wavelet based corner detection abstract a non parametric algorithm for detecting and locating corners of planar curves is proposed the algorithm is based on the multiscale wavelet transform of the orientation of the curve which can effectively utilize both the information of local extrema positions and magnitudes of the transform results the corner candidates can then be selected easily based on this information according to the angle preserving concept intrinsic ratios of several corner models have been derived and used to evaluate the corner candidates the corner angles can also be obtained during these processes to make the evaluation process robust a masking algorithm is proposed experiments depict that our detector is more effective than the single scale corner detectors while is more efficient than the multiscale corner detector by rattarangsi and chin proc int conf pattern recognition pp 923 930 1990

the hellinger correlation in this paper the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones shown to imply other usu

transitivity bounds in additive fuzzy preference structures transitivity plays a crucial role in preference modeling and related fields in this paper we discuss this property in the general context of additive fuzzy preference structures of particular interest is the decomposition of a large preference relation r in its symmetric part i indifference relation and its asymmetric part p strict preference relation by means of a so called indifference generator i given the type of transitivity of a large preference relation r w r t a conjunctor and a generator we establish basic lower bounds and general upper bounds on the transitivity of p and i these bounds are due to the careful design of generic counterexamples moreover we identify the situations in which these bounds are effectively reached thereby establishing connections with interesting properties such as dominance bisymmetry the 1 lipschitz property and rotation invariance

biseparating maps between operator algebras we prove that a biseparating map between spaces b e and some other banach algebras is automatically continuous and a multiple of an algebra isomorphism

a characterization of the orthogonal grid constructions of copulas a framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with non overlapping rectangles as patches is studied in de baets b de meyer h 2007 orthogonal grid constructions of copulas ieee trans fuzzy syst 15 1053 1062 where the authors provide sufficient conditions to derive a family of construction methods our aim in this note is to provide a characterization of such constructions msc primary 60e05 secondary 62h20

ortholinear and paralinear semi copulas abstract a new method to construct semi copulas is introduced these semi copulas are called ortholinear resp paralinear semi copulas and their construction is based on linear interpolation on segments that are perpendicular resp parallel to the diagonal of the unit square the classes of ortholinear and paralinear quasi copulas are characterized as well

meta theorems on inequalities for scalar fuzzy set cardinalities we present meta theorems stating general conditions ensuring that certain inequalities for cardinalities of ordinary sets are preserved under fuzzification when adopting a scalar approach to fuzzy set cardinality the conditions pertain to the commutative conjunctor used for modelling fuzzy set intersection in particular this conjunctor should fulfil a number of bell type inequalities the advantage of these meta theorems is that repetitious calculations can be avoided this is illustrated in the demonstration of the lukasiewicz transitivity of fuzzified versions of the simple matching coefficient and the jaccard coefficient or equivalently the triangle inequality of the corresponding dissimilarity measures

classification of partially occluded objects using 3 point matching and distance transformation abstract recognition of partially occluded objects has been recently made possible by describing an object boundary with a sequence of local feature segments localized with control or dominant points and then matching the representations with those of a set of known reference shapes when part of the object boundary is being occluded contiguous intact feature segments will be used for identifying the object and distorted elements will be rejected in the matching process the main problem associated with this method is that the nature of occlusion may separate the object contour into discrete regions resulting in the degeneration of an individual representation into small isolated clusters reflecting only weak evidence on the object identity in this paper a new scheme capable of combining the isolated clusters for object classification is presented in essence curvature guided polygonal approximation is employed for detecting the dominant points of the boundaries a 3 point matching technique is developed for extracting cluster s of dominant points on an unknown boundary which matched against reference objects and to link up the scattered clusters to form a complete representation the chamfer 3 4 distance transform together with a quantitative measurement on the boundary covered by the matched dominant points is employed for calculating the similarity between the unknown and the reference contours the scheme has been successfully applied for recognizing multiple overlapped handtools in different sizes and orientations

