Image Structure

Florack, Luc

doi:10.1007/978-94-015-8845-4

Cited by 167 publications

(144 citation statements)

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“…Gaussian scalespace goes back to Iijima [26,61]. It became popular in the western world by the work of Witkin [63], Koenderink [34], Lindeberg [36], Florack [21], and many others; see e.g. [55] and the references therein.…”

Section: Examples Of Lsi Scale-spacesmentioning

confidence: 99%

Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

Schmidt

Weickert

2016

J Math Imaging Vis

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It is well-known that there are striking analogies between linear shift-invariant systems and morphological systems for image analysis. So far, however, the relations between both system theories are mainly understood on a pure convolution / erosion level. A formal connection on the level of differential or pseudodifferential equations and their induced scale-spaces is still missing. The goal of our paper is to close this gap. We present a simple and fairly general dictionary that allows to translate any linear shift-invariant evolution equation into its morphological counterpart and vice versa. It is based on a scale-space representation by means of the symbol of its (pseudo)differential operator. Introducing a novel transformation, the Cramér-Fourier transform, puts us in a position to relate the symbol to the structuring function of a morphological scale-space of Hamilton-Jacobi type. As an application of our general theory, we derive the morphological counterparts of many linear shift-invariant scale-spaces, such as the Poisson scale-space, α-scale-spaces, summed α-scale-spaces, relativistic scale-spaces, and their anisotropic variants. Our findings are illustrated by experiments.

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Section: Examples Of Lsi Scale-spacesmentioning

confidence: 99%

Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

Schmidt

Weickert

2016

J Math Imaging Vis

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“…Based on a classification of continuous and discrete scalespace kernels in (Lindeberg 1994), (Lindeberg & Fagerström 1996) presented another set of time-causal scale-space kernels based on cascaded recursive filters for discrete time and first-order integrators in the case of continuous time, with close relations to an earlier approach for estimating optical flow (Fleet & Langley 1995). Follow-up works based on Koenderinks logarithmic mapping of the time axis have then been presented by (Florack 1997 and (Lindeberg 2001).…”

Section: Smoothed -Warpingmentioning

confidence: 99%

“…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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“…As Florack argues in [5], we should not impose a topology or geometry directly on the space of photographs. Rather than impose properties on physical entities, we should instead impose them on the space of measurements and on measurement results.…”

Section: Greyscale Photograph Geometrymentioning

confidence: 99%

Greyscale Photograph Geometry Informed by Dodging and Burning

Phillips

Siddiqi

2006

Computer Vision, Graphics and Image Processing

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Abstract. Photographs are often used as input to image processing and computer vision tasks. Prints from the same negative may vary in intensity values due, in part, to the liberal use of dodging and burning in photography. Measurements which are invariant to these transformations can be used to extract information from photographs which is not sensitive to certain alterations in the development process. These measurements are explored through the construction of a differential geometry which is itself invariant to linear dodging and burning.

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Image Structure

Cited by 167 publications

References 0 publications

Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

Morphological Counterparts of Linear Shift-Invariant Scale-Spaces

Linear spatio-temporal scale-space

Greyscale Photograph Geometry Informed by Dodging and Burning

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