A Link Between the Multiplicative and Additive Functional Asplund’s Metrics

Noyel, Guillaume

doi:10.1007/978-3-030-20867-7_4

Cited by 2 publications

(2 citation statements)

References 23 publications

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“…is the restriction of f to the neighbourhood D b (x) centred on x ∈ D. The map of Asplund distances Asp △ + b which was related to MM in [46], [47], [48], is equal to…”

Section: Link With Lmmmentioning

confidence: 99%

Logarithmic Mathematical Morphology: A New Framework Adaptive to Illumination Changes

Noyel

2019

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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A new set of mathematical morphology (MM) operators adaptive to illumination changes caused by variation of exposure time or light intensity is defined thanks to the Logarithmic Image Processing (LIP) model. This model based on the physics of acquisition is consistent with human vision. The fundamental operators, the logarithmic-dilation and the logarithmic-erosion, are defined with the LIP-addition of a structuring function. The combination of these two adjunct operators gives morphological filters, namely the logarithmic-opening and closing, useful for pattern recognition. The mathematical relation existing between "classical" dilation and erosion and their logarithmic-versions is established facilitating their implementation. Results on simulated and real images show that logarithmic-MM is more efficient on low-contrasted information than "classical" MM.

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“…is the restriction of f to the neighbourhood D b (x) centred on x ∈ D. The map of Asplund distances Asp △ + b which was related to MM in [46], [47], [48], is equal to…”

Section: Link With Lmmmentioning

confidence: 99%

Logarithmic Mathematical Morphology: A New Framework Adaptive to Illumination Changes

Noyel

2019

Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications

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“…(1) Firstly, we extend the preliminary works defining the functional metrics and their corresponding maps of distances between a template and an image (Jourlin et al, 2012;Jourlin, 2016;Noyel and Jourlin, 2017a;b;Noyel, 2019a). Beyond the prior work, we add theoretical work at two stages.…”

Section: Introductionmentioning

confidence: 99%

Functional Asplund metrics for pattern matching, robust to variable lighting conditions

Noyel

Jourlin

2020

Image Anal Stereol

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In this paper, we propose a complete framework to process images captured under uncontrolled lighting and especially under low lighting. By taking advantage of the Logarithmic Image Processing (LIP) context, we study two novel functional metrics: i) the LIP-multiplicative Asplund metric which is robust to object absorption variations and ii) the LIP-additive Asplund metric which is robust to variations of source intensity or camera exposure-time. We introduce robust to noise versions of these metrics. We demonstrate that the maps of their corresponding distances between an image and a reference template are linked to Mathematical Morphology. This facilitates their implementation. We assess them in various situations with different lightings and movement. Results show that those maps of distances are robust to lighting variations. Importantly, they are efficient to detect patterns in low-contrast images with a template acquired under a different lighting.

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A Link Between the Multiplicative and Additive Functional Asplund’s Metrics

Cited by 2 publications

References 23 publications

Logarithmic Mathematical Morphology: A New Framework Adaptive to Illumination Changes

Logarithmic Mathematical Morphology: A New Framework Adaptive to Illumination Changes

Functional Asplund metrics for pattern matching, robust to variable lighting conditions

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