally to the generalized functional equation of associativity ggu v w hu hv w involving four unknown 2 place continuous functions the functional equation is solved under some regularity conditions motivated by the properties of coherent continuous systems the solutions obtained give rise to generalized notions of parallel and series system structures

fuzzy logics as the logics of chains the paper proposes a formal delimitation of the class of fuzzy logics and answers some objections that can be raised against the definition the focus is put on informal and motivational aspects of the problem

solving quadratic distance problems an lmi based approach the computation of the minimum distance of a point to a surface in a finite dimensional space is a key issue in several system analysis and control problems the paper presents a general framework in which some classes of minimum distance problems are tackled via linear matrix inequality lmi techniques exploiting a suitable representation of homogeneous forms a lower bound to the solution of a canonical quadratic distance problem is obtained by solving a one parameter family of lmi optimization problems several properties of the proposed technique are discussed in particular tightness of the lower bound is investigated providing both a simple algorithmic procedure for a posteriori optimality testing and a structural condition on the related homogeneous form that ensures optimality a priori extensive numerical simulations are reported showing promising performances of the proposed method

universal approximation using radial basis function networks there have been several recent studies concerning feedforward networks and the problem of approximating arbitrary functionals of a finite number of real variables some of these studies deal with cases in which the hidden layer nonlinearity is not a sigmoid this was motivated by successful applications of feedforward networks with nonsigmoidal hidden layer units this paper reports on a related study of radial basis function rbf networks and it is proved that rbf networks having one hidden layer are capable of universal approximation here the emphasis is on the case of typical rbf networks and the results show that a certain class of rbf networks with the same smoothing factor in each kernel node is broad enough for universal approximation

on local triangle algebras abstract in this paper we have introduced the notion of local and semilocal triangle algebras and propose the theorems that characterize these algebraic structures additionally we have established the new properties of these algebraic structures and discussed the relations between local triangle algebras and some interval valued residuated lattice ivrl filters such as n fold ivrl extended integral filters and ivrl extended maximal filters the obtained results proved that the mtl triangle algebra is a subdirect product of local triangle algebras moreover a correlation was observed between the set of the dense elements and local triangle algebras finally semilocal triangle algebras were introduced and assessed in detail and an association was observed between the semilocal triangle algebras and quotient triangle algebras

a riemannian approach to graph embedding in this paper we make use of the relationship between the laplace beltrami operator and the graph laplacian for the purposes of embedding a graph onto a riemannian manifold to embark on this study we review some of the basics of riemannian geometry and explain the relationship between the laplace beltrami operator and the graph laplacian using the properties of jacobi fields we show how to compute an edge weight matrix in which the elements reflect the sectional curvatures associated with the geodesic paths on the manifold between nodes for the particular case of a constant sectional curvature surface we use the kruskal coordinates to compute edge weights that are proportional to the geodesic distance between points we use the resulting edge weight matrix to embed the nodes of the graph onto a riemannian manifold to do this we develop a method that can be used to perform double centring on the laplacian matrix computed from the edge weights the embedding coordinates are given by the eigenvectors of the centred laplacian with the set of embedding coordinates at hand a number of graph manipulation tasks can be performed in this paper we are primarily interested in graph matching we recast the graph matching problem as that of aligning pairs of manifolds subject to a geometric transformation we show that this transformation is pro crustean in nature we illustrate the utility of the method on image matching using the coil database

another paraconsistent algebraic semantics for lukasiewicz pavelka logic abstract as recently proved in a previous work of turunen tsoukias and ozturk starting from an evidence pair a b on the real unit square and associated with a propositional statement we can construct evidence matrices expressed in terms of four values t f k u that respectively represent the logical valuations true false contradiction both true and false and unknown neither true nor false regarding the statement the components of the evidence pair a b are to be understood as evidence for and against respectively moreover the set of all evidence matrices can be equipped with an injective mv algebra structure thus the set of evidence matrices can play the role of truth values of a lukasiewicz pavelka fuzzy logic a rich and applicable mathematical foundation for fuzzy reasoning and in such a way that the obtained new logic is paraconsistent in this paper we show that a similar result can be also obtained when the evidence pair a b is given on the real unit triangle since the real unit triangle does not admit a natural mv structure we introduce some mathematical results to show how this shortcoming can be overcome and another injective mv algebra structure in the corresponding set of evidence matrices is obtained also we derive several formulas to explicitly calculate the evidence matrices for the operations associated to the usual connectives

the pseudo linear semantics of interval valued fuzzy logics triangle algebras are equationally defined structures that are equivalent with certain residuated lattices on a set of intervals which are called interval valued residuated lattices ivrls triangle algebras have been used to construct triangle logic tl a formal fuzzy logic that is sound and complete w r t the class of ivrls in this paper we prove that the so called pseudo prelinear triangle algebras are subdirect products of pseudo linear triangle algebras this can be compared with mtl algebras prelinear residuated lattices being subdirect products of linear residuated lattices as a consequence we are able to prove the pseudo chain completeness of pseudo linear triangle logic ptl an axiomatic extension of tl introduced in this paper this kind of completeness is the analogue of the chain completeness of monoidal t norm based logic mtl this result also provides a better insight in the structure of triangle algebras it enables us amongst others to prove properties of pseudo prelinear triangle algebras more easily it is known that there is a one to one correspondence between triangle algebras and couples l a in which l is a residuated lattice and a an element in that residuated lattice we give a schematic overview of some properties of pseudo prelinear triangle algebras and a number of others that can be imposed on a triangle algebra and the according necessary and sufficient conditions on l and a

