generalized means as model of compensative connectives abstract empirical investigations have shown that instead of strong logical and and or connectives there is often some degree of compensation in between in this paper the generalized means are proposed as connective operators for fuzzy set theory which easily allow for modelling the degree of compensation in a natural manner including the arithmetic and geometric means as well as the maximum and minimum operators as special cases numerical examples with empirical data form an illustration of this concept some aspects of applications to decision making are discussed

a chain code for representing 3d curves abstract a chain code for representing three dimensional 3d curves is defined any 3d continuous curve can be digitalized and represented as a 3d discrete curve this 3d discrete curve is composed of constant straight line segments thus the chain elements represent the orthogonal direction changes of the constant straight line segments of the discrete curve the proposed chain code only considers relative direction changes which allows us to have a curve descriptor invariant under translation and rotation also this curve descriptor may be starting point normalized for open and closed curves and invariant under mirroring transformation in the content of this work the main characteristics of this chain code are presented this chain code is inspired by the work of guzman mcc technical report number aca 254 87 july 13 1987 for representing 3d stick bodies finally we present some results of this chain code to represent and process 3d discrete curves as linear features over the terrain by means of digital elevation model dem data also we use this chain code for representing solids composed of voxels thus each solid represents a dem which is described by only one chain

global description of edge patterns using moments abstract shape recognition has traditionally been accomplished using well bounded segmented regions or their closed contours in this way the internal edge details of the objects are ignored there are cases such as in character recognition and in object recognition when patterns are not closed contours in this paper such patterns are defined as edge patterns and edge standard moments esm are developed which are invariant to location scale and rotation results of patterns matching with character recognition and polyhedral object recognition are presented

inspection of 2 d objects using pattern matching method abstract a pattern matching scheme is developed for the inspection of objects in industrial environment the inspection includes dimensional verification and shape matching which compares a 2 dimensional image of an object to a pattern image the method proves to be computationally efficient and accurate for real time application

stochastic models for closed boundary analysis representation and reconstruction the analysis of closed boundaries of arbitrary shapes on a plane is discussed specifically the problems of representation and reconstruction are considered a one to one correspondence between the given closed boundary and a univariate or multivariate sequence of real numbers is set up univariate or multivariate circular autoregressive models are suggested for the representation of the sequence of numbers derived from the closed boundary the stochastic model representing the closed boundary is invariant to transformations like sealing translation choice of starting point and rotation over angles that are multiples of 2 pi n where n is the number of observations methods for estimating the unknown parameters of the model are given and a decision rule for choosing the appropriate number of coefficients is included constraints on the estimates are derived so that the estimates are invariant to the transformations of the boundaries the stochastic model enables the reconstruction of a dosed boundary using fft algorithms results of simulations are included and the application to contour coding is discussed

two dimensional object recognition using a two dimensional polar transform abstract a two dimensional 2d transform is proposed for the classification of planar objects with a centroid referenced polar representation it samples the multiple intersections of n radii with the object using the mass center translation invariance is achieved and with an appropriate amplitude normalization the transform is also made invariant to scaling the modules of its 2d fast fourier transform coefficients which are rotation invariant are used as the feature vector simultaneously translation scaling and rotation parameters are estimated the high performance of this algorithm is shown with computer simulations and its advantages and disadvantages are analysed in comparison with existing methods

some quantities represented by the choquet integral this paper shows that the choquet integral can represent some useful quantities such as supremum infimum essential supremum essential infimum mean median quantile 100 percentile and l estimators including trimmed mean

shape matching of two dimensional objects in this paper we present results in the areas of shape matching of nonoccluded and occluded two dimensional objects shape matching is viewed as a segment matching problem unlike the previous work the technique is based on a stochastic labeling procedure which explicitly maximizes a criterion function based on the ambiguity and inconsistency of classification to reduce the computation time the technique is hierarchical and uses results obtained at low levels to speed up and improve the accuracy of results at higher levels this basic technique has been extended to the situation where various objects partially occlude each other to form an apparent object and our interest is to find all the objects participating in the occlusion in such a case several hierarchical processes are executed in parallel for every object participating in the occlusion and are coordinated in such a way that the same segment of the apparent object is not matched to the segments of different actual objects these techniques have been applied to two dimensional simple closed curves represented by polygons and the power of the techniques is demonstrated by the examples taken from synthetic aerial industrial and biological images where the matching is done after using the actual segmentation methods

