openness of versality via coherent functors we give a proof of openness of versality using coherent functors as an application we streamline artin s criterion for algebraicity of a stack we also introduce multi step obstruction theories employing them to produce obstruction theories for the stack of coherent sheaves the quot functor and spaces of maps in the presence of non atness

spatial reasoning and similarity retrieval of images using 2d c string knowledge representation abstract the data structure called 2d string to represent symbolic pictures was proposed by chang et al it allows a natural way to construct iconic indexes for pictures a new spatial knowledge representation of a 2d c string with accompanying cutting mechanism and a set of spatial operators are proposed 2d c string is more characteristic of spatial knowledge in images and is more efficient in representation and manipulation of images since a spatial relationship is a fuzzy concept the capability of similarity retrieval is essential in image database systems the spatial query and spatial reasoning based on a 2d c string representation are presented the similarity measure is defined and the algorithm for similarity retrieval of iconic images is also proposed

solving the process of hysteresis without determining the optimal thresholds hysteresis is an important edge detection technique but the unsupervised determination of hysteresis thresholds is a difficult problem thus hysteresis has limited practical applicability unimodal thresholding techniques are another edge detection method they are useful because the histogram of a feature image usually the feature image is an approximation of the gradient image is unimodal and there are many unsupervised methods to solve this problem but such techniques do not use spatial information to detect edge points so their performance is worse than that of the hysteresis in this paper we show how to formulate the hysteresis process as a unimodal thresholding problem without determining the optimal hysteresis thresholds using similar steps of the canny edge detector to obtain an approximation of the gradient image we compare the performance of our method against that of a method that determines the best parameters of an edge detector and show that our method performs relatively well additionally our method can adjust its sensitivity by using different unimodal thresholding techniques

galois groups and the multiplicative structure of field extensions let k k be a finite galois field extension and assume k is not an algebraic extension of a finite field let k be the multiplicative group of k and let k k be the product of the multiplicative groups of the proper intermediate fields the condition that the quotient group k k k be torsion is shown to depend only on the galois group g for algebraic number fields and function fields we give a complete classification of those g for which is nontrivial

the revised fundamental theorem of moment invariants a revised fundamental theorem of moment invariants for pattern recognition which corrects the fundamental theorem proposed by m k hu 1962 is presented the correction affects neither similitude scale nor rotation invariants derived using the original theorem but it does affect features invariant to general linear transformations four of the latter invariants were presented originally by hu these are revised to take the correction to the fundamental theorem into account furthermore these four invariants are combined to yield three new invariants which are additionally invariant to changes in the illumination of an image

the grothendieck duality theorem via bousfield s techniques and brown representability grothendieck proved that if f x y is a proper morphism of nice schemes then rf has a right adjoint which is given as tensor product with the relative canonical bundle the original proof was by patching local data deligne proved the existence of the adjoint by a global argument and verdier showed that this global adjoint may be computed locally in this article we show that the existence of the adjoint is an immediate consequence of brown s representability theorem lit follows almost as imme diately by smashing arguments that the adjoint is given by tensor product with a dualising complex verdier s base change theorem is an easy conse quence department of mathematics university of virginia charlottesville virginia 22903 e mail address an3rqvirginia edu this content downloaded from 157 55 39 27 on wed 07 sep 2016 06 26 19 utc all use subject to http about jstor org terms

non effective deformations of grothendieck s hilbert functor we show that the hilbert functor of rank one families on a non separated scheme x admits deformations that are not effective for such ambient schemes we have that the hilbert functor is not representable by a scheme or an algebraic space

normalization of modules we introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of rees algebras of modules and to bound the length of normalization processes in the case of regular base rings the bounds are expressed in terms of buchsbaum rim multiplicities and a module version of briancon skoda numbers

groupe de chow de codimension deux des varietes definies sur un corps de nombres un theoreme de finitude pour la torsion letx be a smooth projective variety defined over a number field and let ch2 x denote the chow group of codimension two cycles modulo rational equivalence we show that if the cohomology grouph2 x ox vanishes then the torsion subgroup of ch2 x is a finite group this result covers all previous results in this direction the hypothesish2 x ox 0 is used to lift line bundles

the method of normalization to determine invariants the determination of invariant characteristics is an important problem in pattern recognition many invariants are known which have been obtained either by normalization or by other methods this paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well to this end the normalization method is generalized and is presented in such a way that it is easy to apply thus unifying and simplifying the determination of invariants furthermore this paper discusses the advantages and disadvantages of the invariants obtained by normalization their main advantage is that the normalization process provides us with a standard position of the object because of the generality of the method also new invariants are obtained such as normalized moments more stable than known ones legendre descriptors and zernike descriptors to affine transformations two dimensional fourier descriptors and affine moment invariants obtained by combining hu s moment invariants and normalized moments

