di domains as prime information systems abstract this paper introduces prime information systems prime information systems determine di domains and stable approximable mappings give stable functions and vice versa the notion of rigid embedding is captured by a subsystem relation under this relation prime information systems form a complete partial order cpo constructions like lifting sum product and function space are proposed which induce continuous functions on the cpo in this way recursive prime information systems can be defined using fixed point theory

relation algebraic domain constructions abstract aiming at a constructive approach to domain theory the definition of domains with deflations is presented this class of domains is closed with respect to the common domain constructions another concern of this paper is to provide a formal calculus for a uniform algebraic treatment of order theoretic and functional aspects of domain theory the abstract relation algebra turns out to be an appropriate technical means for the characterization and construction of domains as partial functions present no problems in relation algebra domains need not contain an additional element and functions between domains are generally not total using symmetric quotients the relation algebraic approach is extended to cope with higher order functions

stability of evolutionary algorithms we prove under mild conditions the convergence of some evolutionary algorithm to the solution of the global optimization problem in the proof the lyapunov function s techniques is applied to some semi dynamical system generated by a foias operator on the space of the probability measures defined on the set of admissible solutions

cartesian closed categories of algebraic cpos abstract the results presented in this paper were inspired by the work of smyth who showed that there is a largest cartesian closed full subcategory inside the category of countably based algebraic cpos with least element namely the category of profinite domains removing the countability condition we show that there are exactly two maximal cartesian closed full subcategories inside the category of algebraic cpos with least element one is the natural extension of the class of profinite domains to the uncountable case the other is a new class of domains which are characterized by the property that every principal ideal is a complete lattice the name l domain is introduced for cpos with this property passing to the general situation where no least element is required anymore we find a pair of categories in place of each the profinite domains and the algebraic l domains thus there are four maximal cartesian closed categories of algebraic cpos in this case this complete overview over the possible classes of domains allows to prove general theorems about them this is illustrated by the result that a cpo has an algebraic function space if and only if its space of strict continuous functions is algebraic

multiseeded segmentation using fuzzy connectedness fuzzy connectedness has been effectively used to segment out an object in a badly corrupted image we generalize the approach by providing a definition which is shown to always determine a simultaneous segmentation of multiple objects for any set of seed points the segmentation is uniquely determined by the definition an algorithm for finding this segmentation is presented and its output is illustrated the algorithm is fast as compared to other segmentation algorithms in current use we also report on an evaluation of the accuracy and robustness of the algorithm based on experiments in which several users were repeatedly asked to identify the seed points for the algorithm in a number of images

maximality and totality of stable functions in the category of stable bifinite domains this paper studies maximality and totality of stable functions in the category of stable bifinite domains we present three main results as follows o 1 every maximum preserving function is a maximal element in the stable function spaces 2 a maximal stable function f d e is maximum preserving if d is maximum separable and e is completely separable and 3 a stable bifinite domain d is maximum separable if and only if for any locally distributive stable bifinite domain e each maximal stable function f d e is maximum preserving

quasi prime algebraic domains abstract the purpose of this paper is to introduce a new class of domains called quasi prime algebraic domains we show that this class is a good candidate for the purpose of denotational semantics of programming languages this is achieved by exhibiting many constructions usually needed for denotational semantics on quasi prime algebraic domains in the first part we motivate the notion of quasi primes and quasi prime algebraic domains by studying the effect of linear functions on domains that are not prime algebraic in the second part we study categories of quasi prime algebraic domains by representing them as irreducible information systems we introduce a symmetric monoidal closed category of quasi prime algebraic domains with quasi linear functions we show further that with the usual scott continuous functions as morphisms quasi prime algebraic domains are cartesian closed in the third part we show the existence of a saturated quasi prime algebraic domain and introduce a framework for solving domain equations in quasi prime algebraic domains it is then possible to give for example a model for the un typed lambda calculus with a reflexive quasi prime algebraic domain

grayscale level connectivity theory and applications a novel notion of connectivity for grayscale images is introduced defined by means of a binary connectivity assigned at image level sets in this framework a grayscale image is connected if all level sets below a prespecified threshold are connected the proposed notion is referred to as grayscale level connectivity and includes as special cases other well known notions of grayscale connectivity such as fuzzy grayscale connectivity and grayscale blobs in contrast to those approaches the present framework does not require all image level sets to be connected moreover a connected grayscale object may contain more than one regional maximum grayscale level connectivity is studied in the rigorous framework of connectivity classes the use of grayscale level connectivity in image analysis applications such as object extraction image segmentation object based filtering and hierarchical image representation is discussed and illustrated

nonlinear image labeling for multivalued segmentation we describe a framework for multivalued segmentation and demonstrate that some of the problems affecting common region based algorithms can be overcome by integrating statistical and topological methods in a nonlinear fashion we address the sensitivity to parameter setting the difficulty with handling global contextual information and the dependence of results on analysis order and on initial conditions we develop our method within a theoretical framework and resort to the definition of image segmentation as an estimation problem we show that thanks to an adaptive image scanning mechanism there is no need of iterations to propagate a global context efficiently the keyword multivalued refers to a result property which spans over a set of solutions the advantage is twofold first there is no necessity for setting a priori input thresholds secondly we are able to cope successfully with the problem of uncertainties in the signal model to this end we adopt a modified version of fuzzy connectedness which proves particularly useful to account for densitometric and topological information simultaneously the algorithm was tested on several synthetic and real images the peculiarities of the method are assessed both qualitatively and quantitatively

