an axiomatic approach to fuzzy cardinalities of finite fuzzy sets an axiomatic definition of fuzzy cardinalities for finite fuzzy sets defined by means of a convex fuzzy set on the natural numbers is presented in such a way that it includes the fuzzy cardinalities defined by authors like zadeh ralescu dubois wygralak and characterizes the cardinalities that fulfill the additivity property by means of the extended addition of fuzzy numbers such cardinalities result defined by two functions one nondecreasing and the other nonincreasing in a similar way to the scalar cardinality fuzzy sets and systems 110 2000 175

questions of cardinality of finite fuzzy sets abstract in this paper we focus our attention on finite fuzzy sets a complete simple and easily applicable cardinality theory for them is presented questions of equipotency and non classically understood cardinal numbers of finite fuzzy sets are discussed in detail also problems of arithmetical operations addition subtraction multiplication division and exponentiation on as well as ordering relation for those cardinals are carefully investigated

type fuzzy quantifiers determined by fuzzy measures defined on residuated lattices part ii permutation and isomorphism invariances abstract we study the properties of permutation invariance and isomorphism invariance of fuzzy quantifiers of type 1 1 defined using fuzzy measures and integrals these properties hold if fuzzy quantifiers are invariant with respect to permutations bijective mappings on the universe of discourse permutation invariance and with respect to bijections between different universes of discourse isomorphism invariance in other words fuzzy quantifiers with these properties are sensitive only to the cardinality of subsets of the universe of discourse and not to the individual nature of the elements of these subsets we characterize these properties by means of the corresponding properties of functionals used in the definition of the fuzzy quantifiers

a probabilistic definition of a nonconvex fuzzy cardinality the existing methods to assess the cardinality of a fuzzy set with finite support are intended to preserve the properties of classical cardinality in particular the main objective of researchers in this area has been to ensure the convexity of fuzzy cardinalities in order to preserve some properties based on the addition of cardinalities such as the additivity property we have found that in order to solve many real world problems such as the induction of fuzzy rules in data mining convex cardinalities are not always appropriate in this paper we propose a possibilistic and a probabilistic cardinality of a fuzzy set with finite support these cardinalities are not convex in general but they are most suitable for solving problems and contrary to the generalizing opinion they are found to be more intuitive for humans their suitability relies mainly on the fact that they assume dependency among objects with respect to the property to be in a fuzzy set the cardinality measures are generalized to relative ones among pairs of fuzzy sets we also introduce a definition of the entropy of a fuzzy set by using one of our probabilistic measures finally a fuzzy ranking of the cardinality of fuzzy sets is proposed and a definition of graded equipotency is introduced

linguistic quantifiers modeled by sugeno integrals since quantifiers have the ability of summarizing the properties of a class of objects without enumerating them linguistic quantification is a very important topic in the field of high level knowledge representation and reasoning this paper introduces a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures and the truth value of a quantified proposition is evaluated by using sugeno s integral this framework allows us to have some elegant logical properties of linguistic quantifiers we compare carefully our new model of quantification and other approaches to linguistic quantifiers a set of criteria for linguistic quantification was proposed in the previous literature the relationship between these criteria and the results obtained in the present paper is clarified some simple applications of the sugeno s integral semantics of quantifiers are presented

inference by aggregation of evidence with applications to fuzzy probabilities abstract optimal aggregation plays an important role towards developing a theory of aggregation of fuzzy concepts based on non additive set functions and nonlinear choquet or fuzzy integrals this paper presents a framework supporting such aggregations and argues that such a framework is useful to decision making based on distributed sources of evidence

digital analysis of rotated images the problem of estimating the relative rotations of two images taken from the same scene is considered and a numerical method for computing such rotations is presented the main features of the proposed method consist of the possibility of fast in place computations with no preliminary interpolation of the data and a considerable precision for moderate rotation angles the final estimate is performed with a least square criterion but in the present case even such computations can be substantially simplified a detailed analysis shows that for practical applications the influence of discretization errors does not affect in a relevant way the precision of the results that is also confirmed by numerical experiments

