An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation

• URL: http://arxiv.org/abs/2312.13792v1
• Date: Thu, 21 Dec 2023 12:32:34 GMT
• Title: An Approach to Colour Morphological Supremum Formation using the LogSumExp Approximation
• Authors: Marvin Kahra, Michael Breu{\ss}, Andreas Kleefeld, Martin Welk
• Abstract summary: We present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We apply this to the embedding of an RGB image in a field of symmetric $2times2$ matrices.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Mathematical morphology is a part of image processing that has proven to be fruitful for numerous applications. Two main operations in mathematical morphology are dilation and erosion. These are based on the construction of a supremum or infimum with respect to an order over the tonal range in a certain section of the image. The tonal ordering can easily be realised in grey-scale morphology, and some morphological methods have been proposed for colour morphology. However, all of these have certain limitations. In this paper we present a novel approach to colour morphology extending upon previous work in the field based on the Loewner order. We propose to consider an approximation of the supremum by means of a log-sum exponentiation introduced by Maslov. We apply this to the embedding of an RGB image in a field of symmetric $2\times2$ matrices. In this way we obtain nearly isotropic matrices representing colours and the structural advantage of transitivity. In numerical experiments we highlight some remarkable properties of the proposed approach.

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