cross weighted moments and affine invariants for image registration and matching a framework for deriving a class of new global affine invariants for both object matching and positioning based on a novel concept of cross weighted moments with fractional weights is presented the fractional weight factor allows for a more flexible range to balance between the capability to discriminate between objects that differ only in small shape details and the sensitivity of small shape details to the presence of the noise moreover it makes it possible to arrive at low order zero order affine invariants that are more robust than those derived from higher order regular moments the affine transformation parameters are recovered from the zero and the first order cross weighted moments without requiring any feature point correspondence information the equations used to find the affine transformation parameters are linear algebraic the sensitivity of the cross weighted moment invariants to noise missing data and perspective effects is shown on real images

pattern recognition by affine moment invariants abstract the paper deals with moment invariants which are invariant under general affine transformation and may be used for recognition of affine deformed objects our approach is based on the theory of algebraic invariants the invariants from second and third order moments are derived and shown to be complete the paper is a significant extension and generalization of recent works several numerical experiments dealing with pattern recognition by means of the affine moment invariants as the features are described

an equivalent definition of the histogram of forces theoretical and algorithmic implications the relative position between two 2 d spatial regions is often represented quantitatively by a force histogram in the case of raster data force histograms are usually computed in o email protected n time where n is the number of pixels in the image and k is the number of directions in which forces are considered when the regions are defined as fuzzy sets instead of crisp sets the complexity also depends on the number m of possible membership degrees in this paper we show that the force histogram can be defined in a completely different but equivalent way one which leads to an o nlogn algorithm with complexity independent of k and m moreover the equivalent definition is better adapted to the solving of theoretical issues we use it here to determine the behavior of the force histogram towards any invertible affine transformation

a novel method to look for the hysteresis thresholds for the canny edge detector in the last few years several works have been proposed to solve the problem of determining the hysteresis thresholds in an unsupervised way in this paper a novel method to solve this problem is proposed given a set of candidates for hysteresis thresholds the basic idea of the proposed method is to combine gradient information with information obtained when the linking process is applied to all candidates using the same dataset and the same evaluation methodology already proposed by other works the results obtained by our method show a performance better than that of the previous methods the results obtained by the proposed method have been validated only for the canny edge detector but there are no restrictions on applying the proposed method to any other edge detector whose strategy is based on the hysteresis mechanism

a new way to represent the relative position between areal objects the fuzzy qualitative evaluation of directional spatial relationships such as to the right of to the south of between areal objects often relies on the computation of a histogram of angles which is considered to provide a good representation of the relative position of an object with regard to another in this paper the notion of the histogram of forces is introduced it generalizes and may supersede the histogram of angles the objects 2d entities are handled as longitudinal sections 1d entities not as points od entities it is thus possible to fully benefit from the power of integral calculus and so ensure rapid processing of raster data as well as of vector data explicitly considering both angular and metric information

cohen macaulay rees algebras and degrees of polynomial relations e mail aron sunrnp vfba br 2 department of mathematics michigan state university east lansing mi 48824 usa e mail 21144bfu msu edu 3 department of mathematics rutgers university new brunswick nj 08903 usa e mail vasconce rings rutgers edu received 5 october 1993

unramified class field theory of arithmetical surfaces let k be an algebraic number field 9k its ring of integers and v a non empty open subscheme of spec ck let x be a projective smooth geometrically irreducible scheme over k and x a regular proper flat scheme over v such that x x vk x the purpose of this paper is to give an explicit description of the abelian fundamental groups ab x and 7t b x using some idele class groups attached to x and x by a k theoretical method its outline is as follows in general for a noetherian scheme z and i 0 or 1 we define the group ski z to be the cokernel of

finite element method and constitutive modelling and computation for unsaturated soils abstract this paper presents a numerical model for the finite element analysis of transient deformation and seepage problems in unsaturated soils a definition of the generalized effective stress for unsaturated soils is introduced and its rational formula is derived on the basis of the classical definition of the effective stress for saturated soils by terzaghi and the two stress variables formula accepted for unsaturated soils the governing equations for unsaturated soils modelled as deforming porous media with immiscible porous water and air are re formulated the passive air assumption is then introduced to result in a simplified form of the governing equations for unsaturated soils the finite element method is applied to discretize the governing equations in space the alonso constitutive model to simulate the non linear mechanical behaviour of unsaturated soils is integrated into the present numerical model with introduction of the natural coordinate system in the stress space a backward euler integration algorithm and a consistent elastoplastic tangent modulus matrix for the non smooth multisurface pressure dependent plasticity are derived for the model numerical results are illustrated to demonstrate the capability and performance of the present model

development of elasto plastic material models in a natural coordinate system abstract by the introduction of a new set of coordinates for the normal stresses a framework is developed which facilitates the implementation and modification of a variety of yield surfaces an internal variable is proposed which allows the simultaneous description of two strain hardening paths one in tension the other in compression finally the numerical aspects of the problem are presented

a geometric theory of the buchsbaum rim multiplicity abstract we develop a self contained theory of a generalized buchsbaum rim multiplicity based on elementary abstract algebraic geometry we define the multiplicity as the sum of certain natural intersection numbers and recover the traditional definition in terms of the leading coefficient of the polynomial that gives the appropriate lengths we interpret the partial sums as the multiplicities in certain closely associated cases we prove an additivity formula in the rings and relate constancy to a generalized notion of reductions we establish a polar multiplicity formula and a mixed multiplicity formula and we determine when each of the four types of multiplicities vanish we end by generalizing the height inequality for maximal minors and a celebrated theorem of boger