fuzzy probabilistic approximation spaces and their information measures rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information by introducing probability into fuzzy approximation space a theory about fuzzy probabilistic approximation spaces is proposed in this paper which combines three types of uncertainty probability fuzziness and roughness into a rough set model we introduce shannon s entropy to measure information quantity implied in a pawlak s approximation space and then present a novel representation of shannon s entropy with a relation matrix based on the modified formulas some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space respectively as a result uniform representations of approximation spaces and their information measures are formed with this work

on fuzzy type theory this paper is a generalization of classical simple type theory we have developed a formal system of fuzzy type theory which differs from the classical one essentially in extension of truth values from two to infinitely many the structure of truth values is assumed to be an imtl algebra residuated lattice with prelinearity and double negation extended by the baaz delta operation various properties of fuzzy type theory are proved including its completeness

trace inference curvature consistency and curve detection an approach is described for curve inference that is based on curvature information the inference procedure is divided into two stages a trace inference stage which is the subject of the present work and a curve synthesis stage it is shown that recovery of the trace of a curve requires estimating local models for the curve at the same time and that tangent and curvature information are sufficient these make it possible to specify powerful constraints between estimated tangents to a curve in terms of a neighborhood relationship called cocircularity and between curvature estimates in terms of a curvature consistency relation because all curve information is quantized special care must be taken to obtain accurate estimates of trace points tangents and curvatures this issue is addressed specifically to the introduction of a smoothness constraint and a maximum curvature constraint the procedure is applied to two types of images artificial images designed to evaluate curvature and noise sensitivity and natural images

fuzzy integral representation abstract in this paper we give representation results for nonlinear functionals in arbitrary spaces as fuzzy integrals the main assumption is that of comonotonic maxitivity i e i f g if ig for comonotonic f g under the more restrictive condition of stochastic dominance we prove a more specific representation as a fuzzy integral with respect to a distorted probability measure we discuss the particular cases of possibility measures and upper fuzzy expectations some partial randon nikodym results are proved for both the choquet and the fuzzy integrals finally an example is shown where the fuzzy integral representation is useful

on the registration of an object translating on a static background this work considers the determination of the relative movements between consecutive images taken from the same scene registration a problem arising in many application fields with the exception of specialized techniques for specific applications the most reliable registration algorithms are based on the use of 2 d fourier transforms they typically require a relevant computational effort the computational bulkiness typical of such methods can be overcome by 1 d techniques needless to say at the price of a degraded performance in presence of disturbances this paper proposes a new 1 d method which exploits the availability of several frames typical of practical contexts in order to determine the translation of an object moving between two endpoints on a static background the noise performance of the new technique is shown to be quite superior to that of the reported 1 d methods for sufficiently long sequences the noise performance favourably compares with that of 2 d techniques with considerable computational savings the possibilities of the method are exemplified by a number of practical examples

on the defect of complementarity of fuzzy measures it is well known that the fuzzy measures are non additive this means that the sum between the measure of a set and the measure of its complement is not equal with the measure of space as a consequence in this paper we introduce the concept of defect of complementarity also for large classes of fuzzy measures this defect of complementarity is calculated or estimated finally some applications and interpretations are presented

fuzzy sets the approximation of semisets abstract this paper deals with alternative set theory which substantially departs from classical set theory the main notion of it a semiset is proposed to model the same intuitive notion as fuzzy set but it is more general the reasonable tool for grasping semisets could be provided by fuzzy sets whose applicability is beyond discussion in the paper reasons for such an approximation are given and two ways how to provide it are proposed the fact that the membership function is modeled within the theory should be stressed at the end some problems and an indication for further investigation are discussed