scale based description and recognition of planar curves and two dimensional shapes the problem of finding a description at varying levels of detail for planar curves and matching two such descriptions is posed and solved in this paper a number of necessary criteria are imposed on any candidate solution method path based gaussian smoothing techniques are applied to the curve to find zeros of curvature at varying levels of detail the result is the generalized scale space image of a planar curve which is invariant under rotation uniform scaling and translation of the curve these properties make the scale space image suitable for matching the matching algorithm is a modification of the uniform cost algorithm and finds the lowest cost match of contours in the scale space images it is argued that this is preferable to matching in a so called stable scale of the curve because no such scale may exist for a given curve this technique is applied to register a landsat satellite image of the strait of georgia b c manually corrected for skew to a map containing the shorelines of an overlapping area

shape representation by multiscale contour approximation an approach is presented for deriving qualitative descriptions of contours containing structures at different unknown scales the descriptions are in terms of straight arcs curved arcs with sign of curvature corners and points delimiting the arcs inflexion points and transitions from straight to curved furthermore the tangents at these points are derived the approach is based on the construction of a hierarchic family of polygons having the scale space property of causality structure can only disappear as scale goes from fine to coarse using the principle that structures that are stable over scale represent significant properties the features of the descriptive representations are then derived

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

zero sets of copulas abstract we study conditions on sets in order to be zero sets of semi copulas quasi copulas and with special attention of copulas we find necessary and sufficient conditions for characterizing the zero sets of absolutely continuous copulas and copulas whose support coincides with the closure of the complementary of the zero set moreover we study several topological properties and the lattice theoretic structure and characterize the zero sets of the class of archimedean copulas

measure based aggregation operators in analogy to the representation of the standard probabilistic average as an expected value of a random variable a geometric approach to aggregation is proposed generalizing imaoka s integral based on copulas several properties of such aggregation operators are investigated and the relationship with distinguished classes of aggregation operators is discussed

zero product preserving linear maps of ccr c algebras with hausdorff spectrum in this paper we try to attack a conjecture of araujo and jarosz that every bijective linear map between c algebras with both and its inverse 1 preserving zero products arises from an algebra isomorphism followed by a central multiplier we show it is true for ccr c algebras with hausdorff spectrum and in general some special c algebras associated to continuous fields of c algebras

symbolic construction of a 2 d scale space image a symbolic approach to constructing a multiscale primitive shape description to 2 d binary silhouette shape images is presented in contrast to contour or region smoothing techniques grouping operations are performed over collections of tokens residing on a scale space blackboard two types of grouping operations are identified that respectively aggregate edge primitives at one scale into edge primitives at a coarser scale and group edge primitives into partial region assertions including curved contours primitive corners and bars procedures to perform these computations are presented

the distribution of the probability mass of biconic copulas we study the probability mass distribution of biconic copulas provide a counterexample to a result given in jwaid et al 2012 29 concerning a characterization of singular biconic copulas and provide a new one

image analysis using multigrid relaxation methods image analysis problems posed mathematically as variational principles or as partial differential equations are amenable to numerical solution by relaxation algorithms that are local iterative and often parallel although they are well suited structurally for implementation on massively parallel locally interconnected computational architectures such distributed algorithms are seriously handi capped by an inherent inefficiency at propagating constraints between widely separated processing elements hence they converge extremely slowly when confronted by the large representations of early vision application of multigrid methods can overcome this drawback as we showed in previous work on 3 d surface reconstruction in this paper we develop multiresolution iterative algorithms for computing lightness shape from shading and optical flow and we examine the efficiency of these algorithms using synthetic image inputs the multigrid methodology that we describe is broadly applicable in early vision notably it is an appealing strategy to use in conjunction with regularization analysis for the efficient solution of a wide range of ill posed image analysis problems