on equivalence classes of fuzzy connectives the case of fuzzy integrals an equivalence relation between connectives or operators in the framework of multiple criteria decision making is introduced two operators are said to be equivalent if they lead to the same ranking of alternatives some general results to find equivalence classes of operators are given through the concept of level surfaces in a second part these results are applied to the case of discrete fuzzy integrals which are considered here as n place operators first some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals

image normalization by complex moments the role of moments in image normalization and invariant pattern recognition is addressed the classical idea of the principal axes is analyzed and extended to a more general definition the relationship between moment based normalization moment invariants and circular harmonics is established invariance properties of moments as opposed to their recognition properties are identified using a new class of normalization procedures the application of moment based normalization in pattern recognition is demonstrated by experiment

a measure of tortuosity based on chain coding a measure of tortuosity for 2d curves is presented tortuosity is a very important property of curves and has many applications such as how to measure the tortuosity of retinal blood vessels intracerebral vasculature aluminum foams etc the measure of tortuosity proposed here is based on a chain code called slope chain code scc the scc uses some ideas which were described in a geometric structure for 2d shapes and 3d surfaces pattern recognition 25 1992 483 496 the scc of a curve is obtained by placing straight line segments of constant length around the curve the endpoints of the straight line segments always touching the curve and calculating the slope changes between contiguous straight line segments scaled to a continuous range from 1 to 1 the scc of a curve is independent of translation rotation and optionally of scaling which is an important advantage for computing tortuosity also the minimum and maximum values of tortuosity for curves and a measure of normalized tortuosity are described finally an application of the proposed measure of tortuosity is presented which corresponds to the computation of retinal blood vessel tortuosity

fuzzy measure of fuzzy events defined by fuzzy integrals abstract we define the concept of fuzzy measure of a fuzzy event by using a general form of fuzzy integral proposed by murofushi called fuzzy t conorm integral encompassing previous definitions zadeh defined the probability measure of a fuzzy event and later the possibility measure of fuzzy event using a duality property of fuzzy t conorm integral we propose a general definition of fuzzy measure of fuzzy events which is compatible with previous definitions of zadeh and possesses all properties of a fuzzy measure in particular the duality property using our definition we examine the case of decomposable measures and belief functions a comparison with previous works is provided

principal component analysis of speech spectrogram images abstract recent research has demonstrated that spectrograms containing human speech utterances can be analyzed using image processing techniques to yield a high recognition rate in particular fourier descriptors fds have been proved very useful for characterizing the boundary of segmented isolated words containing the english semivowels w y 1 and r this study examines the appropriateness of fds combined with 17 other general features for classifying objects contained in binary spectrogram images principal components pcs are used for feature reduction on a speaker dependent data set consisting of 80 sounds representing 20 speakerdependent words containing english semivowels with only eight features including four 32 point fds and four general features obtained from principal component analysis a 97 5 recognition rate was obtained 1997 pattern recognition society published by elsevier science ltd

a potential based approach for shape matching and recognition this paper presents a novel potential based approach for recognizing the shape of a two dimensional 2d region by identifying the best match from a selected group of shape templates the proposed model assumes that the border of every 2d region is uniformly charged an initially small shape template placed inside a shape sample will experience the repulsive force and torque arising from the potential field a better match in the shape between the template and the sample can be obtained if the template translates and reorients itself to reduce the potential while growing in size the shape template with the largest final size corresponds to the best match and represents the shape of the given sample the potential and the associated repulsive force and torque between the polygonal contours are analytically tractable hence resulting in high computational efficiency of the matching process the proposed approach is intrinsically invariant under translation rotation and size changes of the shape sample moreover not only can the matching be carried out directly for shape contours at different viewscales but the contours can also be unconnected provided that the template is confined within the shape sample throughout the matching process

morse theory and finiteness properties of groups we examine the finiteness properties of certain subgroups of right angled artin groups in particular we find an example of a group that is of type fp z but is not finitely presented

pictorial representations of fuzzy connectives part i cases of t norms t conorms and averaging operators part i of this paper shows a number of examples of existing t norms and t conorms which are known as good models of fuzzy set theoretic intersection and union and then the pictorial representations of t norms and t conorms are made with the aid of a computer several new examples of t norms and t conorms are also given averaging operators between min and max are summarized and their pictorial representations are also made

fuzzy systems as universal approximators an additive fuzzy system can uniformly approximate any real continuous function on a compact domain to any degree of accuracy an additive fuzzy system approximates the function by covering its graph with fuzzy patches in the input output state space and averaging patches that overlap the fuzzy system computes a conditional expectation e y x if we view the fuzzy sets as random sets each fuzzy rule defines a fuzzy patch and connects commonsense knowledge with state space geometry neural or statistical clustering systems can approximate the unknown fuzzy patches from training data these adaptive fuzzy systems approximate a function at two levels at the local level the neural system approximates and tunes the fuzzy rules at the global level the rules or patches approximate the function