nonautonomous stochastic search for global minimum in continuous optimization abstract various iterative stochastic optimization schemes can be represented as discrete time markov processes defined by the nonautonomous equation x t 1 t t x t y t where y t is an independent sequence and t t is a sequence of mappings this paper presents a general framework for the study of the stability and convergence of such optimization processes some applications are given the mathematical convergence analysis of two optimization methods the elitist evolution strategy and the grenade explosion method is presented

computational surface flattening a voxel based approach a voxel based method for flattening a surface in 3d space into 2d while best preserving distances is presented triangulation or polyhedral approximation of the voxel data are not required the problem is divided into two main parts voxel based calculation of the minimal geodesic distances between points on the surface and finding a configuration of points in 2d that has euclidean distances as close as possible to these distances the method suggested combines an efficient voxel based hybrid distance estimation method that takes the continuity of the underlying surface into account with classical multidimensional scaling mds for finding the 2d point configuration the proposed algorithm is efficient simple and can be applied to surfaces that are not functions experimental results are shown

adaptive segmentation of speckled images using a hierarchical random field model a two level hierarchical random field model developed for speckled images and in particular for synthetic aperture radar sar imagery is described at the higher level is a gibbs random field governing the grouping of image pixels into regions while at the lower level are speckle processes for the different regions which are also modeled as random fields in accordance with the physical phenomena that cause speckle the speckle processes are modeled as circularly symmetric complex gaussian random fields as with real gaussian fields certain forms of autocovariance of complex gaussian field lead to markovianity properties with the assumption of a separable autocovariance for the complex gaussian random fields local joint statistics of the resulting speckle intensity fields magnitude squared of the complex field are determined the speckle model concurs with the known marginal statistics and also accounts for the autocorrelation observed in actual speckled images a map segmentation using simulated annealing and based on the hierarchical model is presented the algorithm is adaptive in that it recursively segments the image and estimates the model parameters necessary for the segmentation

the common order theoretic structure of version spaces and atmss abstract we demonstrate how order theoretic abstractions can be useful in identifying formalizing and exploiting relationships between seemingly dissimilar ai algorithms that perform computations on partially ordered sets in particular we show how the order theoretic concept of an anti chain can be used to provide an efficient representation for such sets when they satisfy certain special properties we use anti chains to identify and analyze the basic operations and representation optimizations in the version space learning algorithm and the assumption based truth maintenance system atms our analysis allows us to 1 extend the known theory of admissibility of concept spaces for incremental version space merging and 2 develop new simpler label update algorithms for atmss with dnf assumption formulas

implicit brain imaging we describe how implicit surface representations can be used to solve fundamental problems in brain imaging this kind of representation is not only natural following the state of the art segmentation algorithms reported in the literature to extract the different brain tissues but it is also as shown in this paper the most appropriate one from the computational point of view examples are provided for finding constrained special curves on the cortex such as sulcal beds regularizing surface based measures such as cortical thickness and for computing warping fields between surfaces such as the brain cortex all these result from efficiently solving partial differential equations pdes and variational problems on surfaces represented in implicit form the implicit framework avoids the need to construct intermediate mappings between 3 d anatomical surfaces and parametric objects such planes or spheres a complex step that introduces errors and is required by many other cortical processing approaches

an approach to innocent strategies as graphs this paper proposes an approach for extending to graphs the close relation between proofs and innocent strategies we work in the setting of l nets introduced by faggian and maurel as a game model of concurrent interaction we show how l nets satisfying an additional condition which we call l s nets can be sequentialized into traditional tree like strategies conversely sequential strategies can be relaxed into more asynchronous ones we develop an algebra of constructors and destructors that serve to build and decompose graph strategies and to describe a class of minimally sequential graph strategies which can be seen as an abstract kind of multiplicative additive proof nets

a maximal monoidal closed category of distributive algebraic domains abstract we study the category bc of bounded complete dcpos and maps preserving all suprema linear maps bc is a symmetric monoidal closed category if sup denotes the full subcategory of bc with dcpos with one as objects we realize a categorical semantics of linear logic in sup the multiplicatives are fully distributive w r t the additives given prime the full subcategory of bc with prime algebraic dcpos as objects we introduce a prime algebraic quotient a which preserves all the logical operations in sup up to isomorphism therefore if c is a categorical semantics in bc then c is a categorical semantics in prime in particular sup the full subcategory of bc with all prime algebraic lattices as objects is such a categorical semantics prime is symmetric monoidal closed and maximal with respect to being closed under formula and if we demand that all objects are algebraic and distributive thus sup is a maximal categorical semantics with respect to these conditions we discuss the modalities and in sup

