deformable contours modeling and extraction this paper considers the problem of modeling and extracting arbitrary deformable contours from noisy images we propose a global contour model based on a stable and regenerative shape matrix which is invariant and unique under rigid motions combined with markov random field to model local deformations this yields prior distribution that exerts influence over a global model while allowing for deformations we then cast the problem of extraction into posterior estimation and show its equivalence to energy minimization of a generalized active contour model we discuss pertinent issues in shape training energy minimization line search strategies minimax regularization and initialization by generalized hough transform finally we present experimental results and compare its performance to rigid template matching

polish group actions dichotomies and generalized elementary embeddings the results in this paper involve two different topics in the descriptive theory of polish group actions the book becker kechris 6 is an introduction to that theory our two topics and two collections of theorems are rather unrelated but the proofs for both topics are essentially the same locally compact polish groups i e second countable locally compact groups are the traditional objects of study in the field known as topological groups more recently there has been interest in nonlocally compact polish groups such as s the symmetric group on n topologized as a subspace of nn much of this paper is concerned with a proper subclass of the class of polish groups namely those polish groups which admit a complete left invariant metric we call these cli groups the class of cli groups includes all locally compact groups proposition 3 c 2 d but also much more for example all solvable groups are cli hjorth solecki see proposition 3 c 2 f and a closed subgroup g of s is cli iff g is closed in nn see example 3 c 3 a we study continuous actions by polish groups on polish spaces and the associated orbit equivalence relation for locally compact groups all of our results are known or trivial or both but some of our results can be viewed as generalizations of known theorems about locally compact groups to the larger class of cli groups one of the two topics considered in this paper is dichotomy theorems for equivalence relations these are theorems which assert that either the quotient space is small or else it contains a copy of a specific large set we prove some dichotomy theorems for the orbit space of actions by cli groups there are two types of dichotomies which we call the silver vaught dichotomy and the glimm effros dichotomy the silver vaught dichotomy asserts that either there are only countably many equivalence classes or else there is a perfect set of pairwise inequivalent elements assuming the negation of the continuum hypothesis the silver vaught dichotomy is equivalent to the proposition that there are either countably many equivalence classes or 2 0 equivalence classes the topological vaught conjecture which is open is for any continuous action by a polish group g on a polish space x the orbit equivalence relation satisfies the silver vaught dichotomy this conjecture implies and was motivated by the vaught conjecture in model theory indeed

refining strategic ability in alternating time temporal logic we propose extending alternating time temporal logic atl by a unary operator i about distributing the powers of some given agent i to a given set of sub agents i means that i s powers can be distributed in a way which satisfies the atl condition on the strategic ability of the coalitions the members of may form possibly together with others agents we prove the decidability of model checking of formulas whose subformulas have the form i11imm with no further occurrences of in we also give some axioms and proof rules about the new operator

on the number of permutatively inequivalent basic sequences in a banach space let x be a banach space with a schauder basis en n n the relation e0 is borel reducible to permutative equivalence between normalized block sequences of en n n or x is c0 or lp saturated for some 1 p if en n n is shrinking unconditional then either it is equivalent to the canonical basis of c0 or lp 1 p or the relation e0 is borel reducible to permutative equivalence between sequences of normalized disjoint blocks of x or of x if en n n is unconditional then either x is isomorphic to l2 or x contains 2 subspaces or 2 quotients which are spanned by pairwise permutatively inequivalent normalized unconditional bases

a glimm effros dichotomy for borel equivalence relations a basic dichotomy concerning the structure of the orbit space of a transformation group has been discovered by glimm g12 in the locally compact group action case and extended by effros e 1 e2 in the polish group action case when additionally the induced equivalence relation is f it is the purpose of this paper to extend the glimm effros dichotomy to the very general context of an arbitrary borel equivalence relation not even necessarily induced by a group action despite the totally classical descriptive set theoretic nature of our result our proof requires the employment of methods of effective descriptive set theory and thus ultimately makes crucial use of computability or recursion theory on the integers