valued preference structures abstract an approach to the axiomatics of valued preference modelling is suggested in the framework of this approach general definitions of strict preference indifference and incomparability relations associated with a valued preference relation are established via solving a system of functional equations any solution of this system satisfies most of the classical properties characterizations of important particular solutions are also proved

variable domain fuzzy sets part i representation abstract despite the fact that fuzzy sets can generally have different domains standard definitions of fuzzy set operations assume a common reference set for all their operands the usual way to satisfy this precondition is to assign zero membership to elements outside the domain of each operand in part i of this two part paper we point out several issues with this method and argue that keeping track of the original domains is necessary to ensure the intended behavior of numerous fuzzy set operations we discuss several ways of representing fuzzy sets with variable domains preparing the grounds for the apparatus of variable domain fuzzy set theory described in part ii of the paper

uniqueness and estimation of three dimensional motion parameters of rigid objects with curved surfaces two main results are established in this paper first we show that seven point correspondences are sufficient to uniquely determine from two perspective views the three dimensional motion parameters within a scale factor for the translations of a rigid object with curved surfaces the seven points should not be traversed by two planes with one plane containing the origin nor by a cone containing the origin second a set of essential parameters are introduced which uniquely determine the motion parameters up to a scale factor for the translations and can be estimated by solving a set of linear equations which are derived from the correspondences of eight image points the actual motion parameters can subsequently be determined by computing the singular value decomposition svd of a 3 3 matrix containing the essential parameters

an algorithm for projective point matching in the presence of spurious points point matching is the task of finding correspondences between two sets of points such that the two sets of points are aligned with each other pure point matching uses only the location of the points to constrain the problem this is a problem with broad practical applications but it has only been well studied when the geometric transformation relating the two point sets is of a relatively low order here we present a heuristic local search algorithm that can find correspondences between point sets in two dimensions that are related by a projective transform point matching is a harder problem when spurious points appear in the sets to be matched we present a heuristic algorithm which minimizes the effects of spurious points

sequential updating of projective and affine structure from motion a structure from motion algorithm is described which recovers structure and camera position modulo a projective ambiguity camera calibration is not required and camera parameters such as focal length can be altered freely during motion the structure is updated sequentially over an image sequence in contrast to schemes which employ a batch process a specialisation of the algorithm to recover structure and camera position modulo an affine transformation is described together with a method to periodically update the affine coordinate frame to prevent drift over time we describe the constraint used to obtain this specialisation structure is recovered from image corners detected and matched automatically and reliably in real image sequences results are shown for reference objects and indoor environments and accuracy of recovered structure is fully evaluated and compared for a number of reconstruction schemes a specific application of the work is demonstrated affine structure is used to compute free space maps enabling navigation through unstructured environments and avoidance of obstacles the path planning involves only affine constructions

on v filters and normal v filters of a residuated lattice with a weak vt operator in this paper we study further the filter theory of residuated lattices first we discuss the concepts of filters and normal filters of residuated lattices and propose some equivalent conditions for them then we introduce and investigate the notions of v filter and normal v filter of a residuated lattice with a weak vt operator and lay bare the formulas for calculating the v filters and the normal v filters generated by subsets finally we show that the lattices of v filters and normal v filters of a residuated lattice with a vt operator are both complete brouwerian lattices

sequential subspace robustness assessment and sensitivity analysis to avoid an overconservative design and to ensure desired performance in an optimal way the product quality and robustness are considered in terms of the product performance mean and variance in this paper to facilitate robust design exploration under uncertainty a new sequential subspace robustness assessment method is presented to assess not only the mean and variance of performance but also their sensitivities with respect to design parameters the proposed method is based on the computational framework that integrates the univariate revolving integration and surrogate modeling of univariate integral functions the proposed framework enables consideration of bivariate interaction effects approximately by the aggregation of multiple revolving integration terms in a partial set of bivariate subspaces it is found that the proposed method provides better accuracy with comparable computational cost in assessing the statistical moments and sensitivities of product performance than existing methods suc

global propagation of affine invariant features for robust matching local invariant features have been successfully used in image matching to cope with viewpoint change partial occlusion and clutters however when these factors become too strong there will be a lot of mismatches due to the limited repeatability and discriminative power of features in this paper we present an efficient approach to remove the false matches and propagate the correct ones for the affine invariant features which represent the state of the art local invariance first a pair wise affine consistency measure is proposed to evaluate the consensus of the matches of affine invariant regions the measure takes into account both the keypoint location and the region shape size and orientation based on this measure a geometric filter is then presented which can efficiently remove the outliers from the initial matches and is robust to severe clutters and non rigid deformation to increase the correct matches we propose a global match refinement and propagation method that simultaneously finds a optimal group of local affine transforms to relate the features in two images the global method is capable of producing a quasi dense set of matches even for the weakly textured surfaces that suffer strong rigid transformation or non rigid deformation the strong capability of the proposed method in dealing with significant viewpoint change non rigid deformation and low texture objects is demonstrated in experiments of image matching object recognition and image based rendering