on stable domains abstract in denotational semantics of programming languages various categories of domains with continuous functions as morphisms and their closure properties under operations like taking products or function space have been intensively studied however classes of domains which like bifinite domains are also closed under the plotkin powerdomain operation are rare here we investigate stable domains they naturally generalize the concept of di domains studied by berry and others and satisfy a strong finiteness condition for compact elements but in general no distributivity assumption these classes recently were shown in joint work with r gobel to contain universal objects we first derive an order theoretic characterization of stability and then show that the class of all stable domains is closed under countable cartesian products stable function space and the plotkin powerdomain operation as a consequence we also obtain that the categories of all stable l domains and of all distributive stable l domains with stable functions as morphisms are cartesian closed

bayesian clustering for unsupervised estimation of surface and texture models a method of calculating the maximum likelihood clustering for the unsupervised estimation of polynomial models for the data in images of smooth surfaces or for range data for such surfaces is presented an image or a depth map of a region of smooth 3 d surface is modeled as a polynomial plus white noise a region of physically meaningful textured image such as the image of foliage grass or road in outdoor scenes or conductor or lintburn on a thick film substrate is modeled as a colored gaussian markov random field mrf with a polynomial mean value function unsupervised model parameter estimation is accomplished by determining the segmentation and model parameter values that maximize the likelihood of the data or a more general bayesian performance functional agglomerative clustering is used for this purpose

categories of embeddings abstract we present a categorical generalisation of the notion of domains which is closed under suitable exponentiation the goal was originally to generalise girard s model of polymorphism to f if we specialise this notion in the poset case we get new cartesian closed categories of domains

on an open problem of amadio and curien the finite antichain condition more than a dozen years ago amadio bifinite domains stable case in lecture notes in computer science vol 530 1991 pp 16 33 see amadio and curien domains and lambda calculi cambridge tracts in theoretical computer science vol 46 cambridge university press 1998 as well raised the question of whether the category of stable bifinite domains of amadio droste r m amadio bifinite domains stable case in lecture notes in computer science vol 530 1991 pp 16 33 m droste on stable domains theor comput sci 111 1993 89 101 m droste cartesian closed categories of stable domains for polymorphism preprint universitat ghs essen is the largest cartesian closed full sub category of the category of w algebraic meet cpos with stable functions an affirmative solution to this problem has two major steps 1 show that for any w algebraic meet cpo d if all higher order stable function spaces built from d are w algebraic then d is finitary i e it satisfies the so called axiom i 2 show that for any w algebraic meet cpo d if d violates mi then d d violates either m or i we solve the first part of the problem in this paper i e for any w algebraic meet cpo d if the stable function space d d satisfies m then d is finitary our notion of mub meet closed set which is introduced for step 1 will also be used for treating some example cases in step 2

global convergence of discrete time inhomogeneous markov processes from dynamical systems perspective abstract given the continuous real valued objective function f and the discrete time inhomogeneous markov process x t defined by the recursive equation of the form x t 1 t t x t y t where y t is an independent sequence we target the problem of finding conditions under which the x t converges towards the set of global minimums of f our methodology is based on the lyapunov function technique and extends the previous results to cover the case in which the sequence f x t is not assumed to be a supermartingale we provide a general convergence theorem an application example is presented the general result is applied to the simulated annealing algorithm

non deterministic information systems and their domains abstract in the theory of denotational semantics of programming languages dedekind complete algebraic partial orders domains frequently have been considered since scott s and strachey s fundamental work in 1971 stoy 1977 as scott 1982 showed these domains can be represented canonically by deterministic information systems however recently more complicated constructions such as power domains have led to more general domains plotkin 1976 smyth and plotkin 1977 smyth 1983 we introduce non deterministic information systems and establish the representation theorem similar to scott 1982 for these more general domains this result will be the basis for solving recursive domain equations

cartesian closedness of a category of non frame valued complete fuzzy orders abstract let h 0 1 2 1 with the natural order and p q max p q 1 0 for all p q h we know that the category of liminf complete h ordered sets is cartesian closed in this paper it is proved that the category of conically cocomplete h ordered sets with liminf continuous functions as morphisms is cartesian closed more importantly a counterexample is given which shows that the function spaces consisting of liminf continuous functions of complete h ordered sets need not be complete thus the category of complete h ordered sets with liminf continuous functions as morphisms is not cartesian closed

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

using information systems to solve recursive domain equations abstract this paper aims to make the following main contribution to show how to use the concrete nature of scott s information systems to advantage in solving recursive domain equations the method is based on the substructure relation between information systems this essentially makes a complete partial order cpo of information systems standard domain constructions like function space can be made continous on this cpo so the solution of recursive domain equations reduces to the more familiar construction of forming the least fixed point of a continuous function

a decomposition theorem for domains a domain constructor that generalizes the product is defined it is shown that with this constructor exactly the prime algebraic coherent scott domains can be generated from two chains and boolean flat domains