a discontinuous galerkin finite element method for dynamic and wave propagation problems in non linear solids and saturated porous media a time discontinuous galerkin finite element method dgfem for dynamics and wave propagation in non linear solids and saturated porous media is presented the main distinct characteristic of the proposed dgfem is that the specific p3 p1 interpolation approximation which uses piecewise cubic hermite s polynomial and linear interpolations for both displacements and velocities in the time domain is particularly proposed consequently continuity of the displacement vector at each discrete time instant is exactly ensured whereas discontinuity of the velocity vector at the discrete time levels still remains the computational cost is then obviously saved particularly in the materially non linear problems as compared with that required for the existing dgfem both the implicit and explicit algorithms are developed to solve the derived formulations for linear and materially non linear problems numerical results illustrate good performance of the present method in eliminating spurious numerical oscillations and in providing much more accurate solutions over the traditional galerkin finite element method using the newmark algorithm in the time domain copyright 2003 john wiley sons ltd

cohomology and base change for algebraic stacks we prove that cohomology and base change holds for algebraic stacks generalizing work of brochard in the tame case we also show that hom spaces on algebraic stacks are represented by abelian cones generalizing results of grothendieck brochard olsson lieblich and roth starr to accomplish all of this we prove that a wide class of relative ext functors in algebraic geometry are coherent in the sense of m auslander

consistent tangent operators for rate independent elastoplasticity abstract it is shown that for problems involving rate constitutive equations such as rate independent elastoplasticity the notion of consistency between the tangent stiffness operator and the integration algorithm employed in the solution of the incremental problem plays a crucial role in preserving the quadratic rate of asymptotic convergence of iterative solution schemes based upon newton s method within the framework of closest point projection algorithms a methodology is presented whereby tangent operators consistent with this class of algorithms may be systematically developed to wit associative j 2 flow rules with general nonlinear kinematic and isotropic hardening rules as well as a class of non associative flow rules are considered the resulting iterative solution scheme preserves the asymptotic quadratic convergence characteristic of newton s method whereas use of the socalled elastoplastic tangent in conjunction with a radial return integration algorithm a procedure often employed results in newton type of algorithms with suboptimal rate of convergence application is made to a set of numerical examples which include saturation hardening laws of exponential type

rees algebras of modules we study rees algebras of modules within a fairly general framework we introduce an approach through the notion of bourbaki ideals that allows the use of deformation theory one can talk about the essentially unique generic bourbaki ideal i e of a module e which in many situations allows one to reduce the nature of the rees algebra of e to that of its bourbaki ideal i e properties such as cohen macaulayness normality and being of linear type are viewed from this perspective the known numerical invariants such as the analytic spread the reduction number and the analytic deviation of an ideal and its associated algebras are considered in the case of modules corresponding notions of complete intersection almost complete intersection and equimultiple modules are examined in some detail special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way for these modules one is able to estimate the reduction number and other invariants in terms of the buchsbaum rim multiplicity

degree of adjacency or surroundedness abstract definitions of the degree of adjacency of two regions in the plane and the degree of surroundedness of one region by another are proposed some elementary properties of these concepts are established and it is also shown that they have natural generalizations to fuzzy subsets of the plane applications of the proposed measures to digital polygons are demonstrated and fast algorithms for computing these measures are given

sheaves on artin stacks we develop a theory of quasi coherent and constructible sheaves on algebraic stacks correcting a mistake in the recent book of laumon and moret bailly we study basic cohomological properties of such sheaves and prove stack theoretic versions of grothendieck s fundamental theorem for proper morphisms grothendieck s existence theorem zariski s connectedness theorem as well as finiteness theorems for proper pushforwards of coherent and constructible sheaves we also explain how to define a derived pullback functor which enables one to carry through the construction of a cotangent complex for a morphism of algebraic stacks due to laumon and moret bailly 1 1 in the book lm b the lisse etale topos of an algebraic stack was introduced and a theory of quasi coherent and constructible sheaves in this topology was developed unfortunately it was since observed by gabber and behrend independently that the lisse etale topos is not functorial as asserted in loc cit and hence the development of the theory of sheaves in this book is not satisfactory as is in addition since the publication of the book lm b several new results have been obtained such as finiteness of coherent and etale cohomology fa ol and various other consequences of chow s lemma ol the purpose of this paper is to explain how one can modify the arguments of lm b to obtain good theories of quasi coherent and constructible sheaves on algebraic stacks and in addition we provide an account of the theory of sheaves which also includes the more recent results mentioned above 1 2 the paper is organized as follows in section 2 we recall some aspects of the theory of cohomological descent sga4 v which will be used in what follows in section 3 we review the basic definitions of the lisse etale site cartesian sheaves over a sheaf of algebras and verify some basic properties of such sheaves in section 4 we relate the derived category of cartesian sheaves over some sheaf of rings to various derived categories of sheaves on the simplicial space obtained from a covering of the algebraic stack by an algebraic space loosely speaking the main result states that the cohomology of a complex with cartesian cohomology sheaves can be computed by restricting to the simplicial space obtained from a covering and computing cohomology on this simplicial space using the etale topology in section 5 we generalize these results to comparisons between ext groups computed in the lisse etale topos and ext groups computed using the etale topology on a hypercovering in section 6 we specialize the discussion of sections 3 5 to quasi coherent sheaves we show that if x is an algebraic stack and oxlis et denotes the structure sheaf of the lisse etale topos then the triangulated category d qcoh x of bounded below complexes of oxlis et modules with quasi coherent cohomology sheaves satisfies all the basic properties that one would expect from the theory for schemes for example we show in this section that if f x y is a quasi compact morphism of algebraic stacks and m is a quasi coherent sheaf on x date november 2 2005 1