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

radial and angular moment invariants for image identification radial and angular moments of images are presented and methods are shown for deriving moment functions that are invariant with respect to rotation translation reflection and size changes without the aid of the theory of algebraic invariants hu s invariants are expressed in terms of these radial and angular moments and it is claimed that this facilitates visual inspection of invariance properties

groups generated by reflections and aspherical manifolds not covered by euclidean space a coxeter system r v is a group r a coxeter group together with a set of generators v such that each element of v has order two and such that all relations in r are consequences of relations of the form vw m v w 1 where v w e v and m v w denotes the order of vw the m v w s which are positive integers or oo obviously determine the coxeter system up to isomorphism the list of finite coxeter groups is short and well known however general coxeter groups are much more flexible in fact the set v and the m v w s can be specified arbitrarily at least if v is finite subject only to the conditions m v v 1 and m v w m w v 2 if v w suppose that r v is a coxeter system that x is a hausdorff space and that xv v v is a locally finite family of closed subspaces indexed by v the xv are called the panels of x 2 there is a classical method for constructing a transformation group from these data for each x e x let v x denote the set of v in v such that x e xv for each subset s of v let rs be the subgroup generated by s and let xs be the face of x defined by

owa operators on complete lattices considering some aggregation functions we define bf b a weighting vectors then a definition for ordered weighted average owa operators is given based on bf b a weighting vectors moreover we show that our proposed definition for owa operators over complete lattices is a generalization of the given definition by lizasoain and moreno finally a special case is studied

the spirals of the slope chain code abstract generally speaking a spiral is a 2d curve which winds about a fixed point now we present a new alternative and easy way to describe and generate spirals by means of the use of the slope chain code scc e bribiesca a measure of tortuosity based on chain coding pattern recognition 46 2013 716 724 thus each spiral is represented by only one chain the chain elements produce a finite alphabet which allows us to use grammatical techniques for spiral classification spirals are composed of constant straight line segments and their chain elements are obtained by calculating the slope changes between contiguous straight line segments angle of contingence scaled to a continuous range from 1 180 to 1 180 the scc notation is invariant under translation rotation optionally under scaling and it does not use a grid other interesting properties can be derived from this notation such as the mirror symmetry and inverse spirals the accumulated slope the slope change mean and tortuosity for spirals we introduce new concepts of projective polygonal paths and osculating polygons we present a new spiral called the scc polygonal spiral and its chain which is described by the numerical sequence 2 n for n 3 to the best of our knowledge this is the first time that this spiral and its chain are presented the importance of this spiral and its chain is that this chain is covering all the slope changes of all the regular polygons composed of n edges n gons also we describe the chain which generates the spiral of archimedes finally we present some results of different kind of spirals from the real world including spiral patterns in shells

a bivariate autoregressive technique for analysis and classification of planar shapes a bivariate autoregressive model is introduced for the analysis and classification of closed planar shapes the boundary coordinate sequence of a digitized binary image is sampled to produce a polygonal approximation to an object s shape this circular sample sequence is then represented by a vector autoregressive difference equation which models the individual cartesian coordinate sequences as well as coordinate interdependencies several classification features which are functions or transformations of the estimated coefficient matrices and the associated residual error covariance matrices are developed these features are shown to be invariant to object transformations such as translation rotation and scaling laboratory experiments involving object sets representative of industrial shapes are presented superior classification results are demonstrated

contour sequence moments for the classification of closed planar shapes abstract a technique for classifying closed planar shapes is described in which a shape is characterized by a one dimensional sequence that represents the euclidean distance between the centroid and all contour pixels of the shape contour sequences obtained from shapes belonging to the same class are similar and are considered to be different realizations of a stochastic process statistical moment functions derived from contour sequences are used to characterize the process and hence the shapes it is shown that these moment functions are invariant to shape translation rotation and scale transformations examples are presented to illustrate the performance of these moment functions in the classification of noisy shapes

euler classes and bredon cohomology for groups with restricted families of finite subgroups we explore some of the special features with respect to bredon cohomology for groups whose finite subgroups are all either nilpotent or p groups or cyclic p groups we get some results on dimensions and also a formula for the equivariant euler class for certain groups we consider the generalization for bredon cohomology of the properties of being duality or poincare duality and study their behavior under p power index extensions with coefficients in a field of characteristic p

