first order linear fuzzy differential equations under generalized differentiability first order linear fuzzy differential equations are investigated we interpret a fuzzy differential equation by using the strongly generalized differentiability concept because under this interpretation we may obtain solutions which have a decreasing length of their support which means a decreasing uncertainty in several applications the behaviour of these solutions better reflects the behaviour of some real world systems derivatives of the h difference and the product of two functions are obtained and we provide solutions of first order linear fuzzy differential equations using different versions of the variation of constants formula some examples show the rich behaviour of the solutions obtained

open fuzzy cubature rule with application to nonlinear fuzzy volterra integral equations in two dimensions abstract in this paper we propose an open fuzzy cubature formula and as application we construct an iterative numerical method for solving nonlinear fuzzy volterra integral equations in two dimensions the convergence of the method is proved by providing the error estimate and it is tested on two numerical experiments

the henstock stieltjes integral for fuzzy number valued functions in this paper we firstly define and discuss the henstock stieltjes integral for fuzzy number valued functions which is an extension of the usual fuzzy riemann stieltjes integral in addition several necessary and sufficient conditions of the integrability for fuzzy number valued functions are given by means of the henstock stieltjes integral of real valued functions and henstock integral of fuzzy number valued functions secondly the continuity and the differentiability of the primitive for the fuzzy henstock stieltjes integral are discussed we find that there exists a fuzzy number valued function which is fuzzy henstock stieltjes integrable but whose primitive is not a differentiable almost everywhere thirdly we introduce some quadrature rules for the fuzzy henstock stieltjes integral by giving error bounds for the mappings of bounded variation and of lipschitz type we also consider the generalization of classical quadrature rules such as midpoint type trapezoidal and simpson s quadrature finally we propose the concept of weak equi integrability for sequences of fuzzy henstock stieltjes integrable functions under this concept we prove two convergence theorems for sequences of the fuzzy henstock stieltjes integrable functions at the same time the formula of integration by parts is also studied

go icp a globally optimal solution to 3d icp point set registration the iterative closest point icp algorithm is one of the most widely used methods for point set registration however being based on local iterative optimization icp is known to be susceptible to local minima its performance critically relies on the quality of the initialization and only local optimality is guaranteed this paper presents the first globally optimal algorithm named go icp for euclidean rigid registration of two 3d point sets under the l 2 error metric defined in icp the go icp method is based on a branch and bound scheme that searches the entire 3d motion space se 3 by exploiting the special structure of se 3 geometry we derive novel upper and lower bounds for the registration error function local icp is integrated into the bnb scheme which speeds up the new method while guaranteeing global optimality we also discuss extensions addressing the issue of outlier robustness the evaluation demonstrates that the proposed method is able to produce reliable registration results regardless of the initialization go icp can be applied in scenarios where an optimal solution is desirable or where a good initialization is not always available

the improper fuzzy riemann integral and its numerical integration abstract the improper fuzzy riemann integral and its numerical integration are proposed in this paper under the setting of the improper fuzzy riemann integral we can find the expectation of fuzzy random variable the level set of the improper fuzzy riemann integral is a closed interval whose end points are the improper riemann integrals thus we provide a numerical method to approximate the improper fuzzy riemann integral by invoking the simpson s rule we also fit the end points closed interval of the level set of the improper fuzzy riemann integral as polynomials with variable in a least squares sense finally the membership function of the improper fuzzy riemann integral can be transformed into nonlinear programming problem and be solved by any presented optimizer

the effect of spatial information characterization on 3d local feature descriptors designing local feature descriptors for 3d objects is a fundamental yet challenging task in 3d computer vision both geometry and spatial information descriptions are critical for a 3d local descriptor while most previous studies concentrate on the former one this paper investigates on how the characterization of spatial information would affect a 3d local descriptor in terms of descriptiveness robustness compactness and efficiency the evaluation process is deployed as follows first based on the analysis of representative spatial information characterization methods of existing local shape descriptors six typical characterization methods with different spatial dimensions and partition principles of spatial information are presented second three geometric attributes i e normal deviation local depth and shape index are respectively assigned to each point in the local surface for local geometry description creating a total of 18 different feature descriptors then a quantitative analysis of performance i e descriptiveness robustness compactness and efficiency for these descriptors is carried out on three benchmark datasets grounded on the experimental outcomes the traits merits and demerits of each spatial information encoding approach are eventually summarized this study reveals that different spatial information encoding approaches would bring significant effect on a local shape descriptor with respect to its discriminative power stability compactness and efficiency highlightsthe effect of spatial information encoding sie on 3d local descriptors is emphasized eighteen types of 3d local descriptors with different sie approaches are proposed quantitative evaluation of sie approaches is performed on three standard datasets the merits demerits and suitable applications of different sie ways are summarized instructive guidance is concluded for the design of a 3d local descriptor

