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Measuring the Irregularity of Vector-Valued Morphological Operators using Wasserstein Metric

Abstract : Mathematical morphology is a useful theory of nonlinear operators widely used for image processing and analysis. Despite the successful application of morphological operators for binary and gray-scale images, extending them to vector-valued images is not straightforward because there are no unambiguous orderings for vectors. Among the many approaches to multivalued mathematical morphology, those based on total orders are particularly promising. Morphological operators based on total orders do not produce the so-called false-colors. On the downside, they often introduce irregularities in the output image. Although the irregularity issue has a rigorous mathematical formulation, we are not aware of an efficient method to quantify it. In this paper, we propose to quantify the irregularity of a vector-valued morphological operator using the Wasserstein metric. The Wasserstein metric yields the minimal transport cost for transforming the input into the output image. We illustrate by examples how to quantify the irregularity of vector-valued morphological operators using the Wasserstein metric.
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https://hal.archives-ouvertes.fr/hal-03221651
Contributor : Santiago Velasco-Forero Connect in order to contact the contributor
Submitted on : Sunday, May 9, 2021 - 1:33:37 PM
Last modification on : Wednesday, November 17, 2021 - 12:27:19 PM
Long-term archiving on: : Tuesday, August 10, 2021 - 6:07:49 PM

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  • HAL Id : hal-03221651, version 1

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Marcos Valle, Samuel Francisco, Marco Aurélio Granero, Santiago Velasco-Forero. Measuring the Irregularity of Vector-Valued Morphological Operators using Wasserstein Metric. IAPR International Conference on Discrete Geometry and Mathematical Morphology, May 2021, Uppsala (virtual event), Sweden. ⟨hal-03221651⟩

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