the use of maximum curvature points for the recognition of partially occluded objects abstract a graph theoretic optimization method is used to recognize partially occluded objects from a 2 d image through the use of maximal cliques and a weight matching algorithm the vertices of an occluded object image with high curvature values are classified by the objects which are hypothesized to be involved in the occlusion a heuristic method is also developed to further improve the computational speed a few typical examples are given to illustrate the accuracy of the optimization model as well as the simplicity of the companion heuristic method

automatic continuity of orthogonality preservers on a non commutative lp τ space abstract elements a and b of a non commutative l p space associated to a von neumann algebra n equipped with a normal semifinite faithful trace are called orthogonal if l a l b r a r b 0 where l x and r x denote the left and right support projections of x a linear map t from l p n to a normed space y is said to be orthogonality to p orthogonality preserving if t a t b p a p b p whenever a and b are orthogonal in this paper we prove that an orthogonality to p orthogonality preserving linear bijection from l p n 1 p p 2 to a banach space x is automatically continuous whenever n is a separably acting von neumann algebra if n is a semifinite factor not of type i 2 we establish that every orthogonality to p orthogonality preserving linear mapping t l p n x is continuous and invertible whenever t 0 furthermore there exists a positive constant c p 1 p p 2 so that t t 1 c p 2 for every non zero orthogonality to p orthogonality preserving linear mapping t l p n x for p 1 this inequality holds with c p 1 that is t is a multiple of an isometry

occluded objects recognition using multiscale features and hopfield neural network abstract a new method to recognize partially visible two dimensional objects by means of multiscale features and hopfield neural network was proposed the hopfield network was employed to perform global feature matching since the network only guarantees to converge to a local optimal state the matching results heavily depend on the initial network state determined by the extracted features to acquire more satisfactory initial matching results a new feature vector was developed which consists of the multiscale evolution of the extremal position and magnitude of the wavelet transformed contour orientation these features can even be used to discriminate dominant points hence good initial states can be obtained the good initiation enables our proposed method to recognize objects even heavily occluded that cannot be achieved by using the nasrabadi li s method in addition to make the matching results more insensitive to the threshold value selection of the network we replace the step like thresholding function by a ramp like one experimental results have shown that our method is effective even for noisy occluded objects

a theory for multiresolution signal decomposition the wavelet representation multiresolution representations are effective for analyzing the information content of images the properties of the operator which approximates a signal at a given resolution were studied it is shown that the difference of information between the approximation of a signal at the resolutions 2 sup j 1 and 2 sup j where j is an integer can be extracted by decomposing this signal on a wavelet orthonormal basis of l sup 2 r sup n the vector space of measurable square integrable n dimensional functions in l sup 2 r a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi x this decomposition defines an orthogonal multiresolution representation called a wavelet representation it is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters wavelet representation lies between the spatial and fourier domains for images the wavelet representation differentiates several spatial orientations the application of this representation to data compression in image coding texture discrimination and fractal analysis is discussed

the distribution of the probability mass of conic copulas in this note we study the probability mass distribution of conic copulas provide counterexamples to a result given in jwaid et al 21 concerning a characterization of singular conic copulas and provide a new one

multivariate archimedean copulas d monotone functions and l1 norm symmetric distributions it is shown that a necessary and sufficient condition for an archimedean copula generator to generate a d dimensional copula is that the generator is a d monotone function the class of d dimensional archimedean copulas is shown to coincide with the class of survival copulas of d dimensional l 1 norm symmetric distributions that place no point mass at the origin the d monotone archimedean copula generators may be characterized using a little known integral transform of williamson duke math j 23 1956 189 207 in an analogous manner to the well known bernstein widder characterization of completely monotone generators in terms of the laplace transform these insights allow the construction of new archimedean copula families and provide a general solution to the problem of sampling multivariate archimedean copulas they also yield useful expressions for the d dimensional kendall function and kendall s rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for archimedean copulas the existence of a sharp lower bound for archimedean copulas with respect to the positive lower orthant dependence ordering is shown