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

a new approach to collaborative filtering operator estimation with spectral regularization we present a general approach for collaborative filtering cf using spectral regularization to learn linear operators mapping a set of users to a set of possibly desired objects in particular several recent low rank type matrix completion methods for cf are shown to be special cases of our proposed framework unlike existing regularization based cf our approach can be used to incorporate additional information such as attributes of the users objects a feature currently lacking in existing regularization based cf approaches using popular and well known kernel methods we provide novel representer theorems that we use to develop new estimation methods we then provide learning algorithms based on low rank decompositions and test them on a standard cf data set the experiments indicate the advantages of generalizing the existing regularization based cf methods to incorporate related information about users and objects finally we show that certain multi task learning methods can be also seen as special cases of our proposed approach

a note on fuzzy volterra integral equations abstract in this paper existence theorems for certain volterra integral equations involving fuzzy set valued mappings whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in r n are obtained

existence theorem to the cauchy problem of fuzzy differential equations under compactness type conditions kaleva fuzzy sets and systems 35 1990 389 396 has concluded that the peano theorem does not hold for fuzzy differential equations on en d this paper deals with the cauchy problem of fuzzy differential equations the existence theorems under compactness type conditions are obtained

error estimation in the approximation of the solution of nonlinear fuzzy fredholm integral equations using a fixed point technique the sequence of successive approximations and a recent quadrature formula for fuzzy number valued functions it is constructed a numerical method for the solution of nonlinear fuzzy fredholm integral equations moreover the error estimate of the method and a criterion to stop the corresponding algorithm are given

3d free form surface registration and object recognition a new technique to recognise 3d free form objects via registration is proposed this technique attempts to register a free form surface represented by a set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d sensed data points to the model surface represented by another set of mathtype mtef 2 1 feaafeart1ev1aaatcvaufebsjuyzl2yd9gzlbvynv2caerbulwbln hiov2dgi1btfmbaexatlxbi9gbaerbd9wdylwzybitldharqqtubsr 4rnchbgeagqivu0je9sqqrpepc0xbbl8f4rqqrffpeea0xe9lq jc9 vqaqpepm0xbba9pwe9q8fs0 yqaqpepae9pg0firpepekkfr0xfr x fr xb9adbaqaaegacigaaiaabeqaamaabaabaagcbagaagomamaala aabagaagymaaqaaiaaikdaaagaamiraaaa 38f8 2 frac 1 2 d model data points without prior knowledge of correspondence or view points between the two point sets with an initial assumption that the sensed surface be part of a more complete model surface the algorithm begins by selecting three dispersed reliable points on the sensed surface to find the three corresponding model points the method uses the principal curvatures and the darboux frames to restrict the search over the model space invariably many possible model 3 typles will be found for each hypothesized model 3 tuple the transformation to match the sensed 3 tuple to the model 3 tuple can be determined a heuristic search is proposed to single out the optimal transformation in low order time for realistic object recognition or registration where the two range images are often extracted from different view points of the model the earlier assumption that the sensed surface be part of a more complete model surface cannot be relied on with this the sensed 3 tuple must be chosen such that the three sensed points lie on the common region visible to both the sensed and model views we propose an algorithm to select a minimal non redundant set of 3 tuples such that at least one of the 3 tuples will lie on the overlap applying the previous algorithm to each 3 tuple within this set the optimal transformation can be determined experiments using data obtained from a range finder have indicated fast registration for relatively complex test cases if the optimal registrations between the sensed data candidate and each of a set of model data are found then for 3d object recognition purposes the minimal best fit error can be used as the decision rule

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

exponentiated gradient versus gradient descent for linear predictors we consider two algorithm for on line prediction based on a linear model the algorithms are the well known gradient descent gd algorithm and a new algorithm which we call eg they both maintain a weight vector using simple updates for the gd algorithm the update is based on subtracting the gradient of the squared error made on a prediction the eg algorithm uses the components of the gradient in the exponents of factors that are used in updating the weight vector multiplicatively we present worst case loss bounds for eg and compare them to previously known bounds for the gd algorithm the bounds suggest that the losses of the algorithms are in general incomparable but eg has a much smaller loss if only a few components of the input are relevant for the predictions we have performed experiments which show that our worst case upper bounds are quite tight already on simple artificial data

kernelization of matrix updates when and how abstract we define what it means for a learning algorithm to be kernelizable in the case when the instances are vectors asymmetric matrices and symmetric matrices respectively we can characterize kernelizability in terms of an invariance of the algorithm to certain orthogonal transformations if we assume that the algorithm s action relies on a linear prediction then we can show that in each case the linear parameter vector must be a certain linear combination of the instances we give a number of examples of how to apply our methods in particular we show how to kernelize multiplicative updates for symmetric instance matrices