the value of the four values in his well known paper how computer should think belnap 1977 argues that four valued semantics is a very suitable setting for computerized reasoning in this paper we vindicate this thesis by showing that the logical role that the four valued structure has among ginsberg s bilattices is similar to the role that the two valued algebra has among boolean algebras specifically we provide several theorems that show that the most useful bilattice valued logics can actually be characterized as four valued inference relations in addition we compare the use of three valued logics with the use of four valued logics and show that at least for the task of handling inconsistent or uncertain information the comparison is in favor of the latter

filters of residuated lattices and triangle algebras an important concept in the theory of residuated lattices and other algebraic structures used for formal fuzzy logic is that of a filter filters can be used amongst others to define congruence relations specific kinds of filters include boolean filters and prime filters in this paper we define several different filters of residuated lattices and triangle algebras and examine their mutual dependencies and connections triangle algebras characterize interval valued residuated lattices

first order saddlepoint approximation for reliability analysis in the approximation methods of reliability analysis nonnormal random variables are transformed into equivalent standard normal random variables this transformation tends to increase the nonlinearity of a limit state function and hence results in less accurate reliability approximation the first order saddlepoint approximation for reliability analysis is proposed to improve the accuracy of reliability analysis by the approximation of a limit state function at the most likelihood point in the original random space and employment of the accurate saddlepoint approximation the proposed method reduces the chance of an increase in the nonlinearity of the limit state function this approach generates more accurate reliability approximation than the first order reliability method without an increase in the computational effort the effectiveness of the proposed method is demonstrated with two examples and is compared with the first and second order reliability methods

some properties of choice functions based on valued binary relations abstract choice functions based on t norms of valued binary relations are introduced strict preference is also specified with the use of a t norm properties of the choice functions are investigated and rationality conditions are studied some classical particular cases are presented

the standard completeness of interval valued monoidal t norm based logic in this paper we prove the strong standard completeness of interval valued monoidal t norm based logic ivmtl and some of its extensions for other extensions we show that they are not strong standard complete we also give a local deduction theorem for ivmtl and other extensions of interval valued monoidal logic similar results are obtained for interval valued fuzzy logics expanded with baaz s delta

enhanced two point diagonal quadratic approximation methods for design optimization abstract based on two point diagonal quadratic approximation referred to as tdqa developed by kim et al min soo kim jong rip kim jae young jeon dong hoon choi efficient mechanical system optimization using two point diagonal approximation in the nonlinear intervening variable space j ksme 15 2001 1257 126 enhanced two point approximation methods are proposed in this paper the suggested methods reinforce tdqa with new quadratic correction terms using the concept of tana 3 these methods overcome the disadvantage of tdqa when the derivatives at two design points have the same sign in addition the values and derivatives of the proposed approximation functions are completely equal to those of an original function at the two design points whether the derivatives at those points have the same sign or not several examples show the numerical performance and accuracy of the proposed methods compared to previous work and optimization examples show that these methods can successfully reach the optimum via sequential approximation optimization

development of a simple and efficient method for robust optimization robust optimization problems are newly formulated and an efficient computational scheme is proposed both design variables and design parameters are considered as random variables about their nominal values to ensure the robustness of objective performance we introduce a new performance index bounding the performance together with a constraint limiting the performance variation the constraint variations are regulated by considering the probability of feasibility each probability constraint is transformed into a sub optimization problem by the advanced first order second moment afosm method for computational efficiency the proposed robust optimization method has the advantages that the mean value and the variation of the performance function are controlled simultaneously and rationally and the second order sensitivity information is not required even in case of gradient based optimization process the suggested method is examined by solving three examples and the results are compared with those for the deterministic case and those available in the literature copyright 2002 john wiley sons ltd

a robust technique for matching two uncalibrated images through the recovery of the unknown epipolar geometry abstract this paper proposes a robust approach to image matching by exploiting the only available geometric constraint namely the epipolar constraint the images are uncalibrated namely the motion between them and the camera parameters are not known thus the images can be taken by different cameras or a single camera at different time instants if we make an exhaustive search for the epipolar geometry the complexity is prohibitively high the idea underlying our approach is to use classical techniques correlation and relaxation methods in our particular implementation to find an initial set of matches and then use a robust technique the least median of squares lmeds to discard false matches in this set the epipolar geometry can then be accurately estimated using a meaningful image criterion more matches are eventually found as in stereo matching by using the recovered epipolar geometry a large number of experiments have been carried out and very good results have been obtained regarding the relaxation technique we define a new measure of matching support which allows a higher tolerance to deformation with respect to rigid transformations in the image plane and a smaller contribution for distant matches than for nearby ones a new strategy for updating matches is developed which only selects those matches having both high matching support and low matching ambiguity the update strategy is different from the classical winner take all which is easily stuck at a local minimum and also from loser take nothing which is usually very slow the proposed algorithm has been widely tested and works remarkably well in a scene with many repetitive patterns

optimal motion and structure estimation the causes of existing linear algorithms exhibiting various high sensitivities to noise are analyzed it is shown that even a small pixel level perturbation may override the epipolar information that is essential for the linear algorithms to distinguish different motions this analysis indicates the need for optimal estimation in the presence of noise methods are introduced for optimal motion and structure estimation under two situations of noise distribution known and unknown computationally the optimal estimation amounts to minimizing a nonlinear function for the correct convergence of this nonlinear minimization a two step approach is used the first step is using a linear algorithm to give a preliminary estimate for the parameters the second step is minimizing the optimal objective function starting from that preliminary estimate as an initial guess a remarkable accuracy improvement has been achieved by this two step approach over using the linear algorithm alone