efficiency of chain codes to represent binary objects we present a study of compression efficiency for binary objects or bi level images for different chain code schemes chain code techniques are used for compression of bi level images because they preserve information and allow a considerable data reduction furthermore chain codes are the standard input format for numerous shape analysis algorithms in this work we apply chain codes to represent object with holes and we compare their compression efficiency for seven chain codes we have also compared all these chain codes with the jbig standard for bi level images

a characterization of the ordered weighted averaging functions based on the ordered bisymmetry property this paper deals with the characterization of a class of aggregation operators this class concerns operators that are symmetric increasing stable for the same positive linear transformations and present a property close to the bisymmetry property the ordered bisymmetry property it is proved that the class investigated contains exactly the ordered weighted averaging operators introduced by yager 1988

invariant planar shape recognition using dynamic alignment abstract closed planar shapes are modelled by an ordered sequence that represents the euclidean distance between the centroid and all contour pixels of the shape shapes belonging to the same class have similar sequences hence a procedure for classifying shapes is based on the degree of similarity between these sequences in order to determine the similarity between sequences a dynamic alignment process is developed to find the best correspondence between the sequences optimum alignment is obtained by expanding segments of the sequences to minimize a dissimilarity function between the sequences normalization with respect to scaling and rotation is described and an example illustrating the use of dynamic alignment for the classification of noisy shapes is presented

aggregation functions means this two part state of the art overview on aggregation theory summarizes the essential information concerning aggregation issues an overview of aggregation properties is given including the basic classification on aggregation functions in this first part the stress is put on means i e averaging aggregation functions both with fixed arity n ary means and with multiple arities extended means

on dimensions of groups with cocompact classifying spaces for proper actions we construct groups g that are virtually torsion free and have virtual cohomological dimension strictly less than the minimal dimension for any model for the classifying space for proper actions of g they are the first examples that have these properties and also admit cocompact models for this classifying space we exhibit groups g whose virtual cohomological dimension and bredon cohomological dimension are two that do not admit any 2 dimensional contractible proper g cw complex

characterization of some aggregation functions stable for positive linear transformations abstract this paper deals with the characterization of some classes of aggregation functions often used in multicriteria decision making problems the common properties involved in these characterizations are increasing monotonicity and stability for positive linear transformations additional algebraic properties related to associativity allow to completely specify the functions

an interpretation of fuzzy measures and the choquet integral as an integral with respect to a fuzzy measure abstract in this paper the non additivity of sugeno s fuzzy measures is interpreted in terms of addition and the rationality of the choquet integral is discussed it is pointed out that a fuzzy measure on a set x expresses the interaction between the subsets of x and can be represented by an additive measure it is shown through concrete examples that the choquet integral is reasonable as an integral with respect to a fuzzy measure it is also found that the choquet integral is closely related with the representation of a fuzzy measure

fuzzy t conorm integral with respect to fuzzy measures generalization of sugeno integral and choquet integral abstract this article discusses integrals with respect to sugeno s fuzzy measures sugeno integrals and choquet integrals with respect to general fuzzy measures are generalized in the setting of a t conorm algebraic system first t conorm integrals with respect to decomposable measures based on t conorm algebraic system are defined they are a modification of the weber integral secondly they are extended to fuzzy t conorm integrals with respect to general fuzzy measures the extension is made in the same way as the extension of the lebesgue integral to the choquet integral the class of fuzzy t conorm integrals includes choquet integrals and sugeno integrals properties of the integrals especially their representation are discussed

some groups of type vf a group is of type vf if it contains a finite index subgroup which has a finite classifying space we construct groups of type vf in which the centralizers of some elements of finite order are not of type vf and groups of type vf containing infinitely many conjugacy classes of finite subgroups from these examples it follows that a group g of type vf need not admit a finite type or finite classifying space for proper actions sometimes also called the universal proper g space we construct groups g for which the minimal dimension of a universal proper g space is strictly greater than the virtual cohomological dimension of g each of our groups embeds in some general linear group over the rational integers applications to algebraic k theory of group algebras and topological k theory of group c algebras are also considered the groups are constructed as finite extensions of bestvina brady groups

a theory of fuzzy measures representations the choquet integral and null sets abstract some theorems of t murofushi and m sugeno fuzzy sets and systems 29 1989 201 227 concerning representation of fuzzy measures and the choquet integral are generalized it is shown that if there is a certain relation between two measurable functions then the choquet integral is additive for these two functions in addition this article discusses null sets with respect to fuzzy measures and also fuzzy measures defined on a class which is not a algebra