point signatures a new representation for 3d object recognition few systems capable of recognizing complex objects with free form sculptured surfaces have been developed the apparent lack of success is mainly due to the lack of a competent modelling scheme for representing such complex objects in this paper a new form of point representation for describing 3d free form surfaces is proposed this representation which we call the point signature serves to describe the structural neighbourhood of a point in a more complete manner than just using the 3d coordinates of the point being invariant to rotation and translation the point signature can be used directly to hypothesize the correspondence to model points with similar signatures recognition is achieved by matching the signatures of data points representing the sensed surface to the signatures of data points representing the model surface the use of point signatures is not restricted to the recognition of a single object scene to a small library of models instead it can be extended naturally to the recognition of scenes containing multiple partially overlapping objects which may also be juxtaposed with each other against a large model library no preliminary phase of segmenting the scene into the component objects is required in searching for the appropriate candidate model recognition need not proceed in a linear order which can become prohibitive for a large model library for a given scene signatures are extracted at arbitrarily spaced seed points each of these signatures is used to vote for models that contain points having similar signatures inappropriate models with low votes can be rejected while the remaining candidate models are ordered according to the votes they received in this way efficient verification of the hypothesized candidates can proceed by testing the most likely model first experiments using real data obtained from a range finder have shown fast recognition from a library of fifteen models whose complexities vary from that of simple piecewise quadric shapes to complicated face masks results from the recognition of both single object and multiple object scenes are presented

numerical solution of nonlinear fuzzy fredholm integral equations using iterative method in this paper we propose an iterative procedure based on quadrature formula to solve nonlinear fuzzy fredholm integral equations of the second kind moreover the error estimation of the proposed method in terms of uniform and partial modulus of continuity is given finally illustrative examples are included in order to demonstrate the accuracy and the convergence of the proposed method

on the stability of runge kutta methods for delay integral equations we present a class of runge kutta methods for the numerical solution of a class of delay integral equations dies described by two different kernels and with a fixed delay the stability properties of these methods are investigated with respect to a test equation with linear kernels depending on complex parameters the results are then applied to collocation methods in particular we obtain that any collocation method for dies resulting from ana stable collocation method for odes with a stepsize which is submultiple of the delay preserves the asymptotic stability properties of the analytic solutions

fast descriptors and correspondence propagation for robust global point cloud registration in this paper we present a robust global approach for point cloud registration from uniformly sampled points based on eigenvalues and normals computed from multiple scales we design fast descriptors to extract local structures of these points the eigenvalue based descriptor is effective at finding seed matches with low precision using nearest neighbor search generally recovering the transformation from matches with low precision is rather challenging therefore we introduce a mechanism named correspondence propagation to aggregate each seed match into a set of numerous matches with these sets of matches multiple transformations between point clouds are computed a quality function formulated from distance errors is used to identify the best transformation and fulfill a coarse alignment of the point clouds finally we refine the alignment result with the trimmed iterative closest point algorithm the proposed approach can be applied to register point clouds with significant or limited overlaps and small or large transformations more encouragingly it is rather efficient and very robust to noise a comparison to traditional descriptor based methods and other global algorithms demonstrates the fine performance of the proposed approach we also show its promising application in large scale reconstruction with the scans of two real scenes in addition the proposed approach can be used to register low resolution point clouds captured by kinect as well

nonlinear component analysis as a kernel eigenvalue problem a new method for performing a nonlinear form of principal component analysis is proposed by the use of integral operator kernel functions one can efficiently compute principal components in high dimensional feature spaces related to input space by some nonlinear map for instance the space of all possible five pixel products in 16 16 images we give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition

collocation and continuous implicit runge kutta methods for a class of delay volterra integral equations abstract in this paper we present an analysis of the global convergence properties of certain piecewise polynomial collocation methods for a class of volterra integral equations with constant delay this analysis also encompasses continuous implicit m stage volterra runge kutta methods based on collocation techniques

a new bernoulli wavelet method for accurate solutions of nonlinear fuzzy hammerstein volterra delay integral equations in this article bernoulli wavelet method has been developed to solve nonlinear fuzzy hammerstein volterra integral equations with constant delay this type of integral equation has a particular case the fuzzy variant of a mathematical model from epidemiology bernoulli wavelets have been generated by dilation and translation of bernoulli polynomials the properties of bernoulli wavelets and bernoulli polynomials are first presented the present wavelet method reduces these integral equations to a system of nonlinear algebraic equations and again these algebraic systems have been solved numerically by newton s method convergence analysis of the present method has been discussed in this article also the results obtained by present wavelet method have been compared with that of by b spline wavelet method some illustrative examples have been demonstrated to show the applicability and accuracy of the present method

