Morphology on categorical distributions

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Morphology on categorical distributions. / Ørting, Silas Nyboe; Stephensen, Hans Jacob Teglbjærg; Sporring, Jon.

arXiv.org, 2020.

Research output: Book/Report › Report › Research

Harvard

Ørting, SN, Stephensen, HJT & Sporring, J 2020, Morphology on categorical distributions. arXiv.org. <http://arxiv.org/pdf/2012.07315v1>

APA

Ørting, S. N., Stephensen, H. J. T., & Sporring, J. (2020). Morphology on categorical distributions. arXiv.org. http://arxiv.org/pdf/2012.07315v1

Vancouver

Ørting SN, Stephensen HJT, Sporring J. Morphology on categorical distributions. arXiv.org, 2020.

Author

Ørting, Silas Nyboe ; Stephensen, Hans Jacob Teglbjærg ; Sporring, Jon. / Morphology on categorical distributions. arXiv.org, 2020.

Bibtex

@book{45c9a8cb7aef43d58b3ddf96bc9a16e9,
title = "Morphology on categorical distributions",
abstract = " The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range of useful operations. In the general case, applying morphological operations on uncertain multi-class segmentations is not straightforward as an image of categorical distributions is not a complete lattice. Although morphology on color images has received wide attention, this is not so for color-coded or categorical images and even less so for images of categorical distributions. In this work, we establish a set of requirements for morphology on categorical distributions by combining classic morphology with a probabilistic view. We then define operators respecting these requirements, introduce protected operations on categorical distributions and illustrate the utility of these operators on two example tasks: modeling annotator bias in brain tumor segmentations and segmenting vesicle instances from the predictions of a multi-class U-Net. ",
keywords = "cs.CV, Morphology, Categorical distribution",
author = "{\O}rting, {Silas Nyboe} and Stephensen, {Hans Jacob Teglbj{\ae}rg} and Jon Sporring",
year = "2020",
month = dec,
day = "14",
language = "English",
publisher = "arXiv.org",

}

RIS

TY - RPRT

T1 - Morphology on categorical distributions

AU - Ørting, Silas Nyboe

AU - Stephensen, Hans Jacob Teglbjærg

AU - Sporring, Jon

PY - 2020/12/14

Y1 - 2020/12/14

N2 - The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range of useful operations. In the general case, applying morphological operations on uncertain multi-class segmentations is not straightforward as an image of categorical distributions is not a complete lattice. Although morphology on color images has received wide attention, this is not so for color-coded or categorical images and even less so for images of categorical distributions. In this work, we establish a set of requirements for morphology on categorical distributions by combining classic morphology with a probabilistic view. We then define operators respecting these requirements, introduce protected operations on categorical distributions and illustrate the utility of these operators on two example tasks: modeling annotator bias in brain tumor segmentations and segmenting vesicle instances from the predictions of a multi-class U-Net.

AB - The categorical distribution is a natural representation of uncertainty in multi-class segmentations. In the two-class case the categorical distribution reduces to the Bernoulli distribution, for which grayscale morphology provides a range of useful operations. In the general case, applying morphological operations on uncertain multi-class segmentations is not straightforward as an image of categorical distributions is not a complete lattice. Although morphology on color images has received wide attention, this is not so for color-coded or categorical images and even less so for images of categorical distributions. In this work, we establish a set of requirements for morphology on categorical distributions by combining classic morphology with a probabilistic view. We then define operators respecting these requirements, introduce protected operations on categorical distributions and illustrate the utility of these operators on two example tasks: modeling annotator bias in brain tumor segmentations and segmenting vesicle instances from the predictions of a multi-class U-Net.

KW - cs.CV

KW - Morphology

KW - Categorical distribution

M3 - Report

BT - Morphology on categorical distributions

PB - arXiv.org

ER -

ID: 253704279