on culler shalen seminorms and dehn filling if f is a finitely generated discrete group and g a complex algebraic lie group the g character variety of r is an affine algebraic variety whose points correspond to characters of representations of r with values in g marc culler and peter shalen developed the theory of sl2 c character varieties of finitely generated groups and applied their results to study the topology of 3 dimensional manifolds in the papers 6 7 8 consider the exterior m of a hyperbolic knot lying in a closed connected orientable 3 manifold the mostow rigidity theorem implies that the holonomy representation p iri m isom h3 psl2 c is unique up to conjugation and taking complex conjugates the orientability of m can be used to show 1 lifts to a representation p e hom ri m sl2 c whose character determines an essentially unique point of xp of x iri m the sl2 c character variety of irl m culler and shalen 8 proved that the component x0 of x x1ri m which contains x is a curve one of their major contributions was to show how x0 determines a norm on h1 wm r which encodes many topological properties of m in particular it provides information on the dehn fillings of m their construction may be applied to arbitrary curves in the sl2 c character variety of a connected compact orientable irreducible 3manifold whose boundary is a torus though in this generality one can only guarantee that it will define a seminorm the first half of this paper is devoted to the development of the general theory of culler shalen seminorms defined for curves of psl2 c characters by working over psl2 c we obtain a theory that is more generally applicable than its sl2 c counterpart while being only mildly more difficult to set up in the second half of this paper we apply the theory of culler shalen seminorms to study the dehn filling operation in particular we examine the relationship between fillings which yield manifolds having a positive dimen

interpretation of af c algebras in łukasiewicz sentential calculus on donne un critere pour la non simplicite d une af c algebre 7b u en termes de proprietes de la theorie de la recursivite du groupe dimension k 0 7b u

geometrical methods in wajsberg hoops abstract the aim of this paper is to show that certain geometric methods originally developed for investigating ukasiewicz many valued logics may be profitably applied to the study of classes of partially ordered residuated monoids we substantiate this claim by characterizing all free wajsberg hoops in terms of mcnaughton functions over the n cube and by giving complete axiomatizations for all varieties of wajsberg hoops

equational characterization of all varieties of mv algebras abstract it is known that all subvarieties of mv algebras are finitely axiomatizable in the literature one can find equational characterizations of certain subvarieties such as mv n algebras in this paper we write down equational bases for all mv varieties and prove a representation theorem for each subvariety

speckle reducing anisotropic diffusion this paper provides the derivation of speckle reducing anisotropic diffusion srad a diffusion method tailored to ultrasonic and radar imaging applications srad is the edge sensitive diffusion for speckled images in the same way that conventional anisotropic diffusion is the edge sensitive diffusion for images corrupted with additive noise we first show that the lee and frost filters can be cast as partial differential equations and then we derive srad by allowing edge sensitive anisotropic diffusion within this context just as the lee 1980 1981 1986 and frost 1982 filters utilize the coefficient of variation in adaptive filtering srad exploits the instantaneous coefficient of variation which is shown to be a function of the local gradient magnitude and laplacian operators we validate the new algorithm using both synthetic and real linear scan ultrasonic imagery of the carotid artery we also demonstrate the algorithm performance with real sar data the performance measures obtained by means of computer simulation of carotid artery images are compared with three existing speckle reduction schemes in the presence of speckle noise speckle reducing anisotropic diffusion excels over the traditional speckle removal filters and over the conventional anisotropic diffusion method in terms of mean preservation variance reduction and edge localization

snakes active contour models a snake is an energy minimizing spline guided by external constraint forces and influenced by image forces that pull it toward features such as lines and edges snakes are active contour models they lock onto nearby edges localizing them accurately scale space continuation can be used to enlarge the capture region surrounding a feature snakes provide a unified account of a number of visual problems including detection of edges lines and subjective contours motion tracking and stereo matching we have used snakes successfully for interactive interpretation in which user imposed constraint forces guide the snake near features of interest

amalgamation and interpolation in ordered algebras the first part of this paper provides a comprehensive and self contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations in particular proofs are given of known equivalences between the amalgamation property and the robinson property the congruence extension property and the extension property and the flat amalgamation property and the deductive interpolation property as well as various dependencies between these properties these relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice ordered abelian groups and mv algebras and to determine important subvarieties of residuated lattices where these properties hold or fail in particular a full description is given of all subvarieties of commutative gmv algebras possessing the amalgamation property