matrix exponentiated gradient updates for on line learning and bregman projection we address the problem of learning a symmetric positive definite matrix the central issue is to design parameter updates that preserve positive definiteness our updates are motivated with the von neumann divergence rather than treating the most general case we focus on two key applications that exemplify our methods on line learning with a simple square loss and finding a symmetric positive definite matrix subject to linear constraints the updates generalize the exponentiated gradient eg update and adaboost respectively the parameter is now a symmetric positive definite matrix of trace one instead of a probability vector which in this context is a diagonal positive definite matrix with trace one the generalized updates use matrix logarithms and exponentials to preserve positive definiteness most importantly we show how the derivation and the analyses of the original eg update and adaboost generalize to the non diagonal case we apply the resulting matrix exponentiated gradient meg update and definiteboost to the problem of learning a kernel matrix from distance measurements

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

on henstock integrals of interval valued functions and fuzzy valued functions abstract in this paper the h integrals of interval valued functions and fuzzy valued functions are defined and discussed several necessary and sufficient conditions of h integrability for fuzzy number valued functions are given by means of abstract henstock pettis integral theory

on the basic solutions to the generalized fuzzy integral equation abstract for the fuzzy measure space x a the structure of the basic solutions to the generalized fuzzy integral equation esh x x h x d is considered where h x is taken as a nonnegative measurable kernel function 0 is a constant denotes the logic multiplication minimum operator at first the existence of the constant basic solution to eq 1 is investigated and the solvable sufficient and necessary conditions to the eq 1 are characterized then the characteristic functional basic solution to eq 1 is shown in addition two convergent theorems corresponding to the sequences of approximate basic solutions each of which is constituted by the series with the logic addition maximum operator denoted by for the characteristic functions are obtained

an analytical method for solving linear fredholm fuzzy integral equations of the second kind in this paper we use the parametric form of a fuzzy number and convert a linear fuzzy fredholm integral equation to two linear systems of integral equations of the second kind in the crisp case for fuzzy fredholm integral equations with kernels the sign of which is difficult to determine a new parametric form of the fuzzy fredholm integral equation is introduced we use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solutions of the linear fuzzy fredholm integral equation of the second kind the proposed method is illustrated by solving some examples using the ham it is possible to find the exact solution or the approximate solution of the problem in the form of a series

the weighted majority algorithm we study the construction of prediction algorithms in a situation in which a learner faces a sequence of trials with a prediction to be made in each and the goal of the learner is to make few mistakes we are interested in the case where the learner has reason to believe that one of some pool of known algorithms will perform well but the learner does not know which one a simple and effective method based on weighted voting is introduced for constructing a compound algorithm in such a circumstance we call this method the weighted majority algorithm we show that this algorithm is robust in the presence of errors in the data we discuss various versions of the weighted majority algorithm and prove mistake bounds for them that are closely related to the mistake bounds of the best algorithms of the pool for example given a sequence of trials if there is an algorithm in the pool a that makes at most m mistakes then the weighted majority algorithm will make at most c log a m mistakes on that sequence where c is fixed constant

tracking the best linear predictor in most on line learning research the total on line loss of the algorithm is compared to the total loss of the best off line predictor u from a comparison class of predictors we call such bounds static bounds the interesting feature of these bounds is that they hold for an arbitrary sequence of examples recently some work has been done where the predictor ut at each trial t is allowed to change with time and the total on line loss of the algorithm is compared to the sum of the losses of ut at each trial plus the total cost for shifting to successive predictors this is to model situations in which the examples change over time and different predictors from the comparison class are best for different segments of the sequence of examples we call such bounds shifting bounds they hold for arbitrary sequences of examples and arbitrary sequences of predictors naturally shifting bounds are much harder to prove the only known bounds are for the case when the comparison class consists of a sequences of experts or boolean disjunctions in this paper we develop the methodology for lifting known static bounds to the shifting case in particular we obtain bounds when the comparison class consists of linear neurons linear combinations of experts our essential technique is to project the hypothesis of the static algorithm at the end of each trial into a suitably chosen convex region this keeps the hypothesis of the algorithm well behaved and the static bounds can be converted to shifting bounds

the supremum and infimum of the set of fuzzy numbers and its application abstract in this paper we prove that the bounded set of fuzzy numbers must exist supremum and infimum and give the concrete representation of supremum and infimum as an application we obtain that the continuous fuzzy valued function on a closed interval exists supremum and infimum and give the precise representation we also show that the bounded fuzzy valued function on a closed interval can define the lower and upper sums and the lower and upper integrals of riemann and riemann stieltjes by the usual way