impsac synthesis of importance sampling and random sample consensus this paper proposes a new method for recovery of epipolar geometry and feature correspondence between images which have undergone a significant deformation either due to large rotation or wide baseline of the cameras the method also encodes the uncertainty by providing an arbitrarily close approximation to the posterior distribution of the two view relation the method operates on a pyramid from coarse to fine resolution thus raising the problem of how to propagate information from one level to another in a statistically consistent way the distribution of the parameters at each resolution is encoded nonparametrically as a set of particles at the coarsest level a random sample consensus monte carlo markov chain ransac mcmc estimator is used to initialize this set of particles the posterior can then be approximated as a mixture of gaussians fitted to these particles the distribution at a coarser level influences the distribution at a finer level using the technique of sampling importance resampling sir and mcmc which allows for asymptotically correct approximations of the posterior distribution the estimate of the posterior distribution at the level above is being used as the importance sampling function to generate a new set of particles which can be further improved by mcmc it is shown that the method is superior to previous single resolution ransac style feature matchers

fuzzy rationality measures fuzzy preference relations formalize intensity of individual preferences over fixed sets of alternatives it is therefore natural to extend to fuzzy preferences the notion of rationality or consistency with this goal in mind we address in this paper the problem of giving an axiomatic basis for defining the concept of fuzzy rationality specifically we establish a collection of conditions that any fuzzy rationality measure must satisfy some examples of fuzzy rationality measures are then given and analyzed

statistical bias of conic fitting and renormalization introducing a statistical model of noise in terms of the covariance matrix of the n vector we point out that the least squares conic fitting is statistically biased we present a new fitting scheme called renormalization for computing an unbiased estimate by automatically adjusting to noise relationships to existing methods are discussed and our method is tested using real and synthetic data

connectives and quantifiers in fuzzy sets abstract we discuss some of the issues involved in the selection of appropriate operators for implementing the union and intersection of fuzzy subsets we discuss the extension principles used in extending operators to fuzzy subsets we provide a structure for aggregating linguistic variables in the theory of approximate reasoning we look at mean operators on fuzzy subsets as well as the inclusion of importances in aggregation we discuss non monotone set operators we introduce the concept of linguistic quantifiers and look at some applications of these structures we are particularly concerned with their application to linguistic summarizers syllogistic reasoning and multi criteria decision making

robust parameter estimation in computer vision estimation techniques in computer vision applications must estimate accurate model parameters despite small scale noise in the data occasional large scale measurement errors outliers and measurements from multiple populations in the same data set increasingly robust estimation techniques some borrowed from the statistics literature and others described in the computer vision literature have been used in solving these parameter estimation problems ideally these techniques should effectively ignore the outliers and measurements from other populations treating them as outliers when estimating the parameters of a single population two frequently used techniques are least median of squares lms p j rousseeuw j amer statist assoc 79 1984 pp 871 880 and m estimators robust statistics the approach based on influence functions f r hampel et al john wiley 1986 robust statistics p j huber john wiley 1981 lms handles large fractions of outliers up to the theoretical limit of 50 for estimators invariant to affine changes to the data but has low statistical efficiency m estimators have higher statistical efficiency but tolerate much lower percentages of outliers unless properly initialized while robust estimators have been used in a variety of computer vision applications three are considered here in analysis of range images images containing depth or x y z measurements at each pixel instead of intensity measurements robust estimators have been used successfully to estimate surface model parameters in small image regions in stereo and motion analysis they have been used to estimate parameters of what is called the fundamental matrix which characterizes the relative imaging geometry of two cameras imaging the same scene recently robust estimators have been applied to estimating a quadratic image to image transformation model necessary to create a composite mosaic image from a series of images of the human retina in each case a straightforward application of standard robust estimators is insufficient and carefully developed extensions are used to solve the problem

neutrosophic logics prospects and problems neutrosophy has been introduced some years ago by florentin smarandache as a new branch of philosophy dealing with the origin nature and scope of neutralities as well as their interactions with different ideational spectra a variety of new theories have been developed on the basic principles of neutrosophy among them is neutrosophic logics a family of many valued systems that can be regarded as a generalization of fuzzy logics in this paper we present a critical introduction to neutrosophic logics focusing on the problem of defining suitable neutrosophic propositional connectives and discussing the relationship between neutrosophic logics and other well known frameworks for reasoning with uncertainty and vagueness such as intuitionistic and interval valued fuzzy systems and belnap s logic

globally optimal estimates for geometric reconstruction problems we introduce a framework for computing statistically optimal estimates of geometric reconstruction problems while traditional algorithms often suffer from either local minima or non optimality or a combination of both we pursue the goal of achieving global solutions of the statistically optimal cost function our approach is based on a hierarchy of convex relaxations to solve non convex optimization problems with polynomials these convex relaxations generate a monotone sequence of lower bounds and we show how one can detect whether the global optimum is attained at a given relaxation the technique is applied to a number of classical vision problems triangulation camera pose homography estimation and last but not least epipolar geometry estimation experimental validation on both synthetic and real data is provided in practice only a few relaxations are needed for attaining the global optimum

