Atlas generative models and geodesic interpolation

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Standard

Atlas generative models and geodesic interpolation. / Stolberg-Larsen, Jakob; Sommer, Stefan.

I: Image and Vision Computing, Bind 122, 104433, 2022.

Publikation: Bidrag til tidsskriftTidsskriftartikelForskningfagfællebedømt

Harvard

Stolberg-Larsen, J & Sommer, S 2022, 'Atlas generative models and geodesic interpolation', Image and Vision Computing, bind 122, 104433. https://doi.org/10.1016/j.imavis.2022.104433

APA

Stolberg-Larsen, J., & Sommer, S. (2022). Atlas generative models and geodesic interpolation. Image and Vision Computing, 122, [104433]. https://doi.org/10.1016/j.imavis.2022.104433

Vancouver

Stolberg-Larsen J, Sommer S. Atlas generative models and geodesic interpolation. Image and Vision Computing. 2022;122. 104433. https://doi.org/10.1016/j.imavis.2022.104433

Author

Stolberg-Larsen, Jakob ; Sommer, Stefan. / Atlas generative models and geodesic interpolation. I: Image and Vision Computing. 2022 ; Bind 122.

Bibtex

@article{7b39be250c034c00ac914a3b49afab6a,
title = "Atlas generative models and geodesic interpolation",
abstract = "Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit into this class. Due to the atlas interpretation, ideas from non-linear latent space analysis and statistics, e.g. geodesic interpolation, which has previously only been investigated for models with simply connected latent spaces, may be extended to the entire class of AGMs in a natural way. We exemplify this by generalizing an algorithm for graph based geodesic interpolation to the setting of AGMs, and verify its performance experimentally.",
author = "Jakob Stolberg-Larsen and Stefan Sommer",
year = "2022",
doi = "10.1016/j.imavis.2022.104433",
language = "English",
volume = "122",
journal = "Image and Vision Computing",
issn = "0262-8856",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Atlas generative models and geodesic interpolation

AU - Stolberg-Larsen, Jakob

AU - Sommer, Stefan

PY - 2022

Y1 - 2022

N2 - Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit into this class. Due to the atlas interpretation, ideas from non-linear latent space analysis and statistics, e.g. geodesic interpolation, which has previously only been investigated for models with simply connected latent spaces, may be extended to the entire class of AGMs in a natural way. We exemplify this by generalizing an algorithm for graph based geodesic interpolation to the setting of AGMs, and verify its performance experimentally.

AB - Generative neural networks have a well recognized ability to estimate underlying manifold structure of high dimensional data. However, if a single latent space is used, it is not possible to faithfully represent a manifold with topology different from Euclidean space. In this work we define the general class of Atlas Generative Models (AGMs), models with hybrid discrete-continuous latent space that estimate an atlas on the underlying data manifold together with a partition of unity on the data space. We identify existing examples of models from various popular generative paradigms that fit into this class. Due to the atlas interpretation, ideas from non-linear latent space analysis and statistics, e.g. geodesic interpolation, which has previously only been investigated for models with simply connected latent spaces, may be extended to the entire class of AGMs in a natural way. We exemplify this by generalizing an algorithm for graph based geodesic interpolation to the setting of AGMs, and verify its performance experimentally.

U2 - 10.1016/j.imavis.2022.104433

DO - 10.1016/j.imavis.2022.104433

M3 - Journal article

VL - 122

JO - Image and Vision Computing

JF - Image and Vision Computing

SN - 0262-8856

M1 - 104433

ER -

ID: 302814257