real time object recognition in sparse range images using error surface embedding a novel object recognition algorithm is introduced to identify objects and recover their pose from sparse range data the method is based upon comparing the 7 d error surfaces of objects in various poses which result from the registration error function between two convolved surfaces the objects and their pose values are encoded by a small set of feature vectors extracted from the minima of the error surfaces the problem of object recognition is thus reduced to comparing these feature vectors to find the corresponding error surfaces between the runtime data and a preprocessed database the algorithm called potential well space embedding pwse has been implemented and tested on both simulated and real data the experimental results show the technique to be both effective and efficient executing at 122 frames per second on standard hardware and with recognition rates exceeding 97 for a database of 60 objects the performance of pwse on the large size database was also evaluated on the princeton shape benchmark containing 1 814 objects in addition it functions well with very sparse data possibly comprising only hundreds of points per image and is shown to be robust to measurement error and outliers with some small modifications we applied pwse to the problem of object class recognition in experiments with the princeton shape benchmark pwse is able to provides better classification rates than the previous methods in terms of nearest neighbour classification

fuzzy integral equations abstract we introduce a definition of the integral of a fuzzy valued function that is only slightly different from the usual one yet that is more intuitive and that can be applied to a larger class of functions we show that our definition is equivalent to the extension principle for functions of this class we then apply integration theory of fuzzy valued functions to integral equations we define a measure of the fuzziness of a fuzzy valued function and show that using this measure we can view the integration of fuzzy functions as a fuzzy linear transformation from a certain subspace of fuzzy valued functions to the space of fuzzy numbers we then show how this can be used to study fredholm integral equations of the second kind

bounded variation absolute continuity and absolute integrability for fuzzy number valued functions in this paper the concepts of bounded variation and absolute continuity for the fuzzy number valued functions are presented and discussed by means of the representation of the absolute value for fuzzy numbers the relations among bounded variation absolute continuity kaleva s integral and fuzzy henstock integral are characterized especially the representation of absolute continuous fuzzy valued functions is given by henstock kaleva integral of absolutely henstock kaleva integrable fuzzy number valued functions

elementary fuzzy calculus abstract in 2 dubois and prade introduced the notion of fuzzy numbers and defined the basic operations of addition subtraction multiplication and division a slightly modified definition of fuzzy numbers was presented in 4 and in that paper a metric was defined for this family of fuzzy sets another less restrictive definition of fuzzy numbers can be found in 1 in the present paper we consider fuzzy numbers from a somewhat different perspective basically we shall view fuzzy numbers in a topological vector space setting using the customary vector space operations together with the metric given in 4 we will define differentiation and integration of fuzzy valued functions in ways that parallel closely the corresponding definitions for real differentiation and integration

application of simpson quadrature rule and iterative method for solving nonlinear fuzzy delay integral equations abstract in this study firstly we present an iterative method by using simpson quadrature formula for solving nonlinear fuzzy delay integral equations in addition the convergence analysis of the proposed method is investigated also we prove numerical stability analysis of the method by means of choosing the perturbation in the first iteration finally numerical examples to illustrate applicability of this method are presented

iterative method for numerical solution of two dimensional nonlinear fuzzy integral equations in this paper we prove the convergence of the method of successive approximations used to approximate the solution of two dimensional nonlinear fuzzy fredholm integral equations of the second kind also we present an iterative procedure based on quadrature formula to solve such equations the error estimation of the proposed method is given in terms of uniform and partial modulus of continuity finally some numerical experiments confirm the theoretical results and illustrate the accuracy of the method

keypoints based surface representation for 3d modeling and 3d object recognition the three dimensional 3d modeling and recognition of 3d objects have been traditionally performed using local features to represent the underlying 3d surface extraction of features requires cropping of several local surface patches around detected keypoints although an important step the extraction and representation of such local patches adds to the computational complexity of the algorithms this paper proposes a novel keypoints based surface representation ksr technique the proposed technique has the following two characteristics 1 it does not rely on the computation of features on a small surface patch cropped around a detected keypoint rather it exploits the geometrical relationship between the detected 3d keypoints for local surface representation 2 ksr is computationally efficient requiring only seconds to process 3d models with over 50 000 points with a matlab implementation experimental results on the uwa and stanford 3d models dataset suggest that it can accurately perform pairwise and multiview range image registration 3d modeling ksr was also tested for 3d object recognition with occluded scenes recognition results on the uwa dataset show that the proposed technique outperforms existing methods including 3d tensor vd lsd keypoint depth based feature spherical harmonics and spin image with a recognition rate of 95 9 the proposed approach also achieves a recognition rate of 93 5 on the challenging ca fascori dataset compared to 92 5 achieved by game theoretic the proposed method is computationally efficient compared to state of the art local feature methods highlightswe propose a novel technique called keypoint based surface representation ksr the proposed technique does not require local features around detected keypoints ksr exploits geometrical relationships between keypoints for surface representation ksr is tested on 3 popular datasets for 3d modeling and 3d object recognition ksr achieves superior 3d modeling and recognition results