a note on an idempotent transformation of absolutely continuous archimedean copulas abstract in de baets et al 6 the authors define for a copula c an idempotent transformation d c which in some cases generates new copulas in this note we give a negative answer to a question posed in 6 showing that d c is not necessarily a copula when c is an absolutely continuous archimedean copula

linear disjointness preservers of w algebras in this paper we give a complete description of the structure of zero product and orthogonality preserving linear maps between w algebras in particular two w algebras are isomorphic if and only if there is a bijective linear map between them preserving their zero product or orthogonality structure in two directions it is also the case when they have equivalent linear and left right ideal structures

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

short communication a note on the notion of singular copula we clarify the link between the notion of singular copula and the concept of support of the measure induced by a copula

partial shape recognition a landmark based approach a method of recognizing partially occluded objects is presented in which each object is represented by a set of landmarks given a scene consisting of partially occluded objects a model object in the scene is hypothesized by matching the landmarks of the model with those in the scene a measure of similarity between two landmarks is needed to perform this matching a local shape measure sphericity is introduced it is shown that any invariant function under a similarity transformation is a function of the sphericity to match landmarks between the model and the scene a table of compatibility is constructed a technique known as hopping dynamic programming is described to guide the landmark matching through the compatibility table the location of the model in the scene is estimated with a least squares fit among the matched landmarks a heuristic measure is then computed to decide if the model is in the scene

orthogonality preserving linear maps on c algebras with non zero socles abstract we study orthogonality preserving surjective linear maps from a unital c algebra with non zero socle a to a c algebra in particular we prove that when a has essential socle every biorthogonality preserving surjective linear map t a b is automatically bounded and a jordan isomorphism multiplied by an invertible element

partial shape classification using contour matching in distance transformation an algorithm is presented to recognize and locate partially distorted 2d shapes without regard to their orientation location and size the algorithm first calculates the curvature function from the digitized image of an object the points of local maxima and minima extracted from the smooth curvature are used as control points to segment the boundary and to guide the boundary matching procedure the boundary matching procedure considers two shapes at a time one shape from the template databank and the other from the object being classified the procedure tries to match the control points in the unknown shape to those of a shape from the template databank and estimates the translation rotation and scaling factors to be used to normalize the boundary of the unknown shape the chamfer 3 4 distance transformation and a partial distance measurement scheme constitute the final step in measuring the similarity between the two shapes the unknown shape is assigned to the class corresponding to the minimum distance the algorithm has been successfully tested on partial shapes using two sets of data one with sharp corners and the other with curve segments this algorithm not only is computationally simple but also works reasonably well in the presence of a moderate amount of noise

orthogonal grid constructions of copulas we establish a general framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with nonoverlapping rectangles as patches we derive a family of construction methods that require the choice of a single background copula when this background copula is the greatest copula we retrieve the well known ordinal sum construction while in the case of the smallest copula we obtain a construction method that is dual to the ordinal sum construction also nonsingular background copulas lead to suitable construction methods

a theory of multiscale curvature based shape representation for planar curves a shape representation technique suitable for tasks that call for recognition of a noisy curve of arbitrary shape at an arbitrary scale or orientation is presented the method rests on the describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve three different ways of computing the representation are described they result in three different representations the curvature scale space image the renormalized curvature scale space image and the resampled curvature scale space image the process of describing a curve at increasing levels of abstraction is referred to as the evolution or arc length evolution of that curve several evolution and arc length evolution properties of planar curves are discussed

disjointness preservers of aw algebras abstract in this paper we study bijective linear maps a b between a w algebras preserving either zero products or range orthogonality such a map is automatically continuous and provides an algebra or a algebra isomorphism 1 1 from a onto b our results extend previous works for the case of w algebras and also cover such maps between c algebras satisfying an extra assumption on preserving abelian c subalgebras