on emv algebras abstract the paper deals with an algebraic extension of mv algebras based on the definition of generalized boolean algebras we introduce a new class of structures not necessarily with a top element which are called emv algebras in a way that every emv algebra contains an mv algebra first we present basic properties of emv algebras we give some examples introduce and investigate congruence relations ideals and filters on these algebras we establish a basic representation result saying that each emv algebra can be embedded into an emv algebra with top element and we characterize emv algebras either as structures which are termwise equivalent to mv algebras or as maximal ideals of emv algebras with top element we study the lattice of ideals of an emv algebra and prove that every emv algebra has at least one maximal ideal we define an emv clan of fuzzy sets as a special emv algebra where all operations are defined by points we show that any semisimple emv algebra is isomorphic to an emv clan of fuzzy functions on a set the set of emv algebras is neither a variety nor a quasivariety but rather a special class of emv algebras which we call a q variety of emv algebras we present an equational base for each proper q subvariety of the q variety of emv algebras we establish categorical equivalencies among the category of proper emv algebras the category of mv algebras with a fixed special maximal ideal and a special category of abelian unital l groups

natural dualities for varieties of mv algebras i abstract mv algebras are the lindenbaum algebras for ukasiewicz s infinite valued logic just as boolean algebras correspond to the classical propositional calculus the finitely generated subvarieties of the variety m of all mv algebras are generated by finite chains we develop a natural duality in the sense of davey and werner for each subvariety generated by a finite chain and use it to describe the free and the injective members of these classes finally we point out the relations between the dualities and some categorical equivalences discovered by a di nola and a lettieri

snakes shapes and gradient vector flow snakes or active contours are used extensively in computer vision and image processing applications particularly to locate object boundaries problems associated with initialization and poor convergence to boundary concavities however have limited their utility this paper presents a new external force for active contours largely solving both problems this external force which we call gradient vector flow gvf is computed as a diffusion of the gradient vectors of a gray level or binary edge map derived from the image it differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation using several two dimensional 2 d examples and one three dimensional 3 d example we show that gvf has a large capture range and is able to move snakes into boundary concavities

active contour external force using vector field convolution for image segmentation snakes or active contours have been widely used in image processing applications typical roadblocks to consistent performance include limited capture range noise sensitivity and poor convergence to concavities this paper proposes a new external force for active contours called vector field convolution vfc to address these problems vfc is calculated by convolving the edge map generated from the image with the user defined vector field kernel we propose two structures for the magnitude function of the vector field kernel and we provide an analytical method to estimate the parameter of the magnitude function mixed vfc is introduced to alleviate the possible leakage problem caused by choosing inappropriate parameters we also demonstrate that the standard external force and the gradient vector flow gvf external force are special cases of vfc in certain scenarios examples and comparisons with gvf are presented in this paper to show the advantages of this innovation including superior noise robustness reduced computational cost and the flexibility of tailoring the force field

tracking pylorus in ultrasonic image sequences with edge based optical flow tracking pylorus in ultrasonic image sequences is an important step in the analysis of duodenogastric reflux dgr we propose a joint prediction and segmentation method jps which combines optical flow with active contour to track pylorus the goal of the proposed method is to improve the pyloric tracking accuracy by taking account of not only the connection information among edge points but also the spatio temporal information among consecutive frames the proposed method is compared with other four tracking methods by using both synthetic and real ultrasonic image sequences several numerical indexes hausdorff distance hd average distance ad mean edge distance med and edge curvature ec have been calculated to evaluate the performance of each method jps achieves the minimum distance metrics hd ad and med and a smaller ec the experimental results indicate that jps gives a better tracking performance than others by the best agreement with the gold curves while keeping the smoothness of the result

a phase based approach to the estimation of the optical flow field using spatial filtering we introduce a new technique for estimating the optical flow field starting from image sequences as suggested by fleet and jepson 1990 we track contours of constant phase over time since these are more robust to variations in lighting conditions and deviations from pure translation than contours of constant amplitude our phase based approach proceeds in three stages first the image sequence is spatially filtered using a bank of quadrature pairs of gabor filters and the temporal phase gradient is computed yielding estimates of the velocity component in directions orthogonal to the filter pairs orientations second a component velocity is rejected if the corresponding filter pair s phase information is not linear over a given time span third the remaining component velocities at a single spatial location are combined and a recurrent neural network is used to derive the full velocity we test our approach on several image sequences both synthetic and realistic

on n perfect gmv algebras abstract we introduce the class of n perfect gmv algebras such algebras can be split into n 1 comparable slices we present an equational base for the variety generated by n perfect gmv algebras we define the category of strong n perfect gmv algebras and we show that every strong n perfect gmv algebra is always an interval in a lexicographical product of z with an l group we prove that the variety generated by strong n perfect gmv algebras is generated by a one strong n perfect gmv algebra