self calibration of a moving camera from pointcorrespondences and fundamental matrices we address the problem of estimating three dimensional motion and structure from motion with an uncalibrated moving camera we show that point correspondences between three images and the fundamental matrices computed from these point correspondences are sufficient to recover the internal orientation of the camera its calibration the motion parameters and to compute coherent perspective projection matrices which enable us to reconstruct 3 d structure up to a similarity in contrast with other methods no calibration object with a known 3 d shape is needed and no limitations are put upon the unknown motions to be performed or the parameters to be recovered as long as they define a projective camera the theory of the method which is based on the constraint that the observed points are part of a static scene thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic is first detailed several algorithms are then presented and their performances compared by means of extensive simulations and illustrated by several experiments with real images

a voting based computational framework for visual motion analysis and interpretation most approaches for motion analysis and interpretation rely on restrictive parametric models and involve iterative methods which depend heavily on initial conditions and are subject to instability further difficulties are encountered in image regions where motion is not smooth typically around motion boundaries this work addresses the problem of visual motion analysis and interpretation by formulating it as an inference of motion layers from a noisy and possibly sparse point set in a 4d space the core of the method is based on a layered 4d representation of data and a voting scheme for affinity propagation the inherent problem caused by the ambiguity of 2d to 3d interpretation is usually handled by adding additional constraints such as rigidity however enforcing such a global constraint has been problematic in the combined presence of noise and multiple independent motions by decoupling the processes of matching outlier rejection segmentation and interpretation we extract accurate motion layers based on the smoothness of image motion and then locally enforce rigidity for each layer in order to infer its 3d structure and motion the proposed framework is noniterative and consistently handles both smooth moving regions and motion discontinuities without using any prior knowledge of the motion model

bilattice logic properly displayed we introduce a proper display calculus for non distributive lattice logic which is sound complete conservative and enjoys cut elimination and subformula property properness i e closure under uniform substitution of all parametric parts in rules is the main interest and added value of the present proposal and allows for the smoothest belnap style proof of cut elimination and for the most comprehensive account of axiomatic extensions and expansions of lattice logic in a single overarching framework our proposal builds on an algebraic and order theoretic analysis of the semantic environment of lattice logic and applies the guidelines of the multi type methodology in the design of display calculi

the fundamental matrix theory algorithms and stability analysis in this paper we analyze in some detail the geometry of a pair of cameras i e a stereo rig contrarily to what has been done in the past and is still done currently for example in stereo or motion analysis we do not assume that the intrinsic parameters of the cameras are known coordinates of the principal points pixels aspect ratio and focal lengths this is important for two reasons first it is more realistic in applications where these parameters may vary according to the task active vision second the general case considered here captures all the relevant information that is necessary for establishing correspondences between two pairs of images this information is fundamentally projective and is hidden in a confusing manner in the commonlyused formalism of the essential matrix introduced by longuet higgins 1981 this paper clarifies the projective nature of the correspondence problem in stereo and shows that the epipolar geometry can be summarized in one 3 x 3 matrix of rank 2 which we propose to call the fundamental matrix after this theoretical analysis we embark on the task of estimating the fundamental matrix from point corre spondences a task which is of practical importance we analyze theoretically and compare experimentally using synthetic and real data several methods of estimation the problem of the stability of the estimation is studied from two complementary viewpoints first we show that there is an interesting relationship between the fundamental matrix and three dimensional planes which induce homographies between the images and create unstabilities in the estimation procedures second we point to a deep relation between the unstability of the estimation procedure and the presence in the scene of so called critical surfaces which have been studied in the context of motion analysis finally we conclude by stressing the fact that we believe that the fundamental matrix will play a crucial role in future applications of three dimensional computer vision by greatly increasing its versatility robustness and hence applicability to real difficult problems

strict preference relations based on weak t norms abstract in this paper we introduce and investigate weak t norms and related concepts in order to give a general representation of valued strict preference relations associated with a given valued preference relation all the well known forms of valued strict preference relations are particular cases of our results moreover when some types of rationality assumptions are made our unified approach seems to be the only possible one

a probabilistic criterion to detect rigid point matches between two images and estimate the fundamental matrix the perspective projections of n physical points on two views stereovision are constrained as soon as n 8 however to prove in practice the existence of a rigid motion between two images more than 8 point matches are desirable in order to compensate for the limited accuracy of the matches in this paper we propose a computational definition of rigidity and a probabilistic criterion to rate the meaningfulness of a rigid set as a function of both the number of pairs of points n and the accuracy of the matches this criterion yields an objective way to compare say precise matches of a few points and approximate matches of a lot of points it gives a yes no answer to the question could this rigid points correspondence have occurred by chance since it guarantees that the expected number of meaningful rigid sets found by chance in a random distribution of points is as small as desired it also yields absolute accuracy requirements for rigidity detection in the case of non matched points and optimal values of n depending on the expected accuracy of the matches and on the proportion of outliers we use it to build an optimized random sampling algorithm that is able to detect a rigid motion and estimate the fundamental matrix when the set of point matches contains up to 90 of outliers which outperforms the best currently known methods like m estimators lmeds classical ransac and tensor voting

equivalence and compositions of fuzzy rationality measures an axiomatic basis for fuzzy rationality measures has already been introduced by the authors in a previous paper 5 formalizing the fact that there exist degrees of consistency when preferences over a fixed set of alternatives are expressed in terms of fuzzy binary preference relations this paper deals with some practical consequences on the one hand similarities and compositions of fuzzy rationality measures are considered showing natural ways of deriving new measures on the other if basic stability properties are introduced in order to assure that small intensity measurement errors never lead to big changes in the associate rationality value it is shown that crisp i e binary rationality measures present serious difficulties when applied to fuzzy preference relations