fuzzy cardinality and the modeling of imprecise quantification abstract the concept of cardinality of a fuzzy set has received attention from several researchers and has been defined in several apparently independent manners a systematic investigation of this notion is performed which unifies and improves previous attempts the cardinality of a fuzzy set viewed as a fuzzy integer is related to scalar cardinality indices the closely related question of the probability of a fuzzy event is dealt with lastly the usefulness of fuzzy cardinality for meaning representation of statements or queries involving fuzzy linguistic quantifiers is emphasized

the set of fuzzy rational numbers and flexible querying a fuzzy bag is a bag in which each occurrence of an element is associated with a grade of membership this notion can be viewed as a generalization of the concepts of set fuzzy set and bag the set of fuzzy integers n f provides a general characterization in which all these different concepts are treated in a uniform way and can then be composed in the field of databases the use of fuzzy bags is motivated by their ability to manage both quantities and preferences however n f becomes too restricted a framework when dealing with queries based on difference or division operations so a more general structure based on the set of fuzzy relative integers z f in which exact differences can be performed has been first developed in this paper we carry on with this approach and we extend z f to the set of fuzzy rational numbers q f this context leads to define a closed system of multiplicative operations and allows to perform exact divisions applied to flexible querying of databases q f and the notion of division on fuzzy numbers allow to generalize the relational division they define a sound basis for queries involving ratios between quantities

on the location error of curved edges in low pass filtered 2 d and 3 d images the authors study the location error of curved edges in two and three dimensional images after analog and digital low pass filtering the zero crossing of a second derivative filter is a well known edge localization criterion the second derivative in gradient direction sdgd produces a predictable bias in edge location towards the centers of curvature while the linear laplace filter produces a shift in the opposite direction their sum called plus plus laplace sdgd leads to an edge detector that finds curved edges one order more accurately than its constituents this argument holds irrespective of the dimension the influence of commonly used low pass filters such as the psf originating from diffraction limited optics using incoherent light 2 d the gaussian filter with variable cutoff point d d and the isotropic uniform filter d d is studied

statistics of surface curvature estimates reliable curvature estimation is an important goal in image analysis to provide viewpoint independent cues for shape classification this paper presents a model of the relationship between the variance of curvature estimates and the image noise agreement to within 10 is obtained for 3d range data a perturbation error analysis is performed on the local least square surface fitting algorithm which is commonly used to obtain partial derivative estimates in the presence of noise the theoretical results are used to implement adaptive thresholding for surface type classification this is compared with existing constant and semi adaptive thresholding schemes it is concluded that any pixel by pixel thresholding will produce poor results the theoretical relationships provide the basis for a probabilistic approach

on curvature estimation of iso surfaces in 3d gray value images and the computation of shape descriptors in this paper we present a novel method to estimate curvature of iso gray level surfaces in gray value images our method succeeds where standard isophote curvature estimation methods fail there is neither a segmentation of the surface needed nor a parametric model assumed our estimator works on the orientation field of the surface this orientation field and a description of local structure is obtained by the gradient structure tensor the estimated orientation field has discontinuities mod spl pi it is mapped via the knutsson mapping to a continuous representation the principal curvatures of the surface a coordinate invariant property are computed in this mapped representation from these curvatures locally the bending energy is computed to describe the surface shape an extensive evaluation shows that our curvature estimation is robust even in the presence of noise independent of the scale of the object and furthermore the relative error stays small

generalized cardinal numbers and operations on them abstract in this paper we present a cardinality theory for so called vaguely defined objects which are mild generalizations of fuzzy sets obtained by introducing lower and upper approximations of the membership functions the theory makes use of the sentential calculus in the infinite valued ukasiewicz logic and can be applied to fuzzy sets with arbitrary supports some kinds of twofold fuzzy sets partial sets etc the notion of equipotency of vaguely defined objects is studied in detail the resulting generalized cardinal numbers are convenient tools for describing the powers of vaguely defined objects in the second part of the paper basic operations on the generalized cardinals are defined and carefully investigated similarities and anomalies in comparison with the classical arithmetic of the usual cardinals are indicated

