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Dynamic ScaleSpace Paradigm
, 1997
"... Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simplication o ..."
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Cited by 17 (13 self)
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of the set of construction rules is proposed by applying a dynamic scalespace paradigm. Dynamic here refers to a redistribution and recombination of this set and does not correspond to whether the images are static or spatiotemporal. The class of dynamic scalespace theories is constrained by exchange
Dynamic ScaleSpace Paradigms versus Mathematical Morphology?
"... The geometric and statistical physical concepts of dynamic scalespace paradigms are presented and juxtaposed to those of mathematical morphology. It turns out that the dynamic paradigms can be applied to, substantiate and even generalise the morphological techniques and paradigms. In particular the ..."
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The geometric and statistical physical concepts of dynamic scalespace paradigms are presented and juxtaposed to those of mathematical morphology. It turns out that the dynamic paradigms can be applied to, substantiate and even generalise the morphological techniques and paradigms. In particular
Dynamic ScaleSpace Paradigm Versus Mathematical Morphology?
 AeroSense'99, SPIE's 13th Annual International Symposium on Aerospace/Defense Sensing, Simulation, and Control, volume 3716 of Visual Information processing VIII
, 1997
"... Image formation is described by means of modern geometry in terms of topological and geometric curvatures. These curvatures and derived equivalences are a quantisation of the set of rules for constructing the image in particular along discontinuity, singularity and bifurcation sets. A simplification ..."
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Cited by 2 (2 self)
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simplification of the set of construction rules is proposed by applying a dynamic scalespace theory. Dynamic here refers to a redistribution and recombination of this set and does not correspond to whether the images are static or spatiotemporal. The class of dynamic scalespace theories is constrained
The Gaussian ScaleSpace Paradigm and the Multiscale Local Jet
, 1994
"... Abstract. A representation of local image structure is proposed which takes into account both the image’s spatial structure at a given location, as well as its “deep structure”, that is, its local behaviour as a function of scale or resolution (scalespace). This is of interest for several lowlevel ..."
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Abstract. A representation of local image structure is proposed which takes into account both the image’s spatial structure at a given location, as well as its “deep structure”, that is, its local behaviour as a function of scale or resolution (scalespace). This is of interest for several low
The Topological Structure of ScaleSpace Images
, 1998
"... We investigate the "deep structure" of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical pointspoints with vanishing gradientand toppointscritical points with degenerate Hessianand monitor their displacements, respectively generic morsifications ..."
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Cited by 52 (25 self)
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morsifications in scalespace. Relevant parts of catastrophe theory in the context of the scalespace paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined, global coordinate system. 1
Scalespace theories for scalar and vector images
 In ScaleSpace ’01
, 2001
"... Abstract. We dene mutually consistent scalespace theories for scalar and vector images. Consistency pertains to the connection between the already established scalar theory and that for a suitably dened scalar eld induced by the proposed vector scalespace. We show that one is compelled to reject t ..."
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Cited by 2 (0 self)
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the Gaussian scalespace paradigm in certain cases when scalar and vector elds are mutually dependent. Subsequently we investigate the behaviour of critical points of a vectorvalued scalespace imagei.e. points at which the vector eld vanishes as well as their singularities and unfoldings in linear scalespace
c ○ 2000 Kluwer Academic Publishers. Manufactured in The Netherlands. The Topological Structure of ScaleSpace Images
"... Abstract. We investigate the “deep structure ” of a scalespace image. The emphasis is on topology, i.e. we concentrate on critical points—points with vanishing gradient—and toppoints—critical points with degenerate Hessian—and monitor their displacements, respectively generic morsifications in sca ..."
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in scalespace. Relevant parts of catastrophe theory in the context of the scalespace paradigm are briefly reviewed, and subsequently rewritten into coordinate independent form. This enables one to implement topological descriptors using a conveniently defined coordinate system.
Charting Past, Present and Future Research in Ubiquitous Computing
 ACM Transactions on ComputerHuman Interaction
, 2000
"... . The proliferation ofcomputing into the physical world promises more than the ubiquitous availability of computing infrastructure; it suggests new paradigms of interaction inspired by constant access to information and computational capabilities. For the past decade, applicationdriven research in ..."
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Cited by 438 (6 self)
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computing implicitly requires addressing some notion of scale; whether in the number and type of devices, the physical space of distributed computing or the number of people using a system. We posit a new area of applications research, everyday computing, focussed on scaling interaction with respect to time
A metric for distributions with applications to image databases
, 1998
"... We introduce a new distance between two distributions that we call the Earth Mover’s Distance (EMD), which reflects the minimal amount of work that must be performed to transform one distributioninto the other by moving “distribution mass ” around. This is a special case of the transportation proble ..."
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Cited by 438 (6 self)
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databases, especially color and texture. We use the EMD to exhibit the structure of colordistribution and texture spaces by means of MultiDimensional Scaling displays. We also propose a novel approach to the problem of navigating through a collection of color images, which leads to a new paradigm
Regularization, ScaleSpace, and Edge Detection Filters
 Journal of Mathematical Imaging and Vision
"... . Computational vision often needs to deal with derivatives of digital images. Such derivatives are not intrinsic properties of digital data; a paradigm is required to make them welldefined. Normally, a linear filtering is applied. This can be formulated in terms of scalespace, functional mini ..."
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Cited by 39 (8 self)
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. Computational vision often needs to deal with derivatives of digital images. Such derivatives are not intrinsic properties of digital data; a paradigm is required to make them welldefined. Normally, a linear filtering is applied. This can be formulated in terms of scalespace, functional
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