numerical solutions of the nonlinear fuzzy hammerstein volterra delay integral equations in this paper an iterative numerical method that solves nonlinear fuzzy hammerstein volterra integral equations with constant delay is developed by using the error estimates a practical stopping criterion of the algorithm is obtained the convergence and the numerical stability of the method is proved and its accuracy is illustrated on three numerical examples the study of this integral equation is important because it has as a particular case the fuzzy variant of a mathematical model from epidemiology

integration of local and global geometrical cues for 3d face recognition we present a unified feature representation of 2 5d pointclouds and apply it to face recognition the representation integrates local and global geometrical cues in a single compact representation which makes matching a probe to a large database computationally efficient the global cues provide geometrical coherence for the local cues resulting in better descriptiveness of the unified representation multiple rank 0 tensors scalar features are computed at each point from its local neighborhood and from the global structure of the 2 5d pointcloud forming multiple rank 0 tensor fields the pointcloud is then represented by the multiple rank 0 tensor fields which are invariant to rigid transformations each local tensor field is integrated with every global field in a 2d histogram which is indexed by a local field in one dimension and a global field in the other dimension finally pca coefficients of the 2d histograms are concatenated into a single feature vector the representation was tested on frgc v2 0 data set and achieved 93 78 identification and 95 37 verification rate at 0 1 far

some properties of the space of fuzzy valued continuous functions on a compact set in this paper a generalized form of the bolzano theorem in classical analysis to fuzzy number space and a characterization of compact subsets in fuzzy number space are given some properties of the fuzzy valued continuous functions defined on a compact set k are studied completeness of the space c k e 1 of fuzzy valued continuous functions on k endowed with the supremum metric d is proved a characterization of compact subsets in the space c k e 1 d is presented which is a generalization of the arzela ascoli theorem in classical analysis

fuzzy differential equations abstract this paper deals with fuzzy set valued mappings of a real variable whose values are normal convex upper semicontinuous and compactly supported fuzzy sets in rn we study differentiability and integrability properties of such functions and give an existence and uniqueness theorem for a solution to a fuzzy differential equation

theory and applications of fuzzy volterra integral equations formulations of fuzzy integral equations in terms of the aumann integral do not reflect the behavior of corresponding crisp models consequently they are ill adapted to describe physical phenomena even when vagueness and uncertainty are present a similar situation for fuzzy odes has been obviated by interpretation in terms of families of differential inclusions the paper extends this formalism to fuzzy integral equations and shows that the resulting solution sets and attainability sets are fuzzy and far better descriptions of uncertain models involving integral equations the investigation is restricted to volterra type equations with mildly restrictive conditions but the methods are capable of extensive generalization to other types and more general assumptions the results are illustrated by integral equations relating to control models with fuzzy uncertainties

two computational methods for solving linear fredholm fuzzy integral equation of the second kind in this paper we present two methods which will exploit hybrid legendre and block pulse functions and legendre wavelets as bases for l 2 0 1 x 0 1 to find an approximate solution for a system of linear fredholm integral equation of the second kind with two variables we will apply our methods for an applied example linear fredholm fuzzy integral equation of the second kind m friedman ma ming a kandel numerical solutions of fuzzy differential and integral equations fuzzy sets and systems 106 1999 35 48

numerical solution of linear fredholm fuzzy integral equations of the second kind by adomian method using parametric form of fuzzy numbers we convert a linear fuzzy fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case we use adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy fredholm integral equation of the second kind we apply the method to some examples

existence and comparison theorems to volterra fuzzy integral equation in e n d abstract kaleva 1987 studied the measurability and integrability for the fuzzy set valued mappings of a real variable whose values are in the fuzzy number space e n d in this paper by using the embedding theorem of kaleva 1990 on e n d the darbo fixed points theorem in the convex cone c i e n where i denotes a bounded closed interval is given further the criteria for the existence and comparison of solutions to the volterra fuzzy integral equation in e n d are established under the compactness type conditions