ideal models of spaces ideal domains have an elementary order theoretic structure every element is either compact or maximal despite this we establish that 1 they can model any space currently known to possess a countably based model and 2 the metric spaces with ideal models are exactly the completely metrizable spaces

completeness of kozen s axiomatisation of the propositional m calculus propositional calculus is an extension of the propositional modal logic with the least fixpoint operator in the paper introducing the logic kozen posed a question about completeness of the axiomatisation which is a small extension of the axiomatisation of the model system k it is shown that this axiomatisation is complete

the smooth ideal we give a classical proof of the generalization of the characterization of smoothness to quotients of polish spaces by borel equivalence relations as an application we describe the extent to which any given borel equivalence relation on a polish space is encoded by the corresponding ideal generated by the family of borel sets on which it is smooth

arbitrary arrow update logic in this paper we introduce arbitrary arrow update logic aaul the logic aaul takes arrow update logic a dynamic epistemic logic where the accessibility relations of agents are updated rather than the set of possible worlds and adds a quantifier over such arrow updates we investigate the relative expressivity of aaul compared to other logics most notably arbitrary public announcement logic apal additionally we show that the model checking problem for aaul is pspace complete finally we introduce a proof system for aaul and prove it to be sound and complete

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

essential countability of treeable equivalence relations we establish a dichotomy theorem characterizing the circumstances under which a treeable borel equivalence relation e is essentially countable under additional topological assumptions on the treeing we in fact show that e is essentially countable if and only if there is no continuous embedding of e1 into e our techniques also yield the first classical proof of the analogous result for hypersmooth equivalence relations and allow us to show that up to continuous kakutani embeddability there is a minimum borel function which is not essentially countable to one

the undecidability of arbitrary arrow update logic arbitrary arrow update logic is a dynamic modal logic with a modality to quantify over arrow updates some properties of this logic have already been established but until now it remained an open question whether the logic s satisfiability problem is decidable here we show by a reduction of the tiling problem that the satisfiability problem of arbitrary arrow update logic is co re hard and therefore undecidable

the complexity of one agent refinement modal logic we investigate the complexity of satisfiability for one agent refinement modal logic rml a known extension of basic modal logic ml obtained by adding refinement quantifiers on structures it is known that rml has the same expressiveness as ml but the translation of rml into ml is of non elementary complexity and rml is at least doubly exponentially more succinct than ml in this paper we show that rml satisfiability is only singly exponentially harder than ml satisfiability the latter being a well known pspace complete problem more precisely we establish that rml satisfiability is complete for the complexity class aexp pol i e the class of problems solvable by alternating turing machines running in single exponential time but only with a polynomial number of alternations note that nexptime aexp pol expspace 11this work is the revised and expanded version of 1

the complementation problem for bu chi automata with applications to temporal logic the problem of complementing buchi automata arises when developing procedures for temporal logics of programs unfortunately previously known constructions for complementing buchi automata involve a doubly exponential blow up in the size of the automaton we present a construction that involves only an exponential blow up we use this construction to prove a polynomial space upper bound for the propositional temporal logic of regular events and to prove a complexity hierarchy result for quantified propositional temporal logic

turbulence representations and trace preserving actions we establish criteria for turbulence in certain spaces of c algebra repre sentations and apply this to the problem of nonclassiability by countable structures for group actions on a standard atomless probability space x and on the hypernite ii1 factor r we also prove that the conjugacy action on the space of free actions of a countably innite amenable group on r is turbulent and that the conjugacy action on the space of ergodic measure preserving ows on x is generically turbulent

a dichotomy characterizing analytic digraphs of uncountable borel chromatic number in any dimension we study the extension of the kechris solecki todorcevic dichotomy on analytic graphs to dimensions higher than 2 we prove that the extension is possible in any dimension finite or infinite the original proof works in the case of the finite dimension we first prove that the natural extension does not work in the case of the infinite dimension for the notion of continuous homomorphism used in the original theorem then we solve the problem in the case of the infinite dimension finally we prove that the natural extension works in the case of the infinite dimension but for the notion of baire measurable homomorphism

