discrete choquet integral and some of its symmetric extensions classical extensions of the choquet integral defined on 0 1 to 1 1 are the asymmetric and the symmetric choquet integral the second one being called also the sipos integral recently the balancing choquet integral was introduced as another kind of a symmetric extension of the discrete choquet integral we introduce and discuss a new type of such extension the fusion choquet integral and discuss its properties and relationship to the balancing and the symmetric choquet integral the symmetric maximum introduced by grabisch is shown to be a special case of the fusion and the balancing choquet integral several extensions of owa operators are also discussed

class based feature matching across unrestricted transformations we develop a novel method for class based feature matching across large changes in viewing conditions the method is based on the property that when objects share a similar part the similarity is preserved across viewing conditions given a feature and a training set of object images we first identify the subset of objects that share this feature the transformation of the feature s appearance across viewing conditions is determined mainly by properties of the feature rather than of the object in which it is embedded therefore the transformed feature will be shared by approximately the same set of objects based on this consistency requirement corresponding features can be reliably identified from a set of candidate matches unlike previous approaches the proposed scheme compares feature appearances only in similar viewing conditions rather than across different viewing conditions as a result the scheme is not restricted to locally planar objects or affine transformations the approach also does not require examples of correct matches we show that by using the proposed method a dense set of accurate correspondences can be obtained experimental comparisons demonstrate that matching accuracy is significantly improved over previous schemes finally we show that the scheme can be successfully used for invariant object recognition

recognition using region correspondences recognition systems attempt to recover information about the identity of observed objects and their location in the environment a fundamental problem in recognition is pose estimation this is the problem of using a correspondence between some portions of an object model and some portions of an image to determine whether the image contains an instance of the object and in case it does to determine the transformation that relates the model to the image the current approaches to this problem are divided into methods that use global properties of the object e g centroid and moments of inertia and methods that use local properties of the object e g corners and line segments global properties are sensitive to occlusion and specifically to self occlusion local properties are difficult to locate reliably and their matching involves intensive computation we present a novel method for recognition that uses region information in our approach the model and the image are divided into regions given a match between subsets of regions without any explicit correspondence between different pieces of the regions the alignment transformation is computed the method applies to planar objects under similarity affine and projective transformations and to projections of 3 d objects undergoing affine and projective transformations the new approach combines many of the advantages of the previous two approaches while avoiding some of their pitfalls like the global methods our approach makes use of region information that reflects the true shape of the object but like local methods our approach can handle occlusion

tetrahedral mesh generation based on node insertion in crystal lattice arrangements and advancing front delaunay triangulation a method of unstructured technical mesh generation for general three dimensional domains is presented a conventional boundary representation is adopted as the basis for the description of solids with evolving geometry and topology the geometry of the surfaces is represented either analytically or by piecewise polynominal interpolation a preliminary surface mesh is generated by an advancing front method with the nodes inserted by hard sphere packing in physical space in accordance with a prescribed mesh density interior nodes are inserted in a face centered cubic fcc crystal lattice arrangements coupled to octree spatial subdivision with the local lattice parameter determined by a prespecified nodal density function prior to triangulation of the volume the preliminary surface mesh is preprocessed by a combination of local transformations and subdivisions in order to guarantee that the surface triangulation be a subcomplex of the volume delaunay triangulation a joint delaunay triangulation of the interior and boundary nodes which preserves the modified surface mesh is then constructed via an advancing front approach the resulting mesh is finally improved upon by the application of local transformations the overall time complexity of the mesher is o n log n the robustness and versatility of the approach as well as the good quality of the resulting meshes is demostrated with the aid of selected examples

graded tetrahedral finite element meshes vertices in the body centred cubic bcc lattice are used to create a tetrahedral spatial decomposition with this spatial decomposition an octree approach is combined with delaunay triangulations to decompose solids into tetrahedral finite element meshes solids must have their surfaces triangulated and the vertices in the triangulation are finite element nodes local densities of interior tetrahedra are controlled by the densities of surface triangles accuracy of the decomposition into finite elements depends on the accuracy of the surface triangulation which can be constructed with state of the art computer aided design systems