curvature estimation in oriented patterns using curvilinear models applied to gradient vector fields curved oriented patterns are dominated by high frequencies and exhibit zero gradients on ridges and valleys existing curvature estimators fail here the characterization of curved oriented patterns based on translation invariance lacks an estimation of local curvature and yields a biased curvature dependent confidence measure using parameterized curvilinear models we measure the amount of local gradient energy along the model gradient as a function of model curvature minimizing the residual energy yields a closed form solution for the local curvature estimate and the corresponding confidence measure we show that simple curvilinear models are applicable in the analysis of a wide variety of curved oriented patterns

a real time algorithm for the approximation of level set based curve evolution in this paper we present a complete and practical algorithm for the approximation of level set based curve evolution suitable for real time implementation in particular we propose a two cycle algorithm to approximate level set based curve evolution without the need of solving partial differential equations pdes our algorithm is applicable to a broad class of evolution speeds that can be viewed as composed of a data dependent term and a curve smoothness regularization term we achieve curve evolution corresponding to such evolution speeds by separating the evolution process into two different cycles one cycle for the data dependent term and a second cycle for the smoothness regularization the smoothing term is derived from a gaussian filtering process in both cycles the evolution is realized through a simple element switching mechanism between two linked lists that implicitly represents the curve using an integer valued level set function by careful construction all the key evolution steps require only integer operations a consequence is that we obtain significant computation speedups compared to exact pde based approaches while obtaining excellent agreement with these methods for problems of practical engineering interest in particular the resulting algorithm is fast enough for use in real time video processing applications which we demonstrate through several image segmentation and video tracking experiments

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

an axiomatic approach to scalar cardinalities of fuzzy sets abstract we present an axiomatic approach to scalar cardinalities of fuzzy sets which is based on a system of three simple postulates a characterization theorem for those cardinalities is given the infinite family of possible scalar cardinalities of a fuzzy set generated by the postulates contains as particular cases all standard concepts of scalar cardinality e g the sigma count of a fuzzy set the cardinality of its core or support and the cardinality of its t level set

fuzzy quantifiers defined over fuzzy domains abstract in this paper we introduce a generalization of the concept of fuzzy quantifier called fuzzy quantifiers over fuzzy domains the development of this generalization is motivated by the impossibility to satisfactorily define the important operation of relativization for standard fuzzy quantifiers we provide basic examples of these quantifiers and define and investigate also several semantic properties of them finally we prove a theorem saying among other things that all these two argument fuzzy quantifiers that possess properties of extension and conservativity are relativizations of one argument fuzzy quantifiers of this kind

a graded approach to cardinal theory of finite fuzzy sets part i in this article we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent which indicates that they have the same number of elements the concepts of fuzzy sets and fuzzy classes in the class of all sets in zfc are introduced and several standard relations and constructions such as the fuzzy power set and exponentiation are defined a functional approach to the cardinal theory of finite fuzzy sets based on graded equipollence is shown and a relation to generalized cardinals and wygralak s cardinal theory of finite fuzzy sets defined over triangular norms is demonstrated

fuzzy cardinals based on the generalized equality of fuzzy subsets the purpose of this paper is to present a new concept of the cardinality of finite fuzzy subsets which is based on the notion of the generalized equality the proposed idea will be compared with several approaches which were earlier offered in fuzzy literature using the new definition of the fuzzy cardinality we next introduce a notion of fuzzy semicardinals i e we construct fuzzy natural numbers defining degrees to which a finite fuzzy subset has respectively at most least and less than more than k elements various properties of different fuzzy cardinals and semicardinals as well as some interdependences between them are also given