on proper coverings of artin stacks abstract we prove that every separated artin stack of finite type over a noetherian base scheme admits a proper covering by a quasi projective scheme an application of this result is a version of the grothendieck existence theorem for artin stacks

directional relative position between objects in image processing a comparison between fuzzy approaches the importance of describing relationships between objects has been highlighted in works in very different areas including image understanding among these relationships directional relative position relations are important since they provide an important information about the spatial arrangement of objects in the scene such concepts are rather ambiguous they defy precise definitions but human beings have a rather intuitive and common way of understanding and interpreting them therefore in this context fuzzy methods are appropriate to provide consistent definitions that integrate both quantitative and qualitative knowledge thus providing a computational representation and interpretation of imprecise spatial relations expressed in a linguistic way and including quantitative knowledge several fuzzy approaches have been developed in the literature and the aim of this paper is to review and compare them according to their properties and according to the types of questions they seek to answer

quantitative analysis of properties and spatial relations of fuzzy image regions properties of objects and spatial relations between objects play an important role in rule based approaches for high level vision the partial presence or absence of such properties and relationships can supply both positive and negative evidence for region labeling hypotheses similarly fuzzy labeling of a region can generate new hypotheses pertaining to the properties of the region its relation to the neighboring regions and finally hypotheses pertaining to the labels of the neighboring regions a unified methodology that can be used to characterize both properties and spatial relationships of object regions in a digital image is presented the methods proposed for computing the properties and relations of image regions can be used to arrive at more meaningful decisions about the contents of the scene

unimodal thresholding for edge detection in this paper a novel non parametric method is proposed for unimodal thresholding in an edge detection context the proposed method assigns a point in a roc receiver operating characteristic space to each possible threshold without the need of a reference binary image the optimal point and the required corresponding threshold is then determined in the roc graph the berkeley segmentation dataset has been used to evaluate the performance of the proposed method which is compared with another two recent proposals and otsu method

automatic joint classification and segmentation of whole cell 3d images we present a machine learning tool for automatic texton based joint classification and segmentation of mitochondria in mnt 1 cells imaged using ion abrasion scanning electron microscopy ia sem for diagnosing signatures that may be unique to cellular states such as cancer automatic tools with minimal user intervention need to be developed for analysis and mining of high throughput data from these large volume data sets typically 2gb cell challenges for such a tool in 3d electron microscopy arise due to low contrast and signal to noise ratios snr inherent to biological imaging our approach is based on block wise classification of images into a trained list of regions given manually labeled images our goal is to learn models that can localize novel instances of the regions in test datasets since datasets obtained using electron microscopes are intrinsically noisy we improve the snr of the data for automatic segmentation by implementing a 2d texture preserving filter on each slice of the 3d dataset we investigate texton based region features in this work classification is performed by k nearest neighbor k nn classifier support vector machines svms adaptive boosting adaboost and histogram matching using a nn classifier in addition we study the computational complexity vs segmentation accuracy tradeoff of these classifiers segmentation results demonstrate that our approach using minimal training data performs close to semi automatic methods using the variational level set method and manual segmentation carried out by an experienced user using our method which we show to have minimal user intervention and high classification accuracy we investigate quantitative parameters such as volume of the cytoplasm occupied by mitochondria differences between the surface area of inner and outer membranes and mean mitochondrial width which are quantities potentially relevant to distinguishing cancer cells from normal cells to test the accuracy of our approach these quantities are compared against manually computed counterparts we also demonstrate extension of these methods to segment 3d images obtained using electron tomography

the hilbert stack let x s be a morphism of algebraic stacks that is locally of finite presentation with affine stabilizers we prove that there is an algebraic s stack the hilbert stack parameterizing proper a