an axiomatization of bisimulation quantifiers via the µ calculus this paper deals with bisimulation quantifiers logic bql that is the extension of propositional dynamic logic pdl with the so called bisimulation quantifiers this logic is expressively equivalent to the calculus an extension of modal logic with extremal fixpoints albeit its formulas are easier to understand in this work we provide a complete axiomatization of bql based on certain normal form results for the calculus obtained by janin and walukiewicz

refinement modal logic in this paper we present refinement modal logic a refinement is like a bisimulation except that from the three relational requirements only atoms and back need to be satisfied our logic contains a new operator in addition to the standard box modalities for each agent the operator acts as a quantifier over the set of all refinements of a given model as a variation on a bisimulation quantifier this refinement operator or refinement quantifier can be seen as quantifying over a variable not occurring in the formula bound by it the logic combines the simplicity of multi agent modal logic with some powers of monadic second order quantification we present a sound and complete axiomatization of multi agent refinement modal logic we also present an extension of the logic to the modal calculus and an axiomatization for the single agent version of this logic examples and applications are also discussed to software verification and design the set of agents can also be seen as a set of actions and to dynamic epistemic logic we further give detailed results on the complexity of satisfiability and on succinctness

the classification of hypersmooth borel equivalence relations this paper is a contribution to the study of borel equivalence relations in standard borel spaces i e polish spaces equipped with their borel structure a class of such equivalence relations which has received particular attention is the class of hyperfinite borel equivalence relations these can be defined as the increasing unions of sequences of borel equivalence relations all of whose equivalence classes are finite or as it turns out equivalently those induced by the orbits of a single borel auto morphism hyperfinite equivalence relations have been classified in djk under two notions of equivalence borel bi reducibility and borel isomorphism

fast marching methods fast marching methods are numerical schemes for computing solutions to the nonlinear eikonal equation and related static hamilton jacobi equations based on entropy satisfying upwind schemes and fast sorting techniques they yield consistent accurate and highly efficient algorithms they are optimal in the sense that the computational complexity of the algorithms is o n log n where n is the total number of points in the domain the schemes are of use in a variety of applications including problems in shape offsetting computing distances from complex curves and surfaces shape from shading photolithographic development computing first arrivals in seismic travel times construction of shortest geodesics on surfaces optimal path planning around obstacles and visibility and reflection calculations in this paper we review the development of these techniques including the theoretical and numerical underpinnings provide details of the computational schemes including higher order versions and demonstrate the techniques in a collection of different areas

non classification of cartan subalgebras for a class of von neumann algebras abstract we study the complexity of the classification problem for cartan subalgebras in von neumann algebras we construct a large family of ii1 factors whose cartan subalgebras up to unitary conjugacy are not classifiable by countable structures providing the first such examples additionally we construct examples of ii1 factors whose cartan subalgebras up to conjugacy by an automorphism are not classifiable by countable structures finally we show directly that the cartan subalgebras of the hyperfinite ii1 factor up to unitary conjugacy are not classifiable by countable structures and deduce that the same holds for any mcduff ii1 factor with at least one cartan subalgebra

vaught s conjecture and the glimm effros property for polish transformation groups we extend the original glimm effros theorem for locally compact groups to a class of polish groups including the nilpotent ones and those with an invariant metric for this class we thereby obtain the topological vaught conjecture

descriptive complexity of some isomorphism classes of banach spaces abstract we present a topological frame in which it is possible to estimate the complexity of some borel families of separable banach spaces we use this frame for evaluating the complexity of the isomorphism class of the hilbert space l 2 of certain asymptotically hilbertian spaces and of the l p spaces under the condition 1 p the complexity appears to increase with the distance to the hilbert space commented open problems conclude the article