aggregation on boolean multi polar space three types of aggregation operators defined on a boolean multi polar space 0 1 m are compared three different monotonicity conditions that yield different types of aggregation operators are discussed and the structure of these aggregation operators on 0 1 m with additional properties of associativity and commutativity is studied for any m n the commutative associative boolean multi polar aggregation operators are shown to coincide with boolean multi polar uninorms the structure of commutative associative sl aggregation operators is shown to be dependent on the structure of the class of abelian idempotent semigroups based on m 1 elements with an annihilator we show that each commutative associative sl aggregation operator with annihilator 0 corresponds to a lower semi lattice with bottom element 0 for m 2 the class of commutative associative c aggregation operators is proved to be equal to the intersection of the class of commutative associative boolean multi polar aggregation operators and the class of commutative associative sl aggregation operators examples of the three types of commutative associative aggregation operators are shown and discussed for m 1 2 3

multi and multi polar capacities aggregation of inputs from different categories generalizes both unipolar standard and bipolar aggregation this aggregation covers two main cases of multi polar and non monotone aggregation inputs from different categories can be found in classification methods multi criteria decision making game theory and political and sociological sciences two main concepts related to aggregation on the unit interval are capacities and aggregation on grid points boolean functions in this paper multi and multi polar capacities that extend bi and bipolar capacities are introduced the position of these capacities is clarified by means of the connection between boolean crisp functions capacities aggregation and concepts from other domains of science which are shown for the unipolar the bipolar and the multi polar case the connection between multi and multi polar capacities and the concept of games with n players and r alternatives is described

a representation of a comonotone x additive and monotone functional by two sugeno integrals there is obtained a representation of a email protected email protected additive weak email protected homogeneous and monotone functional l defined on the class of functions on finite set as a symmetric maximum of two sugeno integrals this representation is a generalization of certain previous results which are useful for cumulative prospect theory as a consequence of a result on general fuzzy rank and sign dependent functionals considered on functions defined on the infinitely countable basic set x it is obtained that the symmetric sugeno integral is email protected email protected additive functional on the class of functions with finite support

the symmetric sugeno integral we propose an extension of the sugeno integral for negative numbers in the spirit of the symmetric extension of choquet integral also called sipos integral our framework is purely ordinal since the sugeno integral has its interest when the underlying structure is ordinal we begin by defining negative numbers on a linearly ordered set and we endow this new structure with a suitable algebra very close to the ring of real numbers in a second step we introduce the mobius transform on this new structure lastly we define the symmetric sugeno integral and show its similarity with the symmetric choquet integral

discrete bipolar pseudo integrals abstract in the authors paper strboja et al 2016 42 the notion of the bipolar pseudo integral has been introduced this paper extends investigations related to this new type of bipolar integrals defined with respect to decomposable bi capacities we consider the main properties of the discrete bipolar pseudo integral a characterization theorem for the discrete bipolar pseudo integral is proven monotone convergence theorems and the fatou type lemma for the discrete bipolar pseudo integral are considered in order to illustrate obtained results many interesting examples are provided

bipolar fuzzy integrals in decision analysis and especially in multiple criteria decision analysis several non additive integrals have been introduced in the last 60 years these include the choquet integral the shilkret integral and the sugeno integral among others recently a bipolar choquet integral was proposed for cases in which the underlying scale is bipolar in this paper we propose a bipolar shilkret integral and a bipolar sugeno integral moreover we provide an axiomatic characterization of all three bipolar fuzzy integrals

regular fuzzy measure and representation of comonotonically additive functional this paper discusses the functional i defined on the class of continuous functions which is comonotonically additive and monotone the notion of regular fuzzy measure is proposed and the uniqueness theorem of regular fuzzy measure is shown it is also shown that i can be represented by the difference of two choquet integrals with respect to regular fuzzy measures when the universal set x is a locally compact hausdorff space and that i can be represented by one choquet integral with respect to a regular fuzzy measure when x is a compact hausdorff space

the application of fuzzy integrals in multicriteria decision making abstract this paper presents a synthesis on the application of fuzzy integrals as an innovative tool for criteria aggregation in decision problems the main point is that fuzzy integrals are able to model interaction between criteria in a flexible way the methodology has been elaborated mainly in japan and has been applied there successfully in various fields such as design reliability evaluation of goods etc it seems however that this technique is still very little known in europe it is one of the aims of this review to disseminate this emerging technology in many industrial fields

tetrahedral mesh generation based on space indicator functions reference epfl article 184796doi 10 1002 nme 4419view record in web of science record created on 2013 03 04 modified on 2017 07 28