an image understanding system using attributed symbolic representation and inexact graph matching this paper presents a powerful image understanding system that utilizes a semantic syntactic or attributed synibolic representation scheme in the form of attributed relational graphs arg s for comprehending the global information contents of images nodes in the arg represent the global image features while the relations between those features are represented by attributed branches between their corresponding nodes the extraction of arg representation from images is achieved by a multilayer graph transducer scheme this scheme is basically a rule based system that uses a combination of model driven and data driven concepts in performing a hierarchical symbolic mapping of the image information content from the spatial domain representation into a global representation further analysis and inter pretation of the imagery data is performed on the extracted arg representation a distance measure between images is defined in terms of the distance between their respective arg representations the distance between two arg s and the inexact matching of their respective components are calculated by an efficient dynamic programming technique the system handles noise distortion and ambiguity in real world images by two means namely through modeling and embedding them into the transducer s mapping rules as well as through the appropriate cost of error transformation for the inexact matching of the arg image representation two illustrative experiments are presented to demonstrate some capabilities of the proposed system experiment i deals with locating objects in multiobject scenes while experiment ii is concerned with target detection in sar images

numerical methods for interval and fuzzy number comparison based on the probabilistic approach and dempster shafer theory there are many different methods for interval and fuzzy number comparison proposed in the literature which provide the results of comparison in the form of a real or boolean value in this paper we use the dempster shafer theory of evidence with its probabilistic interpretation to justify and construct the method which provides the result of comparison in the form of an interval or fuzzy number the complete and consistent set of expressions for inequality and equality relations between intervals and fuzzy numbers has been obtained in the framework of the probabilistic approach these relations make it possible to compare intervals and fuzzy numbers with real values and may be considered as an asymptotic limit of the results we obtain using the dempster shafer theory a natural fuzzy extension of the proposed approach is considered and discussed using some illustrative examples

the dimension and components of symmetric algebras let r be a commutative noetherian ring and let a4 be any finitely generated r module in this paper we compute the dimension of s m the symmetric algebra of m and identify many of the components of s m while the computation of the dimension of s m is not difficult the answer is intriguing and in view of the recent interest in symmetric algebras we hope the computation will be useful the dimension is given by the for mula dim s m max dim r p p m

similarity measures with complex multimedia data we see the emergence of database systems in which the fundamental operation is similarity assessment before database issues can be addressed it is necessary to give a definition of similarity as an operation we develop a similarity measure based on fuzzy logic that exhibits several features that match experimental findings in humans the model is dubbed fuzzy feature contrast ffc and is an extension to a more general domain of the feature contrast model due to tversky 1977 we show how the ffc model can be used to model similarity assessment from fuzzy judgment of properties and we address the use of fuzzy measures to deal with dependencies among the properties

invariant matching and identification of curves using b splines curve representation there have been many techniques for curve shape representation and analysis ranging from fourier descriptors to moments to implicit polynomials to differential geometry features to time series models to b splines etc the b splines stand as one of the most efficient curve surface representations and possess very attractive properties such as spatial uniqueness boundedness and continuity local shape controllability and invariance to affine transformations these properties made them very attractive for curve representation and consequently they have been extensively used in computer aided design and computer graphics very little work however has been devoted to them for recognition purposes one possible reason might be due to the fact that the b spline curve is not uniquely described by a single set of parameters control points which made the curve matching recognition process difficult when comparing the respective parameters of the curves to be matched this paper is an attempt to find matching solutions despite this limitation and as such it deals the problem of using b splines for shape recognition and identification from curves with an emphasis on the following applications affine invariant matching and classification of 2 d curves with applications in identification of aircraft types based on image silhouettes and writer identification based on handwritten text

on fuzzy distances and their use in image processing under imprecision abstract this paper proposesa classification of fuzzy distances with respect to the requirements needed for applications in image processing under imprecision we distinguish on the one hand distances that basically compare only the membership functions representing the concerned fuzzy objects and on the other hand distances that combine spatial distance between objects and membership functions to our point of view the second class of methods finds more general applications in image processing since these methods take into account both spatial information and information related to the imprecision attached to the image objects new distances based on mathematical morphology are proposed in this second class

a mixed element method in gradient plasticity for pressure dependent materials and modelling of strain localization this paper presents a mixed strain element method in gradient plasticity for pressure dependent materials at large strains and its application to the modelling of strain localization the two yield strength parameters of strain hardening softening materials not only depend on the internal state variable but also on its laplacian the evaluation of the laplacian is based on a least square polynomial approximation of the internal state variable around each integration point the present non local approach allows to satisfy exactly the consistency condition in a pointwise fashion but in the non local sense and at each iteration of a load step to derive the consistent element formulations in the context of mixed finite element with one point quadrature and hourglass control and the non local pressure dependent elasto plasticity a natural coordinate system in the stress space and a new definition of internal state variable are introduced the capability of the present approach to preserve ellipticity as strain softening behaviour is incorporated into a computational model is demonstrated by the numerical results which illustrate that pathological mesh dependence has been overcome