on triangular norm based generalized cardinals and singular fuzzy sets there are three basic types of triangular norm based generalized cardinals of fuzzy sets namely generalized fgcounts flcounts and fecounts all of them are convex fuzzy sets of usual cardinal numbers our attention will be focused on generalized fecounts if nonstrict archimedean triangular norms are involved generalized fecounts of many fuzzy sets become the zero function those singular fuzzy sets being totally dissimilar to any set of any cardinality and their properties are the subject of this paper a relationship between singularity and fuzziness measures suited to fuzzy sets with complements induced by a strict negation will also be discussed

logical linear operators for image curves we propose a language for designing image measurement operators suitable for early vision we refer to them as logical linear l l operators since they unify aspects of linear operator theory and boolean logic a family of these operators appropriate for measuring the low order differential structure of image curves is developed these l l operators are derived by decomposing a linear model into logical components to ensure that certain structural preconditions for the existence of an image curve are upheld tangential conditions guarantee continuity while normal conditions select and categorize contrast profiles the resulting operators allow for coarse measurement of curvilinear differential structure orientation and curvature while successfully segregating edge and line like features by thus reducing the incidence of false positive responses these operators are a substantial improvement over thresholded linear operators which attempt to resolve the same class of features

nonuniform image motion estimation from noisy data image motion estimation is viewed as a problem in nonlinear demodulation the motion d x modulates the intensity of the previous frame s x to result in the intensity of the present frame s x d x an iterative algorithm based on the generalized maximum likelihood criterion is developed and implemented to demodulate d x an advantage of this scheme is the incorporation of the covariance function matrix which is specifically useful in the stationary case to determine the integration region alpha sub x simulation demonstrated the ability of the algorithm to deal with cases such as markov 2 motion

measuring properties of fuzzy sets a general technique and its use in fuzzy query evaluation abstract a fuzzy set can be viewed as a weighted max combination or as a convex combination of a family of nested ordinary sets the latter point of view allows the interpretation of a fuzzy set as a consonant random set then any numerical set function applied to a fuzzy set leads to a result which is a random number the expectation attached to this random number provides a scalar evaluation of the fuzzy set with respect to the considered set function this approach is very general and can be used for various kinds of measurements cardinality confidence measures attached to the occurrence of events diameter or perimeter of a fuzzy region distance between two sets etc also the fuzziness of the set to evaluate naturally induces a fuzzy set of possible evaluations and expected values of the lower and upper bounds of this fuzzy set of numbers can be computed the weighted max combination view which leads to another type of scalar evaluation is also briefly discussed in this paper the above approach is more particularly applied to the treatment of queries asking for some global evaluation of a set of items specified by means of a fuzzy property this kind of query can be managed by languages like sql in case of a crisp set of items when this set is fuzzily specified a scalar answer can still be provided as well as a fuzzy valued or interval valued one if we want to keep track of the effect of the fuzziness of the query the case where the data base contains precise information but also the more general case of fuzzy information data bases are considered

evaluation of ridge seeking operators for multimodality medical image matching ridge like structures in digital images may be extracted by convolving the images with derivatives of gaussians the choice of the convolution operator and of the parameters involved defines a specific ridge image in this paper various ridge measures related to isophote curvature are constructed reviewed and evaluated with respect to their usability in ct mri matching of human brain scans construction is initially done using heuristics in two dimensional images and then established firmly in a mathematical framework attention is paid to the necessity of operator invariance scale of the operator extension to three dimensional images and relations to isophote and principal curvature it is shown that one of the ridge measures appears well suited for the purpose of matching despite the fact that the measure fails to detect ridges in a number of stylized scenes

cardinality quantifiers and the aggregation of fuzzy criteria abstract in this paper we are interested in counting the number of elements of a fuzzy set we study two concepts of fuzzy cardinality one which gives the answer as a fuzzy set or fuzzy number and the other which gives an ordinary integer relationships between these concepts and others which have been studied in the literature e g sigma count are also investigated some properties of the new concepts are studied such as fuzzy convexity monotonicity and additivity the concepts of fuzzy cardinality are important for a better understanding of fuzzy quantified rules of the form qx s are a or qa s are b where q is a fuzzy quantifier and a b are fuzzy sets we study such rules as well as aggregation rules of the form q of a1 ap contain x