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

when is there a representer theorem vector versus matrix regularizers we consider a general class of regularization methods which learn a vector of parameters on the basis of linear measurements it is well known that if the regularizer is a nondecreasing function of the l2 norm then the learned vector is a linear combination of the input data this result known as the representer theorem lies at the basis of kernel based methods in machine learning in this paper we prove the necessity of the above condition in the case of differentiable regularizers we further extend our analysis to regularization methods which learn a matrix a problem which is motivated by the application to multi task learning in this context we study a more general representer theorem which holds for a larger class of regularizers we provide a necessary and sufficient condition characterizing this class of matrix regularizers and we highlight some concrete examples of practical importance our analysis uses basic principles from matrix theory especially the useful notion of matrix nondecreasing functions

positive solutions of nonlinear integral equations arising in infectious diseases on considere l equation integrale non lineaire x t t t f s x s ds on utilise la theorie d indice du point fixe et la technique monotone pour etablir trois theoremes sur les solutions le premier affirme l existence de deux solutions non negatives non triviales de periode les deux autres concernent l existence et l unicite des solutions positives non triviales sous certaines conditions

support vector shape a classifier based shape representation we introduce a novel implicit representation for 2d and 3d shapes based on support vector machine svm theory each shape is represented by an analytic decision function obtained by training svm with a radial basis function rbf kernel so that the interior shape points are given higher values this empowers support vector shape svs with multifold advantages first the representation uses a sparse subset of feature points determined by the support vectors which significantly improves the discriminative power against noise fragmentation and other artifacts that often come with the data second the use of the rbf kernel provides scale rotation and translation invariant features and allows any shape to be represented accurately regardless of its complexity finally the decision function can be used to select reliable feature points these features are described using gradients computed from highly consistent decision functions instead from conventional edges our experiments demonstrate promising results

a note on fuzzy integral equations in this paper existence theorems for certain volterra integral equations and fredholm integral equation for the fuzzy set valued mappings are obtained

3d geometric scale variability in range images features and descriptors despite their ubiquitous presence little has been investigated about the scale variability the relative variations in the spatial extents of local structures of 3d geometric data in this paper we present a comprehensive framework for exploiting this 3d geometric scale variability in range images that provides rich information for characterizing the overall geometry we derive a sound scale space representation which we refer to as the geometric scale space that faithfully encodes the scale variability of the surface geometry and derive novel detectors to extract prominent features and identify their natural scales the result is a hierarchical set of features of different scales which we refer to as scale dependent geometric features we then derive novel local shape descriptors that represent the surface structures that give rise to those features by carving out and encoding the local surface that fall within the support regions of the features this leads to scale dependent or scale invariant local shape descriptors that convey significant discriminative information of the object geometry we demonstrate the effectiveness of geometric scale analysis on range images and show that it enables novel applications in particular fully automatic registration of multiple objects from a mixed set of range images and 3d object recognition in highly cluttered range image scenes

existence of the solutions of fuzzy differential equations with parameters in this paper we study the existence of the solutions of fuzzy differential equations with parameters by the topological degree method

quadrature rules for integrals of fuzzy number valued functions in this paper we introduce some quadrature rules for the henstock integral of fuzzy number valued mappings by giving error bounds for mappings of bounded variation and of lipschitz type we also consider generalizations of classical quadrature rules such as midpoint type trapezoidal and three point type quadrature finally we study fine quadrature rules and we present some numerical applications

fast and accurate surface alignment through an isometry enforcing game surface registration is often performed as a two step process a feature matching scheme is first adopted to find a coarse initial alignment between two meshes subsequently a refinement step which usually operates in the space of rigid motions is applied to reach an optimal registration with respect to pointwise distances between overlapping areas in this paper we propose a novel technique that allows to obtain an accurate surface registration in a single step without the need for an initial motion estimation the main idea of our approach is to cast the selection of correspondences between points on the surfaces in a game theoretic framework where a natural selection process allows matching points that satisfy a mutual rigidity constraint to thrive eliminating all the other correspondences this process yields a very robust inlier selection scheme that does not depend on any particular technique for selecting the initial strategies as it relies only on the global geometric compatibility between correspondences the practical effectiveness of the approach is confirmed by an extensive set of experiments and comparisons with state of the art techniques highlightswe introduce a novel pipeline for rigid surface alignment based on game theory the method allows to obtain accurate solutions without requiring an initial estimate we propose simple descriptors designed to be fast and effective within our pipeline we establish a relation between evolutionary stable states and optimal alignments the technique is efficient and outperforms the state of the art

numerical solutions of fuzzy differential and integral equations using the embedding method numerical procedures for solving fuzzy differential equations fdes and fuzzy integral equations fies with arbitrary kernels have been investigated sufficient conditions for convergence of the proposed algorithms are given and their applicability is illustrated with examples this work and its conclusions may narrow the gap between the theoretical research on fdes and fies and the practical applications already existing in the design of various fuzzy dynamical systems