the use of force histograms for affine invariant relative position description affine invariant descriptors have been widely used for recognition of objects regardless of their position size and orientation in space examples of color texture and shape descriptors abound in the literature however many tasks in computer vision require looking not only at single objects or regions in images but also at their spatial relationships in an earlier work we showed that the relative position of two objects can be quantitatively described by a histogram of forces here we study how affine transformations affect this descriptor the position of an object with respect to another changes when the objects are affine transformed we analyze the link between 1 the applied affinity 2 the relative position before transformation described through a force histogram and 3 the relative position after transformation we show that any two of these elements allow the third one to be recovered moreover it is possible to determine whether or how well two relative positions are actually related through an affine transformation if they are not the affinity that best approximates the unknown transformation can be retrieved and the quality of the approximation assessed

scene matching using f histogram based features with possibilistic c means optimization this paper outlines further advances from initial findings previously reported in o sjahputera j m keller possibilistic c means in scene matching fourth internat conf of the european society for fuzzy logic and technology eusflat 2005 pp 669 675 we propose a scene matching approach based on spatial relationships among objects in the images to determine if two images acquired under different viewing conditions capture the same scene this is a difficult problem in computer vision our approach produces a mapping of objects from one view to the other and recovers the viewing transformation parameters the core of the system relies on capturing spatial relationship information through force histograms as affine invariant image descriptors object mapping across images is performed by finding the best correspondence map fmap between force histograms in the two images the major problem is that the number of potential fmaps is large even for modest numbers of scene objects hence search optimization is required the correct fmap contains histogram correspondences represented by similar feature vectors therefore dense regions in the feature space are suspected to contain these vectors possibilistic c means pcm clustering is used to find these dense regions the centroids of these dense regions are used to generate the fmaps previously the fmap was generated using a nearest neighbor like approach in this study we propose an improved version of this method by incorporating fuzzy memberships into the fmap building process here the fitness of fmap candidates are assessed with respect to all histogram correspondences already in fmap not just from an initial seed point alone the best fmap is selected and translated into a mapping scheme that connects the objects in the two images

a mixed strain element method for pressure dependent elastoplasticity at moderate finite strain this paper presents a framework to describe a mixed element method in the context of pressure dependent elastoplasticity at moderate finite strain a mixed strain element with one point quadrature and hourglass control at moderate finite strain is developed on the basis of the hu washizu principle and the co rotational formulation the element is formulated with reference to the so called natural co ordinate system which allows to derive the consistent tangent modulus matrix and the single step backward euler integration scheme at the element quadrature point for pressure dependent elastoplasticity in an elegant and numerically efficient form in addition with the introduction of the natural co ordinate system a new definition of internal state variable for the pressure dependent elasto plasticity is proposed to allow for the simultaneous description of the two strain hardening softening paths in tension and compression numerical examples are given to demonstrate the performance of the mixed element method presented in this paper 1998 john wiley sons ltd

noetherian approximation of algebraic spaces and stacks we show that every scheme resp algebraic space resp algebraic stack that is quasi compact with quasi finite diagonal can be approximated by a noetherian scheme resp algebraic space resp stack more generally we show that any stack which is etale locally a global quotient stack can be approximated examples of applications are generalizations of chevalley s serre s and zariski s theorems and chow s lemma to the non noetherian setting we also show that every quasi compact algebraic stack with quasi finite diagonal has a finite generically flat cover by a scheme

accurate object recognition with shape masks in this paper we propose an object recognition approach that is based on shape masks generalizations of segmentation masks as shape masks carry information about the extent outline of objects they provide a convenient tool to exploit the geometry of objects we apply our ideas to two common object class recognition tasks classification and localization for classification we extend the orderless bag of features image representation in the proposed setup shape masks can be seen as weak geometrical constraints over bag of features those constraints can be used to reduce background clutter and help recognition for localization we propose a new recognition scheme based on high dimensional hypothesis clustering shape masks allow to go beyond bounding boxes and determine the outline approximate segmentation of the object during localization furthermore the method easily learns and detects possible object viewpoints and articulations which are often well characterized by the object outline our experiments reveal that shape masks can improve recognition accuracy of state of the art methods while returning richer recognition answers at the same time we evaluate the proposed approach on the challenging natural scene graz 02 object classes dataset

failure of cancellation for direct sums of line bundles in answer to a question of murthy and wiegand examples are given of finitely generated projective modules l of rank 1 over a commutative ring r such that l l 1 is stably free but not free examples are also given of projective modules for which the determinant map det aut p r is not onto some related topological questions are also discussed

pic is a contracted functor we show that there is a natural decomposition pic a t t 1 cong pic a oplus npic a oplus npic a oplus h 1 a for any commutative ringa where pic a is the picard group of invertiblea modules andh1 a is the etale cohomology grouph1 spec a a similar decomposition of pic x t t 1 holds for any schemex this makes pic a contracted functor in the sense of bass h1 a is always a torsionfree group and is zero ifa is normal for pseudo geometric rings h1 a is an effectively computable finitely generated free abelian group we also show thath1 a t t 1 h1 a i e nh1 lh1 0 this yields the formula for group rings pic a t 1 t 1 1 t m t m 1 cong pic a oplus coprod limits i 1 m h 1 a oplus coprod limits k 1 m coprod limits i 1 2 k left k m right n k pic a