the space of composants of an indecomposable continuum abstract the family of all composants of an indecomposable continuum is studied we investigate the equivalence relation induced on an indecomposable continuum by its partition into composants we show that up to borel bireducibility such an equivalence relation can be of only two types e 0 and e 1 the e 0 type being simple and the e 1 type being complicated as a consequence of this we show that each indecomposable continuum carries a borel probability measure which assigns 0 to each composant and 0 or 1 to each borel set which is the union of a family of composants in particular it follows that there is no borel transversal for the family of all composants this solves an old problem in the theory of continua we prove that all hereditarily indecomposable continua are of the complicated type that is they fall into the e 1 type we analyze the properties of being of type e 1 or of type e 0 we show using effective descriptive set theory that the first of these properties is analytic and so the second one is coanalytic we construct examples of continua of both types in fact we produce a family of indecomposable continua and use it to prove that these properties are complete analytic and complete coanalytic respectively hence non borel so they do not admit simple topological characterizations we also use continua from this family to show that an indecomposable continuum may be of type e 1 only because of the behavior of composants on a small subset of the continuum this in particular shows that certain natural approaches to solving kuratowski s problem on generic ergodicity of the composant equivalence relation will not work we finish with some open problems

on the classification of positions and complex structures in banach spaces abstract a topological setting is defined to study the complexities of the relation of equivalence of embeddings or position of a banach space into another and of the relation of isomorphism of complex structures on a real banach space the following results are obtained a if x is not uniformly finitely extensible then there exists a space y for which the relation of position of y inside x reduces the relation e 0 and therefore is not smooth b the relation of position of l p inside l p or inside l p p 2 reduces the relation e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group c the relation of position of a space inside another can attain the maximum complexity e max d there exists a subspace of l p 1 p 2 on which isomorphism between complex structures reduces e 1 and therefore is not reducible to an orbit relation induced by the action of a polish group

a robust snake implementation a dual active contour a conventional active contour formulation suffers difficulty in appropriate choice of an initial contour and values of parameters recent approaches have aimed to resolve these problems but can compromise other performance aspects to relieve the problem in initialization we use a dual active contour which is combined with a local shape model to improve the parameterization one contour expands from inside the target feature the other contracts from the outside the two contours are interlinked to provide a balanced technique with an ability to reject weak local energy minima

on isometry and isometric embeddability between ultrametric polish spaces abstract we study the complexity with respect to borel reducibility of the relations of isometry and isometric embeddability between ultrametric polish spaces for which a set d of possible distances is fixed in advance these are respectively an analytic equivalence relation and an analytic quasi order and we show that their complexity depends only on the order type of d when d contains a decreasing sequence isometry is borel bireducible with countable graph isomorphism and isometric embeddability has maximal complexity among analytic quasi orders if d is well ordered the situation is more complex for isometry we have an increasing sequence of borel equivalence relations of length 1 which are cofinal among borel equivalence relations classifiable by countable structures while for isometric embeddability we have an increasing sequence of analytic quasi orders of length at least 3 we then apply our results to solve various open problems in the literature for instance we answer a long standing question of gao and kechris by showing that the relation of isometry on locally compact ultrametric polish spaces is borel bireducible with countable graph isomorphism

uniformisations partielles et criteres a la hurewicz dans le plan we give characterizations of the borel sets potentially in some wadge class among the borel sets with countable vertical sections of a product of two polish spaces to do this we use some partial uniformization results