estimating shortest paths and minimal distances on digitized three dimensional surfaces abstract the estimation of minimal distances and shortest paths between points on a continuous three dimensional 3d surface given in digitized form is considered the suggested approach combines recently developed length estimators for digitized 3d curves with well known algorithms for computing shortest paths in sparse graphs to estimate the minimal distances and the corresponding shortest paths in a systematic computationally efficient way in comparison to differential geometry techniques for solving the continuous geodesic problem and to computational geometry algorithms for solving the discrete geodesic probelm the suggested hybrid continuous discrete approach is well suited to applications in which continuous surfaces are given in digitized form computation time must be relatively short and an approximate solution is acceptable in particular the suggested method can be used to efficiently obtain a good initial approximation as an input to other algorithms thus improving their speed of convergence and reducing their tendency to converge to insignificant local minima some confusion has recently arisen with respect to the relation between the design of length estimators and the optimization of local distances for distance transformations since 3d length estimation is a central concept in the suggested approach an effort is made to resolve discrepancies and to highlight the similarities and differences between these problems it is shown that while in two dimensions the design of length estimators and the design of local weights for distance transformations are rather similar in three dimensions digital geometry dictates that these problems are different the contexts in which each of the two approaches should be preferred are identified

universal homogeneous event structures and domains abstract in the theory of denotational semantics of programming languages several authors established the existence of particular kinds of universal domains here we use a general model theoretic result to show that there exists a unique countable universal homogeneous event structure from this we deduce that the category of all event domains with stable embedding projection pairs as morphisms contains a universal object similarly we also obtain a universal di domain we also show that the category of all event domains is closed under inverse limits similar results are derived for kahn and plotkin s concrete data structures and concrete domains

on maximal stable functions abstract this note studies maximal elements in di domains especially maximal stable functions first a sufficient condition for a stable function to be maximal is provided the condition requires that the function be total in the sense that it preserves maximal elements examples are then given to demonstrate that being total is not necessary for a stable function to be maximal secondly a characterization is given for di domains for which maximal also implies total finally topological properties of maximal elements are investigated di domains for which maximal is the same as total are those having a certain hausdorff property

event structures and domains abstract in the theory of denotational semantics we study event structures which generalize kahn and plotkin s concrete data structures and which model computational processes with each event structure we associate canonically an event domain a particular algebraic complete partial order and conversely we derive a representation result for event domains for a particular class of event structures the canonical event structures we obtain that any two canonical event structures are isomorphic iff they have order isomorphic canonical domains

maximum likelihood parameter estimation for unsupervised stochastic model based image segmentation an unsupervised stochastic model based approach to image segmentation is described and some of its properties investigated in this approach the problem of model parameter estimation is formulated as a problem of parameter estimation from incomplete data and the expectation maximization em algorithm is used to determine a maximum likelihood ml estimate previously the use of the em algorithm in this application has encountered difficulties since an analytical expression for the conditional expectations required in the em procedure is generally unavailable except for the simplest models in this paper two solutions are proposed to solve this problem a monte carlo scheme and a scheme related to besag s 1986 iterated conditional mode icm method both schemes make use of markov random field modeling assumptions examples are provided to illustrate the implementation of the em algorithm for several general classes of image models experimental results on both synthetic and real images are provided

a characterisation of the least fixed point operator by dinaturality simpson a k a characterisation of the least fixed point operator by dinaturality theoretical computer science 118 1993 301 314 the paper addresses the question of when the least fixed point operator in a cartesian closed category of domains is characterised as the unique dinatural transformation from the exponentiation bifunctor to the identity functor we give a sufficient condition on a cartesian closed full subcategory of the category of algebraic cpos for the characterisation to hold the condition is quite mild and the least fixed point operator is so characterised in many of the most commonly used categories of domains by using retractions the characterisation extends to the associated cartesianclosed categories of continuous cpos however dinaturality does not always characterise the leastfixed point operator we show that in cartesian closed full subcategories of the category of continuous lattices the characterisation fails

discrete active models and applications abstract optimization processes based on active models play central roles in many areas of computational vision as well as computational geometry unfortunately current models usually require highly complex and sophisticated mathematical machinery and at the same time they suffer from a number of limitations which impose restrictions on their applicability in this paper a simple class of discrete active models called migration processes mps is presented the processes are based on iterated averaging over neighborhoods defined by constant geodesic distance it is demonstrated that the mp model a system of self organizing active particles has a number of advantages over previous models both parametric active models snakes and implicit contour evolution models due to the generality of the mp model the process can be applied to derive natural solutions to a variety of optimization problems including defining minimal surface patches given their boundary curves finding shortest paths joining sets of points and decomposing objects into primitive parts

convex powerdomains i the study of powerdomains defined as completions via frink ideals is continued it is shown how to represent directed ideals ofp d by certain compact subsets of the original domaind and arbitrary frink ideals by sets of such subsets the operations union and big union are defined and their properties studied finally some results on the relationship of this powerdomain to the classical plotkin powerdomain are presented

recursive domain equations for concrete data structures abstract in the theory of denotational semantics of programming languages we study event structures which combine features of scott s information systems and kahn and plotkin s concrete data structures and model computational processes we show that a simple approximation concept for event structures allows us to obtain straightforward solutions of recursive domain equations for event domains from this we derive a generalization of corresponding theorems of kahn and plotkin respectively berry and curien for concrete data structures and concrete domains

