A Function Space Perspective on Stochastic Shape Evolution

Elizabeth Baker; Thomas Besnier; Stefan Sommer

doi:10.1007/978-3-031-31438-4_19

A Function Space Perspective on Stochastic Shape Evolution

Elizabeth Baker^*, Thomas Besnier, Stefan Sommer

^*Corresponding author for this work

Image Analysis, Computational Modelling and Geometry

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

Modelling randomness in shape data, for example, the evolution of shapes of organisms in biology, requires stochastic models of shapes. This paper presents a new stochastic shape model based on a description of shapes as functions in a Sobolev space. Using an explicit orthonormal basis as a reference frame for the noise, the model is independent of the parameterisation of the mesh. We define the stochastic model, explore its properties, and illustrate examples of stochastic shape evolutions using the resulting numerical framework.

Original language	English
Title of host publication	Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings
Editors	Rikke Gade, Michael Felsberg, Joni-Kristian Kämäräinen
Number of pages	15
Publisher	Springer
Publication date	2023
Pages	278-292
ISBN (Print)	9783031314377
DOIs	https://doi.org/10.1007/978-3-031-31438-4_19
Publication status	Published - 2023
Event	23nd Scandinavian Conference on Image Analysis, SCIA 2023 - Lapland, Finland Duration: 18 Apr 2023 → 21 Apr 2023

Conference

Conference	23nd Scandinavian Conference on Image Analysis, SCIA 2023
Country/Territory	Finland
City	Lapland
Period	18/04/2023 → 21/04/2023

Series	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	13886 LNCS
ISSN	0302-9743

Bibliographical note

Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

Keywords

3D mesh processing
diffusions
shape space

Access to Document

10.1007/978-3-031-31438-4_19

https://arxiv.org/pdf/2302.05382.pdfLicence: CC BY

Cite this

Baker, E., Besnier, T., & Sommer, S. (2023). A Function Space Perspective on Stochastic Shape Evolution. In R. Gade, M. Felsberg, & J-K. Kämäräinen (Eds.), Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings (pp. 278-292). Springer. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Vol. 13886 LNCS https://doi.org/10.1007/978-3-031-31438-4_19

A Function Space Perspective on Stochastic Shape Evolution. / Baker, Elizabeth; Besnier, Thomas; Sommer, Stefan.

Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings. ed. / Rikke Gade; Michael Felsberg; Joni-Kristian Kämäräinen. Springer, 2023. p. 278-292 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13886 LNCS).

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Baker, E, Besnier, T & Sommer, S 2023, A Function Space Perspective on Stochastic Shape Evolution. in R Gade, M Felsberg & J-K Kämäräinen (eds), Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings. Springer, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 13886 LNCS, pp. 278-292, 23nd Scandinavian Conference on Image Analysis, SCIA 2023, Lapland, Finland, 18/04/2023. https://doi.org/10.1007/978-3-031-31438-4_19

Baker E, Besnier T, Sommer S. A Function Space Perspective on Stochastic Shape Evolution. In Gade R, Felsberg M, Kämäräinen J-K, editors, Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings. Springer. 2023. p. 278-292. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13886 LNCS). https://doi.org/10.1007/978-3-031-31438-4_19

Baker, Elizabeth ; Besnier, Thomas ; Sommer, Stefan. / A Function Space Perspective on Stochastic Shape Evolution. Image Analysis - 23rd Scandinavian Conference, SCIA 2023, Proceedings. editor / Rikke Gade ; Michael Felsberg ; Joni-Kristian Kämäräinen. Springer, 2023. pp. 278-292 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Vol. 13886 LNCS).

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