fuzzy sets with triangular norms and their cardinality theory the most advanced and adequate approach to the question of cardinality of a fuzzy set seems to be that offering a fuzzy perception of cardinality the resulting convex fuzzy sets of usual cardinals of nonnegative integers in the finite case are then called generalized cardinal numbers three types of them are of special interest and importance namely fgcounts flcounts and fecounts in this paper first we show that their original forms are suitable only for fuzzy sets with the classical min and max operations second we propose an appropriate generalization to fuzzy sets with triangular norms and conorms further we investigate the resulting generalized fgcounts flcounts and fecounts from the viewpoint of the corresponding equipotency relations inequalities and arithmetical operations

recursive image registration with application to motion estimation an algorithm for real time recursive estimation of the two dimensional shift between successive images in an image sequence occurring e g in a down looking airborne tv sensor is presented the shift which is linearly related to ground velocity is adaptively tracked by means of the gradient of a similarity function relating the two successive images an implementation is presented in which substantial memory capacity and computational complexity are saved by using only a single line in the image frame and by binary quantization of the video signal a detailed analysis of the algorithm is presented using stochastic mathematical models for the terrain texture image noise and velocity variations under some simplifying assumptions closed form solutions for the error statistics including temporal power spectral density are derived the probability of loss of lock in tracking and the expected time for its reacquisition are evaluated and are found to be low at typical operating conditions the analysis also indicates considerable robustness of the algorithm to widely different image statistics numerical examples indicate very good performance in autonomous navigation applications

radial projection an efficient update rule for relaxation labeling relaxation labeling uses contextual information for finding consistent labelings of graphs although relaxation labeling is parallel and iterative the complexity of updating with standard rules is too costly for practical implementation a description is given of a computationally more efficient updating rule that utilizes radial projection instead of normal projection to avoid the complexities incurred by previous update rules when boundaries to the labeling space are encountered this reduction in complexity is achieved by first restricting support vectors to the positive quadrant and then using radial projection onto the constraint instead of normal projection crucial order information is conserved through smooth convergence towards the optimum and a rate of convergence proportional to the magnitudes of the support functions

fuzzy relations an fuzzy functions abstract in this paper we apply the standard element free mathematical definitions of equivalence relation and function as relations to the case of fuzzy relations one of the surprising results of this approach is that fuzzy functions take their values from the complemented elements of a brouwerian lattice thus in the common case of the values being taken from the unit interval the only fuzzy functions of this type are the ordinary functions this might suggest that fuzzy set theory is more than just a generalization of ordinary set theory

cardinality concepts for type two fuzzy sets in this paper we define generalized concepts of cardinality of a fuzzy valued function and obtained some properties of these new concepts also we investigate examples for the calculation of two generalized cardinality of fuzzy valued functions and compared with concepts of cardinality of a fuzzy set and a fuzzy valued function

a discussion on fuzzy cardinality and quantification some applications in image processing in this paper we discuss on some different representations of the cardinality of a fuzzy set and their use in fuzzy quantification we have considered the widely employed sigma count fuzzy numbers and gradual numbers gradual numbers assign numbers to values of a relevance scale typically 0 1 contrary to sigma count and fuzzy numbers they provide a precise representation of the cardinality of a fuzzy set we illustrate our claims by calculating the cardinality of the fuzzy set of pixels that match a certain fuzzy color in an image for that purpose we consider fuzzy color spaces previously defined by the authors consisting of a collection of fuzzy sets providing a suitable conceptual quantization with soft boundaries of crisp color spaces finally we show the suitability of our approaches to fuzzy quantification for different applications in image processing first the calculation of histograms second the definition of the notion of dominant fuzzy color and the calculation of the degree to which we can say that a certain color is dominant in an image