decomposing borel sets and functions and the structure of baire class 1 functions all spaces considered are metric separable and are denoted usually by the letters x y or z w stands for the set of all natural numbers if a metric separable space is additionally complete we call it polish if it is a continuous image of ww or equivalently of a polish space it is called souslin the main subject of the present paper is the structure of baire class 1 functions recent developments in banach space theory in particular discoveries of rosenthal and bourgain fremlin and talagrand see r for a survey of these developments stimulated investigations into the structure of baire class 1 functions the interested reader may consult papers by haydon odel rosenthal hor kechris louveau kl rosenthal r2 and references quoted there these investigations have already provided new applications in banach space theory see for example ri in our study of baire class 1 functions we will be interested in two decomposition properties one of them defined by lusin the other one by jayne and rogers first however we want to consider a more general problem of determining how difficult it is to represent a borel set as a union of simpler borel sets or the graph of a borel function as a union of the graphs of simpler borel functions using effective descriptive set theory in particular louveau s theorem we show that if a c x is borel x polish then a e e or there is a continuous injection q ww a such that q 1 b is meager for any b c a which is e2 this gives a new proof of j stern s result that if a borel set a is the union of cov m sets in e then a is itself e cov m is the smallest cardinality of a family of meager sets covering ill we prove similar results for functions put for f x y and a family of functions g

a computational approach to edge detection this paper describes a computational approach to edge detection the success of the approach depends on the definition of a comprehensive set of goals for the computation of edge points these goals must be precise enough to delimit the desired behavior of the detector while making minimal assumptions about the form of the solution we define detection and localization criteria for a class of edges and present mathematical forms for these criteria as functionals on the operator impulse response a third criterion is then added to ensure that the detector has only one response to a single edge we use the criteria in numerical optimization to derive detectors for several common image features including step edges on specializing the analysis to step edges we find that there is a natural uncertainty principle between detection and localization performance which are the two main goals with this principle we derive a single operator shape which is optimal at any scale the optimal detector has a simple approximate implementation in which edges are marked at maxima in gradient magnitude of a gaussian smoothed image we extend this simple detector using operators of several widths to cope with different signal to noise ratios in the image we present a general method called feature synthesis for the fine to coarse integration of information from operators at different scales finally we show that step edge detector performance improves considerably as the operator point spread function is extended along the edge

borel actions of polish groups we show that a borel action of a polish group on a standard borel space is borel isomorphic to a continuous action of the group on a polish space and we apply this result to three aspects of the theory of borel actions of polish groups universal actions invariant probability measures and the topological vaught conjecture we establish the existence of universal actions for any given polish group extending a result of mackey and varadarajan for the locally compact case we prove an analogue of tarski s theorem on paradoxical decompositions by showing that the existence of an invariant borel probability measure is equivalent to the nonexistence of paradoxical decompositions with countably many borel pieces we show that various natural versions of the topological vaught conjecture are equivalent to each other and in the case of the group of permutations of n with the model theoretic vaught conjecture for infinitary logic this depends on our identification of the universal action for that group

on the complexity of the uniform homeomorphism relation between separable banach spaces we investigate the uniform homeomorphism relation between separable banach spaces and the related relation of local equivalence we completely characterize the descriptive complexity of local equivalence in the borel reducibility hierarchy this also provides a lower bound for the complexity of the uniform homeomorphism

completeness of the isomorphism problem for separable c algebras this paper studies the descriptive set theoretical complexity of the isomorphism problem for separable c algebras we prove that the isomorphism problem for separable simple ai c algebras is complete in the class of orbit equivalence relations this means that any isomorphism problem arising from a continuous action of a separable completely metrizable group can be reduced to the isomorphism of simple separable ai c algebras

an improved time adaptive self organizing map for high speed shape modeling in this paper an improved active contour model based on the time adaptive self organizing map with a high convergence speed and low computational complexity is proposed for this purpose the active contour model based on the original time adaptive self organizing map is modified in two ways adaptation of the speed parameter and reduction of the number of neurons by adapting the speed parameter the neuron motion speed is determined based on the distance of each neuron from the shape boundary which results in an increase in the speed of convergence of the contour using a smaller number of neurons the computational complexity is reduced to achieve this the number of neurons used in the contour is determined based on the boundary curvature the proposed model is studied and compared with the original time adaptive self organizing map both models are used in several experiments including a tracking application results reveal the higher speed and very good performance of the proposed model for real time applications