the wiener askey polynomial chaos for stochastic differential equations we present a new method for solving stochastic differential equations based on galerkin projections and extensions of wiener s polynomial chaos specifically we represent the stochastic processes with an optimum trial basis from the askey family of orthogonal polynomials that reduces the dimensionality of the system and leads to exponential convergence of the error several continuous and discrete processes are treated and numerical examples show substantial speed up compared to monte carlo simulations for low dimensional stochastic inputs

on a family of connectives for fuzzy sets abstract in this paper we find the general solution of the functional equation s t x y t x n y x where s is a t conorm t is a t norm and n is a strong negation on the unit interval in particular the result yields a family of connectives for fuzzy sets

consistency of robust estimators in multi structural visual data segmentation a theoretical framework is presented to study the consistency of robust estimators used in vision problems involving extraction of fine details a strong correlation between asymptotic performance of a robust estimator and the asymptotic bias of its scale estimate is mathematically demonstrated where the structures are assumed to be linear corrupted by gaussian noise a new measure for the inconsistency of scale estimators is defined and formulated by deriving the functional forms of four recent high breakdown robust estimators for each estimator the inconsistency measures are numerically evaluated for a range of mutual distances between structures and inlier ratios and the minimum mutual distance between the structures for which each estimator returns a non bridging fit is calculated

paraconsistent semantics for pavelka style fuzzy sentential logic the root of this work is on the one hand in belnap s four valued paraconsistent logic and on the other hand on pavelka s papers further developed by turunen we do not introduce a new non classical logic but based on a related study of perny and tsoukias we introduce paraconsistent semantics of pavelka style fuzzy sentential logic restricted to lukasiewicz t norm our approach and the approach of perny and tsoukias partly overlap the main difference lies in the interpretation of the logical connectives implication and negation the essential mathematical tool proved in this paper is a one one correspondence between evidence couples and evidence matrices that holds in all injective mv algebras evidence couples associate to each atomic formula p two values a and b that can be interpreted as the degrees of pros and cons for p respectively four values t f k u interpreted as the degrees of the truth falsehood contradiction and unknownness of p respectively can then be calculated by means of a and b and finally the degrees of the truth falsehood contradiction and unknownness of any well formed formula a are available the obtained logic is pavelka style fuzzy sentential logic in such an approach truth and falsehood are not each others complements moreover we solve some open problems presented by perny and tsoukias

uncertainty modeling by bilattice based squares and triangles in this paper ginsberg s fitting s theory of bilattices and in particular the associated constructs of bilattice based squares and triangles is introduced as an attractive framework for the representation of uncertain and potentially conflicting information paralleling goguen s l fuzzy set theory we recall some of the advantages of bilattice based frameworks for handling fuzzy sets and systems provide the related structures with adequately defined graded versions of the basic logical connectives and study their properties and relationships

the development and comparison of robust methodsfor estimating the fundamental matrix this paper has two goals the first is to develop a variety of robust methods for the computation of the fundamental matrix the calibration free representation of camera motion the methods are drawn from the principal categories of robust estimators viz case deletion diagnostics m estimators and random sampling and the paper develops the theory required to apply them to non linear orthogonal regression problems although a considerable amount of interest has focussed on the application of robust estimation in computer vision the relative merits of the many individual methods are unknown leaving the potential practitioner to guess at their value the second goal is therefore to compare and judge the methods comparative tests are carried out using correspondences generated both synthetically in a statistically controlled fashion and from feature matching in real imagery in contrast with previously reported methods the goodness of fit to the synthetic observations is judged not in terms of the fit to the observations per se but in terms of fit to the ground truth a variety of error measures are examined the experiments allow a statistically satisfying and quasi optimal method to be synthesized which is shown to be stable with up to 50 percent outlier contamination and may still be used if there are more than 50 percent outliers performance bounds are established for the method and a variety of robust methods to estimate the standard deviation of the error and covariance matrix of the parameters are examined the results of the comparison have broad applicability to vision algorithms where the input data are corrupted not only by noise but also by gross outliers

on the direct decomposability of t norms on product lattices in this paper a method is presented for constructing t norms on product lattices in other words commutative partially ordered integral monoids over product lattices which are not direct products the method is fairly general and allows to generate a broad class of such t norms this solves an open problem posed in 1999 by de baets and mesiar

on fuzzy strict preference indifference and incomparability relations abstract the existence of fuzzy models for strict preference indifference and incomparability satisfying all classical properties is established a particular class of such models is completely described

camera displacement via constrained minimization of the algebraic error this paper proposes a new approach to estimate the camera displacement of stereo vision systems via minimization of the algebraic error over the essential matrices manifold the proposed approach is based on the use of homogeneous forms and linear matrix inequality lmi optimizations and has the advantages of not presenting local minima and not introducing approximations of nonlinear terms numerical investigations carried out with both synthetic and real data show that the proposed approach provides significantly better results than svd methods as well as minimizations of the algebraic error over the essential matrices manifold via both gradient descent and simplex search algorithms