region tracking via level set pdes without motion computation we propose an approach to region tracking that is derived from a bayesian formulation the novelty of the approach is twofold first no motion field or motion parameters need to be computed this removes a major burden since accurate motion computation has been and remains a challenging problem and the quality of region tracking algorithms based on motion critically depends on the computed motion fields and parameters the second novelty of this approach is that very little a priori information about the region being tracked is used in the algorithm in particular unlike numerous tracking algorithms no assumption is made on the strength of the intensity edges of the boundary of the region being tracked nor is its shape assumed to be of a certain parametric form the problem of region tracking is formulated as a bayesian estimation problem and the resulting tracking algorithm is expressed as a level set partial differential equation we present further extensions to this partial differential equation allowing the possibility of including additional information in the tracking process such as priors on the region s intensity boundaries and we present the details of the numerical implementation very promising experimental results are provided

plane curves associated to character varieties of 3 manifolds consider a compact 3 manifold m with boundary consisting of a single torus the papers cs1 cs2 cgls discuss the variety of characters of sl2 c representations of zl m and some of the ways in which the topological structure of m is reflected in the algebraic geometry of the character variety we will describe in this paper a certain affine algebraic curve dm which is naturally associated to the character variety of m a basis b 9 1 for the peripheral subgroup of m determines an embedding p8 of dm into c x c with coordinates l and m the closure in c 2 of ps dm is a plane algebraic curve and therefore is defined by a polynomial am n0 m that after certain normalizations is uniquely determined up to multiplication by constants the polynomial am b is effectively computable and is an invariant of the manifold m together with the choice of basis b the results in this paper describe how geometric properties of the character variety and hence topological properties of m are reflected by the polynomial am b in the case that m is the complement of a knot k in a homology 3 sphere we may take the basis b to consist of the longitude and meridian of k with the usual orientation conventions this basis is well defined modulo the involution which inverts both the longitude and meridian it will follow from the construction of dm that if the basis b is obtained from b by inverting both generators then the regular maps pb and pb have the same image thus ar am s am b is an invariant of the knot the polynomial am b displays in a striking way information about the incompressible surfaces in m this involves the newton polygon of am b

lucas kanade meets horn schunck combining local and global optic flow methods differential methods belong to the most widely used techniques for optic flow computation in image sequences they can be classified into local methods such as the lucas kanade technique or bigun s structure tensor method and into global methods such as the horn schunck approach and its extensions often local methods are more robust under noise while global techniques yield dense flow fields the goal of this paper is to contribute to a better understanding and the design of novel differential methods in four ways i we juxtapose the role of smoothing regularisation processes that are required in local and global differential methods for optic flow computation ii this discussion motivates us to describe and evaluate a novel method that combines important advantages of local and global approaches it yields dense flow fields that are robust against noise iii spatiotemporal and nonlinear extensions as well as multiresolution frameworks are presented for this hybrid method iv we propose a simple confidence measure for optic flow methods that minimise energy functionals it allows to sparsify a dense flow field gradually depending on the reliability required for the resulting flow comparisons with experiments from the literature demonstrate the favourable performance of the proposed methods and the confidence measure

spatio temporal nonrigid registration for ultrasound cardiac motion estimation we propose a new spatio temporal elastic registration algorithm for motion reconstruction from a series of images the specific application is to estimate displacement fields from two dimensional ultrasound sequences of the heart the basic idea is to find a spatio temporal deformation field that effectively compensates for the motion by minimizing a difference with respect to a reference frame the key feature of our method is the use of a semi local spatio temporal parametric model for the deformation using splines and the reformulation of the registration task as a global optimization problem the scale of the spline model controls the smoothness of the displacement field our algorithm uses a multiresolution optimization strategy to obtain a higher speed and robustness we evaluated the accuracy of our algorithm using a synthetic sequence generated with an ultrasound simulation package together with a realistic cardiac motion model we compared our new global multiframe approach with a previous method based on pairwise registration of consecutive frames to demonstrate the benefits of introducing temporal consistency finally we applied the algorithm to the regional analysis of the left ventricle displacement and strain parameters were evaluated showing significant differences between the normal and pathological segments thereby illustrating the clinical applicability of our method

computation of component image velocity from local phase information we present a technique for the computation of 2d component velocity from image sequences initially the image sequence is represented by a family of spatiotemporal velocity tuned linear filters component velocity computed from spatiotemporal responses of identically tuned filters is expressed in terms of the local first order behavior of surfaces of constant phase justification for this definition is discussed from the perspectives of both 2d image translation and deviations from translation that are typical in perspective projections of 3d scenes the resulting technique is predominantly linear efficient and suitable for parallel processing moreover it is local in space time robust with respect to noise and permits multiple estimates within a single neighborhood promising quantiative results are reported from experiments with realistic image sequences including cases with sizeable perspective deformation