stone duality and representation of stable domain abstract in this paper the author studies the stone duality and representation of l domain w r t stable functions two basic notions are introduced one is d semilattice and the other is semitopological system the author first gives the representation of stable d lattice then establishes the representation theorem of l domain and gives the stone duality of l domains w r t stable functions in the scheme of lattice the author introduces the theory of semitopological systems which is a generalization of vickers topological systems by using it the author gives the stone duality of l domains w r t stable functions and that of scott domains w r t functions preserving the directed sups and meets of nonempty subsets in the scheme of topology

on the foundations of relaxation labeling processes a large class of problems can be formulated in terms of the assignment of labels to objects frequently processes are needed which reduce ambiguity and noise and select the best label among several possible choices relaxation labeling processes are just such a class of algorithms they are based on the parallel use of local constraints between labels this paper develops a theory to characterize the goal of relaxation labeling the theory is founded on a definition of con sistency in labelings extending the notion of constraint satisfaction in certain restricted circumstances an explicit functional exists that can be maximized to guide the search for consistent labelings this functional is used to derive a new relaxation labeling operator when the restrictions are not satisfied the theory relies on variational cal culus it is shown that the problem of finding consistent labelings is equivalent to solving a variational inequality a procedure nearly identical to the relaxation operator derived under restricted circum stances serves in the more general setting further a local convergence result is established for this operator the standard relaxation labeling formulas are shown to approximate our new operator which leads us to conjecture that successful applications of the standard methods are explainable by the theory developed here observations about con vergence and generalizations to higher order compatibility relations are described

digital topology and geometry in medical imaging a survey digital topology and geometry refers to the use of topologic and geometric properties and features for images defined in digital grids such methods have been widely used in many medical imaging applications including image segmentation visualization manipulation interpolation registration surface tracking object representation correction quantitative morphometry etc digital topology and geometry play important roles in medical imaging research by enriching the scope of target outcomes and by adding strong theoretical foundations with enhanced stability fidelity and efficiency this paper presents a comprehensive yet compact survey on results principles and insights of methods related to digital topology and geometry with strong emphasis on understanding their roles in various medical imaging applications specifically this paper reviews methods related to distance analysis and path propagation connectivity surface tracking image segmentation boundary and centerline detection topology preservation and local topological properties skeletonization and object representation correction and quantitative morphometry a common thread among the topics reviewed in this paper is that their theory and algorithms use the principle of digital path connectivity path propagation and neighborhood analysis

a partial solution to an open problem of amadio and curien abstract amadio raised the question of whether the category of stable bifinite domains of amadio droste is the largest cartesian closed full subcategory of the category of algebraic meet cpos with stable functions zhang and jiang showed that for any algebraic meet cpo d if the stable function space d s d with stable order satisfies property m then d is finitary i e each compact element dominates only finitely many elements in this paper we show that for any algebraic meet cpo d and the diamond lattice m the classical non distributive lattice if d s m and d s m s d s m are algebraic then 1 d is finitary 2 if d s m s d s m is finitary then d is stable bifinite so the category of stable bifinite domains is a maximal cartesian closed full subcategory of the category of algebraic meet cpos with stable functions this gives a partial solution to the problem

chain code probabilities and optimal length estimators for digitized three dimensional curves abstract length estimation of three dimensional digitized curves is considered three dimensional 26 directional chain code representation is assumed recent results on three dimensional euclidean distance maps are inapplicable to optimal three dimensional length estimation to support optimal design of three dimensional length estimators chain code probabilities in three dimensional chain encoded digital straight lines are derived optimal three dimensional length estimators are determined and their performance is evaluated analytically and experimentally

vehicle path planning by using adaptive constrained distance transformation abstract the adaptive constrained distance transformation acdt is proposed to solve the vehicle path planning problem the acdt is a generalization of the constrained distance transformation the incremental distance of the constrained distance transformation is modified into the incremental cost by defining the incremental cost according to the incremental distance the vehicle characteristics and the local spatial properties of the terrain the adaptive constrained distance transformation can be applied to solve the vehicle path planning problem that accounts for more than the euclidean distance and hard constraints

computing distance transformations in convex and non convex domains abstract it is shown that the well known two pass sequential local transformation algorithm for computing a distance transformation in rectangular domains may fail in some convex integer domains but that a four pass algorithm is sufficient in all two dimensional convex domains for non convex domains the number of passes necessary is shown to be generally greater two propagation algorithms for computing the distance transformation are described and shown theoretically and experimentally to be computationally more efficient than the sequential local transformation algorithm in non convex domains of complex shape the relationship of the distance transformation in non convex domains to some more general transformations is explored

estimation of the original length of a straight line segment from its digitization in three dimensions abstract estimation of different properties of a continuous predigitized curve from its digitized contour is an important problem with applications in various disciplines of computer science in this context the problem of estimating the original length of a line segment in three dimensions given its quantization in a suitable form is considered four types of characterization schemes for the digitized contour are presented along with a set of estimators the average errors of these estimators are found out experimentally the domains of characterization are formulated for the first three schemes and the theoretical average errors are calculated for the first two the theoretical and the experimental errors are found to tally within computational accuracy