aggregation of owa operators inspired by the real needs of group decision problems aggregation of ordered weighted averaging owa operators is studied and discussed our results can be applied for data acting on any real interval such as the standard scales 0 1 and 0 infty bipolar scales 1 1 and mathbb r infty infty etc a direct aggregation is shown to be rather restrictive allowing the convex combinations to be considered only except the case of dimension n 2 more general is the approach based on the aggregation of related cumulative weighting vectors the piecewise linearity of owa operators allows us to consider bilinear forms of aggregation of related weighting vectors several interesting examples yielding the link between the aggregation of owa operators and the related andness and orness measures are also included some possible applications and generalizations of our results are also discussed

an exact maximum likelihood registration algorithm for data fusion data fusion is a process dealing with the association correlation and combination of data and information from multiple sources to achieve refined position and identity estimates we consider the registration problem which is a prerequisite process of a data fusion system to accurately estimate and correct systematic errors an exact maximum likelihood eml algorithm for registration is presented the algorithm is implemented using a recursive two step optimization that involves a modified gauss newton procedure to ensure fast convergence statistical performance of the algorithm is also investigated including its consistency and efficiency discussions in particular the explicit formulas for both the asymptotic covariance and the cramer rao bound crb are derived finally simulated and real life multiple radar data are used to evaluate the performance of the proposed algorithm

classifying ct image data into material fractions by a scale and rotation invariant edge model a fully automated method is presented to classify 3 d ct data into material fractions an analytical scale invariant description relating the data value to derivatives around gaussian blurred step edges arch model is applied to uniquely combine robustness to noise global signal fluctuations anisotropic scale noncubic voxels and ease of use via a straightforward segmentation of 3 d ct images through material fractions projection of noisy data value and derivatives onto the arch yields a robust alternative to the standard computed gaussian derivatives this results in a superior precision of the method the arch model parameters are derived from a small but over determined set of measurements data values and derivatives along a path following the gradient uphill and downhill starting at an edge voxel the model is first used to identify the expected values of the two pure materials named and and thereby classify the boundary second the model is used to approximate the underlying noise free material fractions for each noisy measurement an iso surface of constant material fraction accurately delineates the material boundary in the presence of noise and global signal fluctuations this approach enables straightforward segmentation of 3 d ct images into objects of interest for computer aided diagnosis and offers an easy tool for the design of otherwise complicated transfer functions in high quality visualizations the method is applied to segment a tooth volume for visualization and digital cleansing for virtual colonoscopy

a framework for fuzzy quantification models analysis a framework for description of fuzzy quantification models is presented within this framework the fuzzy quantified statements evaluation problem is described as the compatibility between the fuzzy quantifier and a fuzzy cardinality or a fuzzy aggregation measure a list of desirable properties for quantification models is presented and those models that fit the framework are confronted with it

on the relation between fuzzy and generalized quantifiers fuzzy quantified sentences have been widely applied for modeling statements in natural language since they allow to represent a broad type of intrinsically imprecise quantified statements that are usually linguistically expressed two different frameworks arise in order to model this imprecision in quantification zadeh s fuzzy quantifiers and the fuzzification of generalized quantification for both models several approaches have been developed for assessing the degree of satisfiability of fuzzy quantified sentences we present and compare both models concluding that although the concept of quantifier in each model has not the same semantics we can establish a connection between them and between the evaluation methods in both theories

fuzzy class theory the paper introduces a simple yet powerful axiomatization of zadeh s notion of fuzzy set based on formal fuzzy logic the presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics its essence is elementary fuzzy set theory cast as two sorted first order theory over fuzzy logic which is generalized to simple type theory we show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism in this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed however we also demonstrate how to add structure to the universe of discourse within our framework

