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Comparing Images Using the Hausdorff Distance
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1993
"... The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide ef ..."
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Cited by 658 (10 self)
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The Hausdorff distance measures the extent to which each point of a `model' set lies near some point of an `image' set and vice versa. Thus this distance can be used to determine the degree of resemblance between two objects that are superimposed on one another. In this paper we provide efficient algorithms for computing the Hausdorff distance between all possible relative positions of a binary image and a model. We focus primarily on the case in which the model is only allowed to translate with respect to the image. Then we consider how to extend the techniques to rigid motion (translation and rotation). The Hausdorff distance computation differs from many other shape comparison methods in that no correspondence between the model and the image is derived. The method is quite tolerant of small position errors as occur with edge detectors and other feature extraction methods. Moreover, we show how the method extends naturally to the problem of comparing a portion of a model against an i...
Stable compactification I
 Journal of the London Mathematical Society
, 1992
"... This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7^) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation. ..."
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Cited by 18 (2 self)
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This paper represents a continuation of our programme [16, 13] of extending various concepts of general topology from the setting of Hausdorff (or, at most, 7^) spaces, in which they are usually embedded, to the larger classes of spaces we need to consider in the theory of computation.
Aspects of locally covariant quantum field theory
, 2008
"... This thesis considers various aspects of locally covariant quantum field theory (see Brunetti et al., Commun. Math. Phys. 237 (2003), 31 68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. Chapter 1 argues that the use of morphisms in this framework can b ..."
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Cited by 11 (3 self)
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This thesis considers various aspects of locally covariant quantum field theory (see Brunetti et al., Commun. Math. Phys. 237 (2003), 31 68), a mathematical framework to describe axiomatic quantum field theories in curved spacetimes. Chapter 1 argues that the use of morphisms in this framework can be seen as a model for modal logic. To our knowledge this is the first interpretative description of this aspect of the framework. Chapter 2 gives an exposition of locally covariant quantum field theory which differs from the original in minor details, notably in the new notion of nowhereclassicality and the sharpened timeslice axiom, which puts a restriction on the state space as well as the algebras. Chapter 3 deals with the wellstudied example of the free real scalar field and includes an elegant proof of the new general result that the commutation relations together with the Hadamard condition on the twopoint distribution of a state completely x the singularity structure of all npoint distributions. Chapter 4 describes the free Dirac field as a locally covariant quantum field, using a new representation independent
Uniform Approximation of Topological Spaces
 TOPOLOGY AND ITS APPLICATIONS 83
, 1996
"... We sharpen the notion of a quasiuniform space to spaces which carry with them functional means of approximating points, opens and compacts. Assuming nothing but sobriety, the requirement of uniform approximation induces that such spaces are compact ordered (in the sense of Nachbin). We study un ..."
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Cited by 7 (0 self)
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We sharpen the notion of a quasiuniform space to spaces which carry with them functional means of approximating points, opens and compacts. Assuming nothing but sobriety, the requirement of uniform approximation induces that such spaces are compact ordered (in the sense of Nachbin). We study uniformly approximated spaces with the means of topology, uniform topology, order theory and locale theory. In each case it turns out that one can give a succinct and meaningful characterization. This leads us to believe that uniform approximation is indeed a concept of central importance.
Convenient Topology
 Math. Japonica
, 1997
"... . A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deficiencies of topological and uniform spaces are remidied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling probl ..."
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Cited by 7 (0 self)
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. A new viewpoint of Topology, summarized under the name Convenient Topology, is considered in such a way that the structural deficiencies of topological and uniform spaces are remidied. This does not mean that these spaces are superfluous. It means exactly that a better framework for handling problems of a topological nature is used. In this context semiuniform convergence spaces play an essential role. They include not only convergence structures such as topological structures and limit space structures, but also uniform convergence structures such as uniform structures and uniform limit space structures, and they are suitable for studying continuity, Cauchy continuity and uniform continuity as well as convergence structures in function spaces, namely simple convergence, continuous convergence and uniform convergence. Several results are presented which cannot be obtained by using topological or uniform spaces respectively. Mathematics Subject Classifications (1991). 54A05, 54A20, 5...
SEMANTIC SPACES IN PRIESTLEY FORM
, 2006
"... To my family. ii Table of Contents Table of Contents iii Abstract vi ..."
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To my family. ii Table of Contents Table of Contents iii Abstract vi
Topological Aspects of Poset Spaces
"... 1 Introduction Recent work in mathematical logic [8, 9, 10] has led to an interest in certain topological spaces formed from filters on partially ordered sets. This paper describes the general topology of these poset spaces. ..."
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Cited by 2 (0 self)
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1 Introduction Recent work in mathematical logic [8, 9, 10] has led to an interest in certain topological spaces formed from filters on partially ordered sets. This paper describes the general topology of these poset spaces.
The essence of ideal completion in quantitative form (Extended Abstract)
, 1995
"... Robert C. Flagg and Philipp Sunderhauf y University of Southern Maine fflagg,psunderg@usm.maine.edu December 12, 1995 Abstract If a posets lacks joins of directed subsets, one can pass to its ideal completion. But doing this means also changing the setting: The universal property of ideal comple ..."
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Robert C. Flagg and Philipp Sunderhauf y University of Southern Maine fflagg,psunderg@usm.maine.edu December 12, 1995 Abstract If a posets lacks joins of directed subsets, one can pass to its ideal completion. But doing this means also changing the setting: The universal property of ideal completion of posets suggests that it should be regarded as a functor from the category of posets with monotone maps to the category of dcpos with Scottcontinuous functions as morphisms. The same applies for the quantitative version of ideal completion suggested in the literature. As in the case of posets, it seems advantageous to consider a different topology with the completed spaces. We introduce Smyth completion as tool to automatically end up with the right topology after completing. 1 Introduction This paper is part of the ongoing foundational work on quantitative domain theory [Smy88, BBR95, Rut95, FW95, Wag94], which refines ordinary do Supported by the Deutsche Forschungsgemeinschaf...
Annals of Properties of DµCompact Spaces in Generalized Topological Spaces
, 2014
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