robust shape tracking with multiple models in ultrasound images this paper addresses object tracking in ultrasound images using a robust multiple model tracker the proposed tracker has the following features 1 it uses multiple dynamic models to track the evolution of the object boundary and 2 it models invalid observations outliers reducing their influence on the shape estimates the problem considered in this paper is the tracking of the left ventricle which is known to be a challenging problem the heart motion presents two phases diastole and systole with different dynamics the multiple models used in this tracker try to solve this difficulty in addition ultrasound images are corrupted by strong multiplicative noise which prevents the use of standard deformable models robust estimation techniques are used to address this difficulty the multiple model data association mmda tracker proposed in this paper is based on a bank of nonlinear filters organized in a tree structure the algorithm determines which model is active at each instant of time and updates its state by propagating the probability distribution using robust estimation techniques

prior knowledge level set representations visual grouping in this paper we propose a level set method for shape driven object extraction we introduce a voxel wise probabilistic level set formulation to account for prior knowledge to this end objects are represented in an implicit form constraints on the segmentation process are imposed by seeking a projection to the image plane of the prior model modulo a similarity transformation the optimization of a statistical metric between the evolving contour and the model leads to motion equations that evolve the contour toward the desired image properties while recovering the pose of the object in the new image upon convergence a solution that is similarity invariant with respect to the model and the corresponding transformation are recovered promising experimental results demonstrate the potential of such an approach

three dimensional manifolds kleinian groups and hyperbolic geometry 1 a conjectural picture of 3 manifolds a major thrust of mathematics in the late 19th century in which poincare had a large role was the uniformization theory for riemann surfaces that every conformai structure on a closed oriented surface is represented by a riemannian metric of constant curvature for the typical case of negative euler characteristic genus greater than 1 such a metric gives a hyperbolic structure any small neighborhood in the surface is isometric to a neighborhood in the hyperbolic plane and the surface itself is the quotient of the hyperbolic plane by a discrete group of motions the exceptional cases the sphere and the torus have spherical and euclidean structures three manifolds are greatly more complicated than surfaces and i think it is fair to say that until recently there was little reason to expect any analogous theory for manifolds of dimension 3 or more except perhaps for the fact that so many 3 manifolds are beautiful the situation has changed so that i feel fairly confident in proposing the

on the geometric theory of local mv algebras abstract we investigate the geometric theory of local mv algebras and its quotients axiomatizing the local mv algebras in a given proper variety of mv algebras we show that whilst the theory of local mv algebras is not of presheaf type each of these quotients is a theory of presheaf type which is morita equivalent to an expansion of the theory of lattice ordered abelian groups di nola lettieri s equivalence is recovered from the morita equivalence for the quotient axiomatizing the local mv algebras in chang s variety that is the perfect mv algebras we establish along the way a number of results of independent interest including a constructive treatment of the radical for mv algebras in a fixed proper variety of mv algebras and a representation theorem for the finitely presentable algebras in such a variety as finite products of local mv algebras

a variety containing emv algebras and pierce sheaves of emv algebras abstract according to 11 we know that the class of all emv algebras emv is not a variety since it is not closed under the subalgebra operator the main aim of this work is to find the least variety containing emv for this reason we introduced the variety wemv of wemv algebras of type 2 2 2 2 0 induced by some identities we show that adding a derived binary operation to each emv algebra m 0 we extend its language so that m 0 called an associated wemv algebra belongs to wemv then using the congruence relations induced by the prime ideals of a wemv algebra we prove that each wemv algebra can be embedded into an associated wemv algebra we show that wemv is the least subvariety of the variety of wemv algebras containing emv finally we study pierce sheaves of proper emv algebras

detection of essential surfaces in 3 manifolds with sl 2 trees according to bass serre theory se given a field f with a discrete valuation v f z there is a canonical way to construct a simplicial tree t tf v on which sl2 f acts simplicially without inversion when a group has a representation into the group sl2 f then there is an induced action of on the tree via the representation if further is the fundamental group of a compact 3 manifoldm and the action of on the tree t is nontrivial meaning that there is no point on t fixed by every element of then the action induces a splitting of m along an essential surface in the following way let m p m be the universal covering there is a 1 m equivariant map f m t which is transverse to the set e of midpoints of edges in t such that p f 1 e is an essential surface in m we say such an essential surface is associated to or detected by an sl2 tree a natural question is which essential surfaces in a compact 3 manifold can be associated to sl2 trees and how do they depend on the choice of the field and discrete valuation this is the main issue we are going to address in this paper any 3 manifold mentioned in this paper is automatically assumed orientable and connected by an essential surface in a compact 3 manifold m we mean an orientable properly embedded incompressible surface each component of which is neither boundary parallel in m nor bounds a 3 ball when it is a 2sphere also recall that a discrete valuation on a field f is a homomorphism v from the multiplicative group f onto the group of integers z such that v a b min v a v b for any a b f with a b 0 let v f z be a discrete valuation the set ov 0 a f v a 0 s schanuel x zhang department of mathematics suny at buffalo buffalo ny 14260 2900 usa e mail schanuel buffalo edu xinzhang math buffalo edu