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

demisting the hough transform for 3d shape recognition and registration in applying the hough transform to the problem of 3d shape recognition and registration we develop two new and powerful improvements to this popular inference method the first intrinsic hough solves the problem of exponential memory requirements of the standard hough transform by exploiting the sparsity of the hough space the second minimum entropy hough explains away incorrect votes substantially reducing the number of modes in the posterior distribution of class and pose and improving precision our experiments demonstrate that these contributions make the hough transform not only tractable but also highly accurate for our example application both contributions can be applied to other tasks that already use the standard hough transform

part ii 3 d object recognition and shape estimation from image contours using b splines shape invariant matching and neural network for pt i see ibid p 1 12 1994 this paper is the second part of a 3 d object recognition and shape estimation system that identifies particular objects by recognizing the special markings text symbols drawings etc on their surfaces the shape of the object is identified from the image curves using b spline curve modeling as described in part i as well as a binocular stereo imaging system this is achieved by first estimating the 3 d control points from the corresponding curves in each image in the stereo imaging system from the 3 d control points the 3 d object curves are generated and these are subsequently used for estimating the 3 d surface parameters a bayesian framework is used for classifying the image into one of c possible surfaces based on the extracted 3 d object curves this is complemented by a neural network nn that recognizes the surface as a particular object e g a pepsi can versus a peanut butter jar by reading the text markings on the surface to reduce the amount of training the nn has to undergo for recognition the object curves are unwarped into planar curves before the matching process this eliminates the need for templates that are surface shape dependent and results in a planar curve that might be a rotated translated and scaled version of the template hence for the matching process we need to use measures that are invariant to these transformations one such measure is the fourier descriptors fd derived from the control points associated with the unwarped parent curves the approach is tried on a variety of images of real objects and appears to hold great promise

cosmos a representation scheme for 3d free form objects we address the problem of representing and recognizing 3d free form objects when 1 the object viewpoint is arbitrary 2 the objects may vary in shape and complexity and 3 no restrictive assumptions are made about the types of surfaces on the object we assume that a range image of a scene is available containing a view of a rigid 3d object without occlusion we propose a new and general surface representation scheme for recognizing objects with free form sculpted surfaces in this scheme an object is described concisely in terms of maximal surface patches of constant shape index the maximal patches that represent the object are mapped onto the unit sphere via their orientations and aggregated via shape spectral functions properties such as surface area curvedness and connectivity which are required to capture local and global information are also built into the representation the scheme yields a meaningful and rich description useful for object recognition a novel concept the shape spectrum of an object is also introduced within the framework of cosmos for object view grouping and matching we demonstrate the generality and the effectiveness of our scheme using real range images of complex objects

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

on the existence and uniqueness of solutions of fuzzy volterra fredholm integral equations abstract in this paper we study the problem of existence and uniqueness of solutions of volterra fredholm integral equation for the fuzzy set valued mappings

on henstock integral of fuzzy number valued functions i abstract in this paper we define and discuss the fh integral for fuzzy number valued functions using a concrete structure into which we embed the fuzzy number space e 1 several necessary and sufficient conditions of integrability for fuzzy number valued functions are given by means of abstract function theory

a novel representation and feature matching algorithm for automatic pairwise registration of range images automatic registration of range images is a fundamental problem in 3d modeling of free from objects various feature matching algorithms have been proposed for this purpose however these algorithms suffer from various limitations mainly related to their applicability efficiency robustness to resolution and the discriminating capability of the used feature representation we present a novel feature matching algorithm for automatic pairwise registration of range images which overcomes these limitations our algorithm uses a novel tensor representation which represents semi local 3d surface patches of a range image by third order tensors multiple tensors are used to represent each range image tensors of two range images are matched to identify correspondences between them correspondences are verified and then used for pairwise registration of the range images experimental results show that our algorithm is accurate and efficient moreover it is robust to the resolution of the range images the number of tensors per view the required amount of overlap and noise comparisons with the spin image representation revealed that our representation has more discriminating capabilities and performs better at a low resolution of the range images

note on numerical solutions of fuzzy differential equations by predictor corrector method in the present note it is shown that the examples presented in a recent paper by allahviranloo et al are incorrect namely the exact solutions proposed by the authors are not solutions of the given fuzzy differential equations fdes the correct exact solutions are also presented here together with some results for characterizing solutions of fdes under hukuhara differentiability by an equivalent system of odes in this way a new direction for the numerical solutions of fdes is proposed

stability of bdf methods for nonlinear volterra integral equations with delay abstract this paper deals with the stability analysis of the backward differential formulas or bdf methods for nonlinear volterra integral equations with delay vides the presented approach is based on a nonclassical lipschitz condition in particular the criteria on the global and the asymptotic stability of the methods are given