discrete markov image modeling and inference on the quadtree noncasual markov or energy based models are widely used in early vision applications for the representation of images in high dimensional inverse problems due to their noncausal nature these models generally lead to iterative inference algorithms that are computationally demanding in this paper we consider a special class of nonlinear markov models which allow one to circumvent this drawback these models are defined as discrete markov random fields mrf attached to the nodes of a quadtree the quadtree induces causality properties which enable the design of exact noniterative inference algorithms similar to those used in the context of markov chain models we first introduce an extension of the viterbi algorithm which enables exact maximum a posteriori map estimation on the quadtree two other algorithms related to the mpm criterion and to bouman and shapiro s 1994 sequential map smap estimator are derived on the same hierarchical structure the estimation of the model hyper parameters is also addressed two expectation maximization em type algorithms allowing unsupervised inference with these models are defined the practical relevance of the different models and inference algorithms is investigated in the context of image classification problem on both synthetic and natural images

adaptive multivlevel methods in three space dimensions we consider the approximate solution of self adjoint elliptic problems in three space dimensions by piecewise linear finite elements with respect to a highly non uniform tetrahedral mesh which is generated adaptively the arising linear systems are solved iteratively by the conjugate gradient method provided with a multilevel preconditioner here the accuracy of the iterative solution is coupled with the discretization error as the performance of hierarchical bases preconditioners deteriorates in three space dimensions the bpx preconditioner is used taking special care of an efficient implementation reliable a posteriori estimates for the discretization error are derived from a local comparison with the approximation resulting from piecewise quadratic elements to illustrate the theoretical results we consider a familiar model problem involving reentrant corners and a real life problem arising from hyperthermia a recent clinical method for cancer therapy

filling space with tetrahedra in the context of 3d finite element meshes various options for filling an indefinite space such as would be approached within a fine mesh with tetrahedra are considered this problem is not trivial as it is in 2 d since unlike equilateral triangles regular tetrahedra cannot be fitted together to fill space various groupings or assemblies which can be repeated indefinitely to fill space are considered by altering the shape of the tetrahedra in one of these to minimize a suitable function a unique shape of tetrahedron is obtained which optimizes the conditioning the mesh thus produced is shown to be better conditioned than alternatives based on assemblies of different shaped tetrahedra a number of conditioning measures are used to confirm this finally actual meshes which fit boundaries are briefly considered copyright 1999 john wiley sons ltd

decomposable and k additive multi capacities and multi polar capacities extensions of several concepts for definition of capacities given by a small number of parameters in the unipolar and bipolar framework to the case of multi polar input spaces are studied the paper covers decomposable symmetric category symmetric additive reduced additive and k additive multi polar capacities and discusses its properties the multi polar mobius transform of multi polar capacities is introduced and its properties for coordinate wisely given additive and k additive multi polar capacities are described

alignment by maximization of mutual information a new information theoretic approach is presented for finding the pose of an object in an image the technique does not require information about the surface properties of the object besides its shape and is robust with respect to variations of illumination in our derivation few assumptions are made about the nature of the imaging process as a result the algorithms are quite general and may foreseeably be used in a wide variety of imaging situations experiments are presented that demonstrate the approach registering magnetic resonance mr images aligning a complex 3d object model to real scenes including clutter and occlusion tracking a human head in a video sequence and aligning a view based 2d object model to real images the method is based on a formulation of the mutual information between the model and the image as applied here the technique is intensity based rather than feature based it works well in domains where edge or gradient magnitude based methods have difficulty yet it is more robust than traditional correlation additionally it has an efficient implementation that is based on stochastic approximation

fully automatic mesh generation for 3 d domains based upon voxel sets fully automatic three dimensional mesh generation is an essential and increasingly crucial requirement for finite element solution of partial derivative equations the results of numerical simulation more precisely the convergence and accuracy of numerical solutions closely depends on the quality of the underlying mesh this work introduces a fully automatic finite element mesh algorithm with simplexes tetrahedra adapted to complex geometries described by disctete data this paper is divided in four sections a brief introduction to discrete geometry is given as well as the basic definition of the domain of interest b description of the voxel approach to tetrahedronization the tetrahedronization process uses a divide and conquer method which provides small elements on the boundary of the domain of interest voxels of the domain are subdivided according to an automatic procedure which preserves the topology specific rules were introduced which allow reducing the number of voxel configurations to be treated and consequently the computation time c presentation of results and performances of the mesh algorithms the resulting algorithm demonstrates an n log n growth rate with respect to the number of elements d optimization of the mesh generation process at hand of a finite octree type of explicit controlling space

