An extended class of scale-invariant and recursive scale space filters

Pauwels, Eric J.; Gool, Luc J. Van; Fiddelaers, Peter; Moons, Theo

doi:10.1109/34.391411

Cited by 80 publications

(84 citation statements)

References 10 publications

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“…This insight is a major motivation for the development of multi-scale representations such as pyramids (Burt 1981, Crowley 1981 and scale-space representation (Iijima 1962, Witkin 1983, Koenderink 1984, Babaud et al 1986, Yuille & Poggio 1986, Koenderink & van Doorn 1992, Lindeberg 1994, Pauwels et al 1995, Florack 1997); see also (Alvarez et al 1993, ter Haar Romeny 1994, Sporring et al 1996, ter Haar Romeny et al 1997, Weickert 1998, Nielsen et al 1999, Kerckhove 2001.…”

Section: Introductionmentioning

confidence: 99%

Linear spatio-temporal scale-space

Lindeberg

1997

Scale-Space Theory in Computer Vision

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This article shows how a linear scale-space formulation previously expressed for spatial domains extends to spatio-temporal data. Starting from the main assumptions that: (i) the scale-space should be generated by convolution with a semi-group of filter kernels and that (ii) local extrema must not be enhanced when the scale parameter increases, a complete taxonomy is given of the linear scale-space concepts that satisfy these conditions on spatial, temporal and spatio-temporal domains, including the cases with continuous as well as discrete data.Key aspects captured by this theory include that: (i) time-causal scale-space kernels must not extend into the future, (ii) filter shapes can be tuned from specific context information, permitting mechanisms such local shifting, shape adaptation and velocity adaptation, all expressed in terms of local diffusion operations.Receptive field profiles generated by the proposed theory show high qualitative similarities to receptive field profiles recorded from biological vision.£ Earlier versions of this manuscript have been presented at

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Section: Introductionmentioning

confidence: 99%

Linear spatio-temporal scale-space

Lindeberg

1997

Scale-Space Theory in Computer Vision

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“…P a u w e l s et al [7], and later D u i t s et al [1] have investigated the use of the fractional powers of Laplacian operator in connection with the scale invariant smoothing and scale space theory. The approach leads to formulation and solving of a fractional heat problem:…”

Section: Fractional Scale Spacesmentioning

confidence: 99%

Selected Applications of Scale Spaces in Microscopic Image Analysis

Prodanov

Konopczyński

Trojnar

2015

Cybernetics and Information Technologies

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Image segmentation methods can be classified broadly into two classes:intensity-based and geometry-based. Edge detection is the base of many geometrybased segmentation approaches. Scale space theory represents a systematic treatment of the issues of spatially uncorrelated noise with its main application being the detection of edges, using multiple resolution scales, which can be used for subsequent segmentation, classification or encoding. The present paper will give an overview of some recent applications of scale spaces into problems of microscopic image analysis. Particular overviews will be given to Gaussian and alpha-scale spaces. Some applications in the analysis of biomedical images will be presented. The implementation of filters will be demonstrated.

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“…The maximally asymmetric, extremal stable density functions are one sided for 0 < α < 1 and θ = ±α, these where the result of an axiomatization of scale spaces with temporal causality in [4]. In [15,2] these result are extended to the Euclidean similarity group, which on R 2 consists of translation in the plane, rotation and scaling.…”

Section: The Affine Linementioning

confidence: 99%

“…diffusion on the half line with the signal as input at the end. Symmetric stable densities, θ = 0 was the result of the scale space axiomatization in [15,2]. The maximally asymmetric, extremal stable density functions are one sided for 0 < α < 1 and θ = ±α, these where the result of an axiomatization of scale spaces with temporal causality in [4].…”

Section: The Affine Linementioning

confidence: 99%

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Spatio-temporal Scale-Spaces

Fagerström

Lecture Notes in Computer Science

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Abstract. A family of spatio-temporal scale-spaces suitable for a moving observer is developed. The scale-spaces are required to be time causal for being usable for real time measurements, and to be "velocity adapted", i.e. to have Galilean covariance to avoid favoring any particular motion. Furthermore standard scale-space axioms: linearity, positivity, continuity, translation invariance, scaling covariance in space and time, rotational invariance in space and recursivity are used. An infinitesimal criterion for scale-spaces is developed, which simplifies calculations and makes it possible to define scale spaces on bounded regions. We show that there are no temporally causal Galilean scale-spaces that are semigroups acting on space and time, but that there are such scale-spaces that are semigroups acting on space and memory (where the memory is the scale-space). The temporally causal scale-space is a time-recursive process using current input and the scale-space as state, i.e. there is no need for storing earlier input. The diffusion equation acting on the memory with the input signal as boundary condition, is a member of this family of scale spaces and is special in the sense that its generator is local.

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An extended class of scale-invariant and recursive scale space filters

Cited by 80 publications

References 10 publications

Linear spatio-temporal scale-space

Linear spatio-temporal scale-space

Selected Applications of Scale Spaces in Microscopic Image Analysis

Spatio-temporal Scale-Spaces

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