effective two point function approximation for design optimization anew two pointapproximationofafunctionthatisverystraightforwardtobuildandthatprovidesaccurateand stable approximation is presented earlier developments of the two point approximations had either incomplete matches at two data points or needed the solution of additional equations to get all of the parameters the present two point approximation is an incomplete second order taylor series expansion in terms of intervening variables thehessianmatrixhasonlydiagonalelements anditdependsondesignvariables theexponentofeachintervening design variable and the unknown constant of the second order terms are evaluated by matching the derivatives and the value of the approximation with the previous data point gradients and the value of the original function respectively all of theunknownsareidentie ed in aclosedform both thefunctionandthegradientof thetwo point approximation are equal to those of the original function at two data points several examples are given to show the accuracy and efe ciency of this method

basic concepts for a theory of evaluation the aggregative operator abstract starting with an explication of the aggregative concept and deducing a general structure which satisfies a number of minimal requirements properties of clustering the main features of a new mathematical theory called theory of evaluation are developed the theory sheds new light on such well known concepts as membership conjunction and disjunction and seems to be a very promising tool to handle representation problems as they grow from the fields of theory of fuzzy set and its many applications of human decision making and of multicriteria analysis

triangle algebras a formal logic approach to interval valued residuated lattices in this paper we introduce triangle algebras a variety of residuated lattices equipped with approximation operators and with a third angular point u different from 0 and 1 we show that these algebras serve as an equational representation of interval valued residuated lattices ivrls furthermore we present triangle logic tl a system of many valued logic capturing the tautologies of ivrls triangle algebras are used to cast the essence of using closed intervals of l as truth values into a set of appropriate logical axioms our results constitute a crucial first step towards solving an important research challenge the axiomatic formalization of residuated t norm based logics on l i the lattice of closed intervals of 0 1 in a similar way as was done for formal fuzzy logics on the unit interval

robust estimation of dispersion matrices and principal components abstract this paper uses monte carlo methods to compare the performances of several robust procedures for estimating a correlation matrix and its principal components the estimators are formed either from separate bivariate analyses or by simultaneous manipulation of all variables by using techniques such as multivariate trimming and m estimation the m estimators stand up exceptionally well they and the multivariate trimming procedure are especially effective at estimating the principal components including a near singularity however the m estimators can break down relatively easily when the dimensionality is large and the outliers are asymmetric with missing data the element wise approach becomes more attractive

determining the epipolar geometry and its uncertainty a review two images of a single scene object are related by the epipolar geometry which can be described by a 3 3 singular matrix called the essential matrix if images internal parameters are known or the fundamental matrix otherwise it captures all geometric information contained in two images and its determination is very important in many applications such as scene modeling and vehicle navigation this paper gives an introduction to the epipolar geometry and provides a complete review of the current techniques for estimating the fundamental matrix and its uncertainty a well founded measure is proposed to compare these techniques projective reconstruction is also reviewed the software which we have developed for this review is available on the internet

adjoint negations more than residuated negations negation operators are useful operators which have extensively been studied and used in different fuzzy settings such as in fuzzy logic this paper introduces a new and flexible kind of negation operator based on adjoint triples and which is called adjoint negation relative to a fixed element besides proving several interesting properties the comparison with weak negations studied by trillas esteva et al and pairs of weak negations introduced by georgescu and popescu is presented furthermore adjoint negations are used in order to define the corresponding dual disjunctive to an adjoint conjunctor

improved two point function approximations for design optimization two point approximations are developed by utilizing both the function and gradient information of two data points the objective of this work is to build a high quality approximation to realize computational savings in solving complex optimization and reliability analysis problems two developments are proposed in the new twopoint approximations 1 calculation of a correction term by matching with the previous known function value and supplementing it to the first order approximation for including the effects of higher order terms and 2 development of a second order approximation without the actual calculation of second order derivatives by using an approximate hessian matrix several highly nonlinear functions and structural examples are used for demonstrating the new two point approximations that improved the accuracy of existing first order methods evelopmentof new and improved constraint approximations has been an active area of research in the mathematical optimization community over the last two decades 1 3 more accurate function approximations reduce the finite element analysis cost and increase the search domain in each iteration of an optimization run recent developments in constraint approximations addressed methods for eigenvalues dynamic response static forces structural reliability etc some of the typical methods are summarized in the following kirsch4 developed a scaling factor for a stiffness matrix and approximated the displacements stresses and forces with respect to sizing and topology variables vanderplaats and salajegheh5 used two levels of approximations for discrete sizing and shape design of structures first for solving the continuous problem and next the discrete one using a dual theory canfield6 developed an approach for eigenvalues by approximating the modal strain and kinetic energies independently thomas et al 7 presented an approximation for the frequency response of damped structures by using the concept of ref 6 a multivariate spline approximation was developed by wang and grandhi8 making use of the previously generated exact finite element analyses similarly a hermite approximation for n dimensional problems used several data points and had the property of reproducing the function and gradient values at the known data points 9 canfield10 used multipoint data in building an approximate hessian matrix and constructed a second order approximation for improving the accuracy toropov et al 11 approximated functions as a linear combination or products of variables and the coefficients of the polynomial were computed by applying a least squared approach on multiple data points fadel et al 12 considered intermediate variables in terms of exponentials and they were computed by matching the approximate function gradients with the previous point s exact values this approach did not compare the function values of the previous point wang and grandhi13 used a single exponential for all of the variables and calculated it by matching the approximate function with the previous point exact value and the gradient information of the previous point was not utilized the proposed paper develops an improved two point approximation utilizing both function and gradient information of two data points in the new two point approximation two developments are proposed 1 calculation of a correction term based on two function values and