a universal integral as common frame for choquet and sugeno integral the choquet and the sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required however their applicability is restricted because of the special operations used in the construction of these integrals therefore we provide a concept of integrals generalizing both the choquet and the sugeno case for functions with values in the nonnegative real numbers universal integrals are introduced and investigated which can be defined on arbitrary measurable spaces and for arbitrary monotone measures for a fixed pseudo multiplication on the nonnegative real numbers the smallest and the greatest universal integrals are given finally another construction method for obtaining universal integrals is introduced and the restriction to the unit interval i e to fuzzy integrals is considered

multi polar t conorms and uninorms abstract transformation of uninorms defined on the unit interval to the bipolar scale yields bipolar t conorms and transformation of nullnorms on the unit interval yields bipolar t norms we use this relation in the investigation of the structure of bipolar and multi polar t norms and t conorms we use the same transformation of the unit interval into the bipolar scale in order to obtain bipolar aggregation operators from ordinal sum t norms and t conorms the extensions of these special bipolar aggregation operators generalize both multi polar t norms and t conorms and therefore we call them multi polar uninorms several examples of multi polar t conorms and uninorms are also presented

eigentracking robust matching and tracking of articulated objects using a view based representation this paper describes an approach for tracking rigid and articulated objects using a view based representation the approach builds on and extends work on eigenspace representations robust estimation techniques and parameterized optical flow estimation first we note that the least squares image reconstruction of standard eigenspace techniques has a number of problems and we reformulate the reconstruction problem as one of robust estimation second we define a subspace constancy assumption that allows us to exploit techniques for parameterized optical flow estimation to simultaneously solve for the view of an object and the affine transformation between the eigenspace and the image to account for large affine transformations between the eigenspace and the image we define a multi scale eigenspace representation and a coarse to fine matching strategy finally we use these techniques to track objects over long image sequences in which the objects simultaneously undergo both affine image motions and changes of view in particular we use this eigentracking technique to track and recognize the gestures of a moving hand

averaging operators in fuzzy classification systems the averaging operators used for aggregation of outputs of fuzzy classification rules are examined several methods used in fuzzy rule based classification systems are discussed and related multi polar averaging operators are shown further new aggregation methods based on the idea used for the definition of owa operators are described the connection between multi polar averaging operators and the multi polar choquet integral is shown and using this connection the conditions under which are the respective averaging operators monotone are studied several examples of special multi polar owa operators with a relation to existing bipolar aggregation operators are included

lattice boltzmann and finite difference simulations for the permeability for three dimensional porous media numerical micropermeametry is performed on three dimensional porous samples having a linear size of approximately 3 mm and a resolution of 7 5 microm one of the samples is a microtomographic image of fontainebleau sandstone two of the samples are stochastic reconstructions with the same porosity specific surface area and two point correlation function as the fontainebleau sample the fourth sample is a physical model that mimics the processes of sedimentation compaction and diagenesis of fontainebleau sandstone the permeabilities of these samples are determined by numerically solving at low reynolds numbers the appropriate stokes equations in the pore spaces of the samples the physical diagenesis model appears to reproduce the permeability of the real sandstone sample quite accurately while the permeabilities of the stochastic reconstructions deviate from the latter by at least an order of magnitude this finding confirms earlier qualitative predictions based on local porosity theory two numerical algorithms were used in these simulations one is based on the lattice boltzmann method and the other on conventional finite difference techniques the accuracy of these two methods is discussed and compared also with experiment

face recognition the problem of compensating for changes in illumination direction a face recognition system must recognize a face from a novel image despite the variations between images of the same face a common approach to overcoming image variations because of changes in the illumination conditions is to use image representations that are relatively insensitive to these variations examples of such representations are edge maps image intensity derivatives and images convolved with 2d gabor like filters here we present an empirical study that evaluates the sensitivity of these representations to changes in illumination as well as viewpoint and facial expression our findings indicated that none of the representations considered is sufficient by itself to overcome image variations because of a change in the direction of illumination similar results were obtained for changes due to viewpoint and expression image representations that emphasized the horizontal features were found to be less sensitive to changes in the direction of illumination however systems based only on such representations failed to recognize up to 20 percent of the faces in our database humans performed considerably better under the same conditions we discuss possible reasons for this superiority and alternative methods for overcoming illumination effects in recognition

the choquet integral with respect to a level dependent capacity we present a generalization of choquet integral in which the capacity depends also on the value of the aggregated variables we show that as particular cases of our generalization of choquet integral there are the sugeno integral the sipos integral and the cumulative prospect theory functional we also show that many concepts such as mobius transform importance index interaction index k order capacities and owa operators introduced in the research about choquet integral can be generalized in the considered context