a graded approach to cardinal theory of finite fuzzy sets part ii fuzzy cardinality measures and their relationship to graded equipollence abstract in this article we propose an axiomatic system for fuzzy cardinality measures referred to as fuzzy c measures for short assigning to each finite fuzzy set a generalized cardinal that expresses the number of elements that the fuzzy set contains the system generalizes an axiomatic system introduced by j casasnovas and j torrens 2003 we show that each fuzzy c measure is determined by two appropriate homomorphisms between the reducts of residuated dually residuated rdr lattices for linearly ordered rdr lattices we prove that each fuzzy c measure is a product of a non decreasing and a non increasing fuzzy c measure which indicates that there is a close relation between fuzzy c measures and fgcount flcount and fecount provided by l a zadeh 1983 and generalized by m wygralak 2001 finally the relationship of fuzzy c measures to graded equipollence introduced in the first part of this contribution is analyzed

a bending energy model for measurement of cardiac shape deformity an approach to analyzing and quantifying the shape characteristics of the endocardial contour of the left ventricle of the heart is described the computation begins by finding the local curvature differences between the contour under consideration and the mean normal contour at each of 100 equidistant points the weighted square of these differences summed over a set of points is shown to be the regional or global bending energy required to deform the mean normal contour to the characteristic shape of the analyzed contour resampling smoothing and curvature computation issues are considered for the image derived digital contours that are used in the analysis experiments were performed on artificial contour data and data derived from contrast ventriculographic cv studies of humans it is also shown that the method has been adapted to measure endocardial shape form equilibrium radionuclide angiocardiography

the cardinality of fuzzy sets and the continuum hypothesis abstract up to now the research of the cardinality of fuzzy sets hardly advanced since it is difficult to give it an appropriate definition in this paper we give a general definition of the cardinality of fuzzy sets based on the fuzzy mappings and not only obtain a large part of the results with respect to the cardinality in cantor s set theory but also get many new properties of the cardinality of fuzzy sets especially from the cardinality of fuzzy sets we may gain some new ideas on the continuum hypothesis which is a well known problem

twofold fuzzy sets and rough sets some issues in knowledge representation abstract this paper deals with the representation of sets where the membership of some elements may be ill known rather than just a matter of degree as in a fuzzy set the notion of a twofold fuzzy set is introduced when the relevant information for determining the membership status is incomplete a twofold fuzzy set is made of a nested pair of fuzzy sets the one which gathers the elements which more or less necessarily belong and the one which gathers the elements which more or less possibly belong twofold fuzzy sets are compared from a frontal and from a semantical point of view with other proposals and particularly with the notion of a rough set recently introduced by pawlak set operations of twofold fuzzy sets are discussed and the cardinality of a twofold fuzzy set is defined twofold fuzzy relations are also introduced finally various applications of twofold fuzzy sets in knowledge representation are briefly discussed

a maximum likelihood approach for image registration using control point and intensity registration of multidate or multisensor images is an essential process in many image processing applications including remote sensing medical image analysis and computer vision control point cp and intensity are the two basic features used separately for image registration in the literature in this paper an exact maximum likelihood eml registration method which combines both cp and intensity is proposed for image alignment the eml registration method maximizes the likelihood function based on cp and intensity to estimate the registration parameters including affine transformation and cp coordinates the explicit formulas of the cramer rao bound crb are also derived for the proposed eml and conventional image registration algorithms the performances of these image registration techniques are evaluated with the crbs

multidimensional orientation estimation with applications to texture analysis and optical flow the problem of detection of orientation in finite dimensional euclidean spaces is solved in the least squares sense the theory is developed for the case when such orientation computations are necessary at all local neighborhoods of the n dimensional euclidean space detection of orientation is shown to correspond to fitting an axis or a plane to the fourier transform of an n dimensional structure the solution of this problem is related to the solution of a well known matrix eigenvalue problem the computations can be performed in the spatial domain without actually doing a fourier transformation along with the orientation estimate a certainty measure based on the error of the fit is proposed two applications in image analysis are considered texture segmentation and optical flow the theory is verified by experiments which confirm accurate orientation estimates and reliable certainty measures in the presence of noise the comparative results indicate that the theory produces algorithms computing robust texture features as well as optical flow