petri nets event structures and domains part i abstract the general aim of this paper is to find a theory of concurrency combining the approaches of petri and scott and others in part i we introduce our formalisms to connect the abstract ideas of events and domains of information we show how casual nets induce certain kinds of domains where the information points are certain sets of events this allows translations between the languages of net theory and domain theory following the idea that events of causal nets are occurrences we generalise causal nets to occurrence nets by adding forwards conflict just as infinite flow charts unfold finite ones so transition nets can be unfolded into occurrence nets next we extend the above connections between nets and domains to these new nets event structures which are intermediate between nets and domains play an important part in all our work finally as an example of how concepts translate from one formalism to the other we show how petri s notion of confusion ties up with kahn and plotkin s concrete domains in part ii we shall continue the job of connecting up notions within net theory and the theory of domains in particular we shall examine the idea of states of computations

a nice labelling for tree like event structures of degree 3 we address the problem of finding nice labellings for event structures of degree 3 we develop a minimum theory by which we prove that the index of an event structure of degree 3 is bounded by a linear function of the height the main theorem of the paper states that event structures of degree 3 whose causality order is a tree have a nice labelling with 3 colors we exemplify how to use this theorem to construct upper bounds for the index of other event structures of degree 3

on connectivity properties of grayscale pictures abstract a grayscale digital picture is called connected if it has only one connected component of constant gray level that is maximal i e not adjacent to any component of higher gray level this note establishes some equivalent conditions for connectedness and also defines a grayscale generalization of the genus in terms of sums of local property values

the category theoretic solution of recursive domain equations recursive specifications of domains plays a crucial role in denotational semantics as developed by scott and strachey and their followers the purpose of the present paper is to set up a categorical framework in which the known techniques for solving these equations find a natural place the idea is to follow the well known analogy between partial orders and categories generalizing from least fixed points of continuous functions over cpos to initial ones of continuous functors over omega categories to apply these general ideas we introduce wand s bf o categories where the morphism sets have a partial order structure and which include almost all the categories occurring in semantics the idea is to find solutions in a derived category of embeddings and we give order theoretic conditions which are easy to verify and which imply the needed categorical ones the main tool is a very general form of the limit colimit coincidence remarked by scott in the concluding section we outline how compatibilit

an event structure semantics for general petri nets abstract in this paper we address the following question what type of event structures are suitable for representing the behaviour of general petri nets as a partial answer to this question we define a new class of event structures called local event structures and identify a subclass called ul event structures we propose that ul event structures are appropriate for capturing the behaviour of general petri nets our answer is a partial one in that in the proposed event structure semantics auto concurrency is filtered out from the behaviour of petri nets it turns out that this limited event structure semantics for petri nets is nevertheless a non trivial and conservative extension of the prime event structure semantics of 1 safe petri nets provided in nielsen et al 1981 we also show that the strong relationship between prime event structures and 1 safe petri nets established in a categorical framework in winskel 1987 can be extended to the present setting provided we restrict our attention to the subclass of petri nets whose behaviours do not exhibit any auto concurrency finally we show that winskel s general and stable event structures can be smoothly related to local event structures and that similarly prime event structures can be related to ul event structures

the interior point revolution in optimization history recent developments and lasting consequences interior methods are a pervasive feature of the optimization landscape today but it was not always so although interior point techniques primarily in the form of barrier methods were widely used during the 1960s for problems with nonlinear constraints their use for the fundamental problem of linear programming was unthinkable because of the total dominance of the simplex method during the 1970s barrier methods were superseded nearly to the point of oblivion by newly emerging and seemingly more efficient alternatives such as augmented lagrangian and sequential quadratic programming methods by the early 1980s barrier methods were almost universally regarded as a closed chapter in the history of optimization this picture changed dramatically in 1984 when narendra karmarkar announced a fast polynomial time interior method for linear programming in 1985 a formal connection was established between his method and classical barrier methods since then interior methods have continued to transform both the theory and practice of constrained optimization we present a condensed unavoidably incomplete look at classical material and recent research about interior methods

a representation of sfp this chapter introduces a representation of the category of sfp domains it uses structures similar to but more general than scott s information systems distilled from gentzen s sequent calculi a basic structure called a sequent structure is produced sequent structures determine a major part of the axioms of information systems a category of special kind of sequent structures called the strongly finite ones is shown to be equivalent to the category of sfp domains constructions like the plotkin power domain and the function space are given as well as a complete partial order of such structures to give solutions to recursively defined systems

stable trace automata vs full trace automata trace automata provide a well studied model for systems with concurrent behavior which is usually given by associated domains of finite or infinite computation systems several authors in the literature have characterized order theoretically these domains which are typically particular scott domains in most of these investigations the question remain open when such a domain can be obtained from some finite automaton in this paper it is shown that finite stable trace automata and finite full trace automata give rise to the same class of coherent di domains the proof of this result involves combinatorial means from graph theory colorings and ramsey s theorem