fibered stable varieties reference epfl article 231103doi 10 1090 tran 6386 url http dx doi org 10 1090 tran 6386 record created on 2017 09 19 modified on 2017 10 02

affine curve moment invariants for shape recognition this paper presents a method of affine curve moment invariants for shape recognition the proposed method extends affine moment invariants from an area domain to a curve domain first a new type of curve moments is defined on a parameterized boundary description of an object a set of affine moment invariants are then derived based on the theory of algebraic invariants the proposed moment invariants only deal with pixels on a shape boundary and are mathematically proven to be invariant under arbitrary affine transformations furthermore after a parameterized object boundary description is acquired through curve fitting the newly defined curve moments can be represented by an integration of the fitting function so that the computation of moment invariants can be obtained from either one by one computation of boundary pixels or a direct integration of the fitting function which makes the computation efficient while at the same time reducing noise effect affine curve moment invariants work well in recognition of affine deformed objects which is demonstrated by processing various 2 d shapes under affine transformations

shape similarity retrieval under affine transforms the maxima of curvature scale space css image have already been used to represent 2 d shapes in different applications the representation has shown robustness under the similarity transformations scaling orientation changes translation and even noise can be easily handled by the representation and its associated matching algorithm in this paper we examine the robustness of the representation under general affine transforms we have a database of 1100 images of marine creatures the contours in this database demonstrate a great range of shape variation a database of 5000 contours has been constructed using 500 real object boundaries and 4500 contours which are the affine transformed versions of real objects the css representation is then used to find similar shapes from this prototype database the results provide substantial evidence of stability of the css image and its contour maxima under affine transformation the method is also evaluated objectively through a large classified database and its performance is compared with the performance of two well known methods namely fourier descriptors and moment invariants the css shape descriptor has been selected for mpeg 7 standardization

invariant pattern recognition by moment fourier descriptor abstract this paper proposes a new shape descriptor called moment fourier descriptor which can describe a complex object composed by a set of closed regions this descriptor is shown to be independent of object s translation rotation and scaling the essential advantage of moment fourier descriptor is that it can be used to recognize more complex patterns than the traditional fourier descriptors simulations are given to show the high performance of the proposed approach

the buchsbaum rim polynomial of a module abstract for a noetherian local ring r m the hilbert functions of m primary ideals provide considerable information about constructions and singularities coded by the ideal for a module e which is the analogue of such ideals e is a proper submodule of a free module so that the quotient has finite length buchsbaum and rim defined a similar function and introduced the notion of buchsbaum rim multiplicity br e of the module unlike in the ideal case the information about these functions is still scant when r is cohen macaulay of dimension d 1 and e has rank r we develop some of their properties sufficiently enough to establish the following bound for the reduction number of the module e r e d r 1 br e 2 1 the same techniques lead to bounds on the number of generators of the integral closure of the powers of certain ideals and modules

fuzzy relative position between objects in image processing a morphological approach in order to cope with the ambiguity of spatial relative position concepts we propose a new definition of the relative position between two objects in a fuzzy set framework this definition is based on a morphological and fuzzy pattern matching approach and consists of comparing an object to a fuzzy landscape representing the degree of satisfaction of a directional relationship to a reference object it has good formal properties it is flexible it fits the intuition and it can be used for structural pattern recognition under imprecision moreover it also applies in 3d and for fuzzy objects issued from images

the intrinsic normal cone let x be an algebraic stack in the sense of deligne mumford we construct a purely 0 dimensional algebraic stack over x in the sense of artin the intrinsic normal cone frak c x the notion of perfect obstruction theory for x is introduced and it is shown how to construct given a perfect obstruction theory for x a pure dimensional virtual fundamental class in the chow group of x we then prove some properties of such classes both in the absolute and in the relative context via a deformation theory interpretation of obstruction theories we prove that several kinds of moduli spaces carry a natural obstruction theory and sometimes a perfect one

a novel shape based non redundant local binary pattern descriptor for object detection motivated by the discriminative ability of shape information and local patterns in object recognition this paper proposes a window based object descriptor that integrates both cues in particular contour templates representing object shape are used to derive a set of so called key points at which local appearance features are extracted these key points are located using an improved template matching method that utilises both spatial and orientation information in a simple and effective way at each of the extracted key points a new local appearance feature namely non redundant local binary pattern nr lbp is computed an object descriptor is formed by concatenating the nr lbp features from all key points to encode the shape as well as the appearance of the object the proposed descriptor was extensively tested in the task of detecting humans from static images on the commonly used mit and inria datasets the experimental results have shown that the proposed descriptor can effectively describe non rigid objects with high articulation and improve the detection rate compared to other state of the art object descriptors

effective normality criteria for algebras of linear type abstract the algebras studied here are subalgebras of rings of polynomials generated by 1 forms so called rees algebras with coefficients in a noetherian ring given a normal domain r and a torsionfree module e with a free resolution f 2 f 1 f 0 e 0 we study the role of the matrices of syzygies in the normality of the rees algebra of e when the rees algebra r e and the symmetric algebra s e coincide the main results characterize normality in terms of the ideal ic s e and of the completeness of the first s symmetric powers of e where c rank and s rankf0 ranke it requires that r be a regular domain special results under broader conditions on r are still more effective