heteroscedastic regression in computer vision problems with bilinear constraint we present an algorithm to estimate the parameters of a linear model in the presence of heteroscedastic noise i e each data point having a different covariance matrix the algorithm is motivated by the recovery of bilinear forms one of the fundamental problems in computer vision which appears whenever the epipolar constraint is imposed or a conic is fit to noisy data points we employ the errors in variables eiv model and show why already at moderate noise levels most available methods fail to provide a satisfactory solution the improved behavior of the new algorithm is due to two factors taking into account the heteroscedastic nature of the errors arising from the linearization of the bilinear form and the use of generalized singular value decomposition gsvd in the computations the performance of the algorithm is compared with several methods proposed in the literature for ellipse fitting and estimation of the fundamental matrix it is shown that the algorithm achieves the accuracy of nonlinear optimization techniques at much less computational cost

a multi frame approach to visual motion perception one of the main issues in the area of motion estimation given the correspondences of some features in a sequence of images is sensitivity to error in the input the main way to attack the problem as with several other problems in science and engineering is redundancy in the data up to now all the algorithms developed either used two frames or depended on assumptions about the motion or the shape of the scene we present in this paper an algorithm based on multiple frames that employs only the rigidity assumption is simple and mathematically elegant and experimentally proves to be a major improvement over the two frame algorithms the algorithm does minimization of the squared error which we prove equivalent to an eigenvalue minimization problem one of the side effects of this mean square method is that the algorithm can have a very descriptive physical interpretation in terms of the loaded spring model

multi valued logic programming semantics an algebraic approach abstract in this paper we introduce the notion of join irreducibility in the context of bilattices and present a procedural semantics for bilattice based logic programs which uses as its basis the join irreducible elements of the knowledge part of the bilattice the join irreducible elements in a bilattice represent the primitive bits of information present within the system in bilattices which have the descending chain property in their knowledge ordering these elements provide a small representative set completely characterizing the bilattice the overall complexity of the inference systems based on such bilattices can thus be reduced by restricting attention to the join irreducible elements

estimation of planar curves surfaces and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation the author addresses the problem of parametric representation and estimation of complex planar curves in 2 d surfaces in 3 d and nonplanar space curves in 3 d curves and surfaces can be defined either parametrically or implicitly with the latter representation used here a planar curve is the set of zeros of a smooth function of two variables x y a surface is the set of zeros of a smooth function of three variables x y z and a space curve is the intersection of two surfaces which are the set of zeros of two linearly independent smooth functions of three variables x y z for example the surface of a complex object in 3 d can be represented as a subset of a single implicit surface with similar results for planar and space curves it is shown how this unified representation can be used for object recognition object position estimation and segmentation of objects into meaningful subobjects that is the detection of interest regions that are more complex than high curvature regions and hence more useful as features for object recognition

a general model for deriving preference structures from data in this paper we comment upon the integrated model for valued preferences introduced by fodor ovchinnikov and roubens in particular while on one hand we revise basic assumptions and point out their intuitive meaning on the other hand we propose an alternative mathematical justification of such a model which allows not only a better understanding of the obtained results but also a functional characterization of the whole family of solutions

monoidal t norm based logic towards a logic for left continuous t norms hajek s bl logic is the fuzzy logic capturing the tautologies of continuous t norms and their residua in this paper we investigate a weaker logic mtl which is intended to cope with the tautologies of left continuous t norms and their residua the corresponding algebraic structures mtl algebras are defined and completeness of mtl with respect to linearly ordered mtl algebras is proved besides several schematic extensions of mtl are also considered as well as their corresponding predicate calculi

robust regression methods for computer vision a review regression analysis fitting a model to noisy data is a basic technique in computer vision robust regression methods that remain reliable in the presence of various types of noise are therefore of considerable importance we review several robust estimation techniques and describe in detail the least median of squares lmeds method the method yields the correct result even when half of the data is severely corrupted its efficiency in the presence of gaussian noise can be improved by complementing it with a weighted least squares based procedure the high time complexity of the lmeds algorithm can be reduced by a monte carlo type speed up technique we discuss the relationship of lmeds with the ransac paradigm and its limitations in the presence of noise corrupting all the data and we compare its performance with the class of robust m estimators references to published applications of robust techniques in computer vision are also given

influence in principal components analysis summary in linear regression the theoretical influence function and the various sample versions of it have an established place as diagnostic tools these same functions are developed here to provide methods for the detection of influential observations in principal components analysis the perturbation theory of real symmetric matrices unifies this development some interesting points of contrast with the regression case are noted and explained theoretically

infinitely distributive t norms on complete lattices and pseudo complements in this paper we have introduced the concepts of t prime element t prime radical element and t semi prime element and have studied their properties we have investigated the construction methods of new infinitely distributive t norms from given infinitely distributive t norms by means of t prime elements and pseudo complements if every element of l is t prime radical element then we show that l is a complete brouwerian lattice and email protected if l is an algebraic lattice t is a t norm on l and every compact element of l is idempotent then we obtain that email protected we show that l r is a complete lattice and that the restriction of t to l r is an infinitely distributive t norm on l r when t is an infinitely distributive t norm on l and 0 is a t prime we present infinitely distributive t norms on a complete sublattice l and study their properties