gem a novel evolutionary optimization method with improved neighborhood search a new optimization technique called grenade explosion method gem is introduced and its underlying ideas including the concept of optimal search direction osd are elaborated the applicability and efficiency of the technique is demonstrated using standard benchmark functions comparison of the results with those of other widely used evolutionary algorithms shows that the proposed algorithm outperforms its rivals both in the success rate and rate of convergence the method is also shown to be capable of finding most or even all optima of functions having multiple global optima moreover it is shown that the performance of gem is invariant against shifting and scaling of the search space and objective function

a logical approach to stable domains building on earlier work by guo qiang zhang on disjunctive information systems and by thomas ehrhard pasquale malacaria and the first author on stable stone duality we develop a framework of disjunctive propositional logic in which theories correspond to algebraic l domains disjunctions in the logic can be indexed by arbitrary sets as in geometric logic but must be provably disjoint this raises several technical issues which have to be addressed before clean notions of axiom system and theory can be defined we show soundness and completeness of the proof system with respect to distributive disjunctive semilattices and prove that every such semilattice arises as the lindenbaum algebra of a disjunctive theory via stable stone duality we show how to use disjunctive propositional logic for a logical description of algebraic l domains

domain theoretic models of polymorphism abstract we give an illustration of a construction useful in producing and describing models of girard and reynolds polymorphic calculus the key unifying ideas are that of a grothendieck fibration and the category of continuous sections associated with it constructions used in indexed category theory the universal types of the calculus are interpreted as the category of continuous sections of the fibration as a major example a new model for the polymorphic calculus is presented in it a type is interpreted as a scott domain in fact understanding universal types of the polymorphic calculus as categories of continuous sections appears to be useful generally for example the technique also applies to the finitary projection model of bruce and longo and a recent model of girard indeed the work here was inspired by girard s and arose through trying to extend the construction of his model to scott domains it is hoped that by pin pointing a key construction this paper will help towards a deeper understanding of models for the polymorphic calculus and the relations between them

re visiting axioms of information systems based on the investigation of the axioms used in the theory of information system the notion of simplified continuous information system is introduced which is considered as a generalization of continuous information systems just like the continuous information system it is also a concrete representation of continuous domains and categorically equivalent to the category of continuous domains and scott continuous functions what is more all types of information systems studied in the literature so far turn out to be special cases of the new type by defining linear information systems and their entailment functions we show that the states of a scott style information system are exactly the fixpoints of its entailment function some axioms about an entailment relation can be characterized by the properties of the corresponding entailment function and in particular the simplified continuous information systems are solely determined by the idempotence of entailment functions

information systems revisited the general continuous case in this paper a new notion of continuous information system is introduced it is shown that the information systems of this kind generate exactly the continuous domains the new information systems are of the same logic oriented style as the information systems first introduced by scott in 1982 they consist of a set of tokens a consistency predicate and an entailment relation satisfying a set of natural axioms it is shown that continuous information systems are closely related to abstract bases indeed both categories are equivalent since it is known that the categories of abstract bases and or continuous domains are equivalent it follows that the category of continuous information systems is also equivalent to that of continuous domains in applications mostly subclasses of continuous domains are considered for example the domains have to be pointed algebraic bounded complete or fs conditions are presented that when fulfilled by a continuous information system force the generated domain to belong to the required subclass in most cases the requirements are not only sufficient but also necessary

computational interpretations of linear logic abstract we study girard s linear logic from the point of view of giving a concrete computational interpretation of the logic based on the curry howard isomorphism in the case of intuitionistic linear logic this leads to a refinement of the lambda calculus giving finer control over order of evaluation and storage allocation while maintaining the logical content of programs as proofs and computation as cut elimination in the classical case it leads to a concurrent process paradigm with an operational semantics in the style of berry and boudol s chemical abstract machine this opens up a promising new approach to the parallel implementation of functional programming languages and offers the prospect of typed concurrent programming in which correctness is guaranteed by the typing

cartesian closed stable categories the aim of this paper is to establish some cartesian closed categories which are between the two cartesian closed categories slp the category of l domains and stable functions and di the full subcategory of slp whose objects are all di domains first we show that the exponentials of every full subcategory of slp are exactly the spaces of stable functions then we prove that the full subcategories sdmbc sdcbc and sdabc of slp which contain di are all cartesian closed where the objects of sdmbc resp sdcbc sdabc are all distributive bc domains which are meet continuous resp continuous algebraic we also obtain many non cartesian closed full subcategories of slp and present some reflective relations between those categories concerned

weak algebraic information systems and a new equivalent category of dom of domains abstract in this paper concepts of generalized algebraic information system in short ga inf and weak algebraic information system in short wa inf are introduced relationships among several algebraicities of information systems are explored main results are 1 a dcpo d is an algebraic domain iff d is represented by an algebraic information system in short a inf and iff d is represented by a ga inf 2 every a inf is a ga inf and a wa inf 3 every c inf s d b induced by a domain with a basis b is a wa inf 4 the category wainf of wa infs and approximable mappings is equivalent to the category dom of domains and scott continuous functions 5 every wa inf s satisfying condition mt is a retract of w s the information structure induced by s in category wainf of wa infs and approximable mappings particularly c inf s d b induced by a domain d with a basis b is a retract of a inf w s d b in category wainf

the largest cartesian closed category of stable domains abstract berry s category of di domains with stable functions is a relatively intricate yet elegant framework for semantics of programming languages despite over 15 years of work in the area the exact reasons for distributivity axiom d and finitariness axiom i have not been fully explicated this paper shows that axiom d and axiom i are important when one works within the realm of scott domains in particular it has been shown that i if d s d has a countable basis then d must be finitary for any scott domain d ii if d s d is bounded complete then d must be distributive for any finitary scott domain d therefore the category of di domains is the largest cartesian closed category within omega algebraic bounded complete domains with the exponential being the stable function space