a luna etale slice theorem for algebraic stacks we prove that every algebraic stack locally of nite type over an algebraically closed eld with ane stabilizers isetale locally a quotient stack in a neighborhood of a point with a linearly reductive stabilizer group the proof uses an equivariant version of artin s algebraization theorem proved in the appendix we provide numerous applications of the main theorems

hypersurfaces in projective schemes and a moving lemma let x s be a quasi projective morphism over an affine base we develop in this article a technique for proving the existence of closed subschemes h s of x s with various favorable properties we offer several applications of this technique including the existence of finite quasi sections in certain projective morphisms and the existence of hypersurfaces in x s containing a given closed subscheme c and intersecting properly a closed set f assume now that the base s is the spectrum of a ring r such that for any finite morphism z s pic z is a torsion group this condition is satisfied if r is the ring of integers of a number field or the ring of functions of a smooth affine curve over a finite field we prove in this context a moving lemma pertaining to horizontal 1 cycles on a regular scheme x quasi projective and flat over s we also show the existence of a finite surjective s morphism to psd for any scheme x projective over s when x s has all its fibers of a fixed dimension d

efficient numerical schemes for gradient vector flow since its publication more than 10 years ago the gradient vector flow gvf technique has been used and adapted to various models and problems its effectiveness has greatly contributed to its popularity the main drawback of gvf and its generalisation however is their expensive computation load and its consequence on the capture range in this work we propose and compare different efficient numerical schemes to solve the gvf and its generalisations

complexity of the normalization of algebras we introduce and develop new techniques to study the complexity of normalization processes of graded algebras the construction of a new degree function on graded modules with a global nature permits a broad extension of recent bounds for the length of the chains of subalgebras that general algorithms must transverse to build the integral closure particularly of blowup algebras it achieves this by relating the values of the new degree with invariants of the algebra known ab initio as a by product it reveals new inequalities among hilbert coefficients

finiteness theorems for the picard objects of an algebraic stack abstract we prove some finiteness theorems for the picard functor of an algebraic stack in the spirit of sga 6 exp xii and xiii in particular we give a stacky version of raynaud s relative representability theorem we give sufficient conditions for the existence of the torsion component of the picard functor and for the finite generation of the neron severi groups or of the picard group itself we give some examples and applications in appendix a we prove the semicontinuity theorem for a non necessarily tame algebraic stack

symmetric powers of complete modules over a two dimensional regular local ring this is the published version also available here http dx doi org 10 1090 s0002 9947 97 01819 9 first published in trans amer math soc in 1997 published by the american mathematical society

moduli of curves grobner bases and the krichever map abstract we study moduli spaces of possibly non nodal curves c p 1 p n of arithmetic genus g with n smooth marked points equipped with nonzero tangent vectors such that o c p 1 p n is ample and h 1 o c a 1 p 1 a n p n 0 for given integer weights a a 1 a n such that a i 0 and a i g we show that each such moduli space u g n n s a is an affine scheme of finite type and the krichever map identifies it with the quotient of an explicit locally closed subscheme of the sato grassmannian by the free action of the group of changes of formal parameters we study the git quotients of u g n n s a by the natural torus action and show that some of the corresponding stack quotients give modular compactifications of m g n with projective coarse moduli spaces more generally using similar techniques we construct moduli spaces of curves with chains of divisors supported at marked points with prescribed number of sections which in the case n 1 corresponds to specifying the weierstrass gap sequence at the marked point

fitting an unknown number of lines and planes to image data through compatible cluster merging abstract a compatible cluster merging algorithm is presented that is specially designed to find the optimum number of linear planar and hyperplanar clusters i e clusters that lie in a subspace of the original space when an upper bound on the number of clusters present is known this algorithm is shown to be superior to more traditional validity measure based approaches the effectiveness and advantages of the proposed technique in 2d and 3d applications is demonstrated with both synthetic and real data the proposed applications include character recognition obtaining straight line descriptions of intensity edge images and obtaining planar approximations of 3d range data

application of affine invariant fourier descriptors to recognition of 3 d objects the method of fourier descriptors is extended to produce a set of normalized coefficients which are invariant under any affine transformation translation rotation scaling and shearing the method is based on a parameterized boundary description which is transformed to the fourier domain and normalized there to eliminate dependencies on the affine transformation and on the starting point invariance to affine transforms allows considerable robustness when applied to images of objects which rotate in all three dimensions as is demonstrated by processing silhouettes of aircraft maneuvering in three space

hom stacks and restriction of scalars fix an algebraic space s and let x and y be separated artin stacks of finite presentation over s with finite diagonals over s we define a stack homs x y classifying morphisms between x and y assume that x is proper and flat over s and assume fppf locally on s that there exists a finite finitely presented flat cover z x with z an algebraic space then we show that homs x y is an artin stack with quasi compact and separated diagonal