a bayesian approach to dynamic contours through stochastic sampling and simulated annealing in many applications of image analysis simply connected objects are to be located in noisy images during the last 5 6 years active contour models have become popular for finding the contours of such objects connected to these models are iterative algorithms for finding the minimizing energy curves making the curves behave dynamically through the iterations these approaches do however have several disadvantages the numerical algorithms that are in use constrain the models that can be used furthermore in many cases only local minima can be achieved in this paper the author discusses a method for curve detection based on a fully bayesian approach a model for image contours which allows the number of nodes on the contours to vary is introduced iterative algorithms based on stochastic sampling is constructed which make it possible to simulate samples from the posterior distribution making estimates and uncertainty measures of specific quantities available further simulated annealing schemes making the curve move dynamically towards the global minimum energy configuration are presented in theory no restrictions on the models are made in practice however computational aspects must be taken into consideration when choosing the models much more general models than the one used for active contours may however be applied the approach is applied to ultrasound images of the left ventricle and to magnetic resonance images of the human brain and show promising results

dichotomy theorems for families of non cofinal essential complexity we prove that for every borel equivalence relation e either e is borel reducible to mathbb e 0 or the family of borel equivalence relations incompatible with e has cofinal essential complexity it follows that if f is a borel equivalence relation and cal f is a family of borel equivalence relations of non cofinal essential complexity which together satisfy the dichotomy that for every borel equivalence relation e either e in cal f or f is borel reducible to e then cal f consists solely of smooth equivalence relations thus the dichotomy is equivalent to a known theorem

dynamic programming for detecting tracking and matching deformable contours the problem of segmenting an image into separate regions and tracking them over time is one of the most significant problems in vision terzopoulos et al 1987 proposed an approach to detect the contour regions of complex shapes assuming a user selected initial contour not very far from the desired solution we propose to further explore the information provided by the user s selected points and apply an optimal method to detect contours which allows a segmentation of the image the method is based on dynamic programming dp and applies to a wide variety of shapes it is exact and not iterative we also consider a multiscale approach capable of speeding up the algorithm by a factor of 20 although at the expense of losing the guaranteed optimality characteristic the problem of tracking and matching these contours is addressed for tracking the final contour obtained at one frame is sampled and used as initial points for the next frame then the same dp process is applied for matching a novel strategy is proposed where the solution is a smooth displacement field in which unmatched regions are allowed while cross vectors are not the algorithm is again based on dp and the optimal solution is guaranteed we have demonstrated the algorithms on natural objects in a large spectrum of applications including interactive segmentation and automatic tracking of the regions of interest in medical images

global minimum for active contour models a minimal path approach a new boundary detection approach for shape modeling is presented it detects the global minimum of an active contour model s energy between two end points initialization is made easier and the curve is not trapped at a local minimum by spurious edges we modify the snake energy by including the internal regularization term in the external potential term our method is based on finding a path of minimal length in a riemannian metric we then make use of a new efficient numerical method to find this shortest path it is shown that the proposed energy though based only on a potential integrated along the curve imposes a regularization effect like snakes we explore the relation between the maximum curvature along the resulting contour and the potential generated from the image the method is capable to close contours given only one point on the objects boundary by using a topology based saddle search routine we show examples of our method applied to real aerial and medical images

a fast minimal path active contour model a new minimal path active contour model for boundary extraction is presented implementing the new approach requires four steps 1 users place some initial end points on or near the desired boundary through an interactive interface 2 a potential searching window is defined between two end points 3 a graph search method based on conic curves is used to search the boundary and 4 a wriggling procedure is used to calibrate the contour and reduce sensitivity of the search results on the selected initial end points the last three steps are performed automatically in the proposed approach the potential window systematically provides a new node connection for the later graph search which is different from the row by row and column by column methods used in the classical graph search furthermore this graph search also suggests ways to design a wriggling procedure to evolve the contour in the direction nearly perpendicular to itself by creating a list of displacement vectors in the potential window the proposed minimal path active contour model speeds up the search and reduces the metrication error frequently encountered in the classical graph search methods e g the dynamic programming minimal path dpmp method