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

two categories of effective continuous cpos this paper presents two categories of effective continuous complete partial orders cpos we define a new criterion on the basis of a cpo so as to make the resulting category of consistently complete continuous cpos cartesian closed we also generalise to continuous cpos the definition of a complete set which was used as a definition of effective bifinite domains in hamrin and stoltenberg hansen cartesian closed categories of effective domains in h schwichtenberg r steinbruggen eds proof and system reliability kluwer academic publishers dordrecht 2002 pp 1 20 and investigate the closure results that can be obtained

constrained connectivity for hierarchical image partitioning and simplification this paper introduces an image partitioning and simplification method based on the constrained connectivity paradigm according to this paradigm two pixels are said to be connected if they satisfy a series of constraints defined in terms of simple measures such as the maximum gray level differences over well defined pixel paths and regions the resulting connectivity relation generates a unique partition of the image definition domain the simplification of the image is then achieved by setting each segment of the partition to the mean value of the pixels falling within this segment fine to coarse partition hierarchies and therefore images of increasing degree of simplification are produced by varying the threshold value associated with each connectivity constraint the paper also includes a generalization to multichannel images application examples a review of related image segmentation techniques and pseudocode for an implementation based on queue and stack data structures

an efficient uniform cost algorithm applied to distance transforms the uniform cost algorithm is a special case of the a algorithm for finding the shortest paths in graphs in the uniform cost algorithm nodes are expanded in order of increasing cost an efficient version of this algorithm is developed for integer cost values nodes are sorted by storing them at predefined places bucket sort keeping the overhead low the algorithm is applied to general distance transformation a constrained distance transform is an operation which calculates at each pixel of an image the distance to the nearest pixel of a reference set distance being defined as minimum path length the uniform cost algorithm in the constrained case proves to be the best solution for distance transformation it is fast the processing time is independent of the complexity of the image and memory requirements are moderate

the discrete geodesic problem we present an algorithm for determining the shortest path between a source and a destination on an arbitrary possibly nonconvex polyhedral surface the path is constrained to lie on the surface and distances are measured according to the euclidean metric our algorithm runs in time o n log n and requires o n2 space where n is the number ofedges ofthe surface afterwe run our algorithm the distance from the source to any other destination may be determined using standard techniques in time o log n by locating the destination in the subdivision created by the algorithm the actual shortest path from the source to a destination can be reported in time o k log n where k is the number of faces crossed by the path the algorithm generalizes to the case of multiple source points to build the voronoi diagram on the surface where n is now the maximum of the number of vertices and the number of sources

a representation of l domains by information systems in this paper we propose the notion of l information systems which provides a concrete representation of l domains in particular we prove that the category of l information systems with approximable mappings as morphisms is equivalent to that of l domains with scott continuous functions as morphisms

the largest cartesian closed category of domains the main result of this paper provides a necessary and sufficient condition that the function space d d of a domain algebraic cpo d be again a domain the condition confirming a conjecture of plotkin is that d be strongly algebraic sfp the importance of this is that it enables us to conclude that sfp is the largest category of domains that is closed under the constructions of interest in semantics in the final section we briefly consider how our results may need to be extended if our admittedly rather restrictive notion of category of domains is relaxed in certain ways

algebraic domains of natural transformations abstract motivated by the semantics of polymorphic programming languages and typed calculi by formal methods in functor category semantics and by well known categorical and domain theoretical constructs we study domains of natural transformations f g of functors f g c with a small category as source and a cartesian closed category of scott domains c as target we put constraints on the image arrows of the functors to obtain that f g is an object in c inf faithful domains f g allow that infima in f g can be computed in each component fa ga separately if f g scott are two functors such that for all f in mor the maps f f preserve finite elements and g f preserve all nonempty infima then f g is inf faithful and all inf faithful domains are scott domains familiar notions like inverse limits small products and strict function spaces are special instances of functors that meet the conditions above we extend these results to retracts of scott domains

universal profinite domains abstract we introduce a bicartesian closed category of what we call profinite domains study of these domains is carried out through the use of an equivalent category of pre orders in a manner similar to the information systems approach advocated by dana scott and others a class of universal profinite domains is defined and used to derive sufficient conditions for the profinite solution of domain equations involving continuous operators as a special instance of this construction a universal domain for the category sfp is demonstrated necessary conditions for the existence of solutions for domain equations over the profinites are also given and used to derive results about solutions of some equations a new universal bounded complete domain is also demonstrated using an operator which has bounded complete domains as its fixed points