A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures

Tahmina Khanam; Hamid Laga; Mohammed Bennamoun; Guanjin Wang; Ferdous Sohel; Farid Boussaid; Guan Wang; Anuj Srivastava

doi:10.1007/978-3-031-72855-6_19

A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures

Tahmina Khanam
, Hamid Laga
, Mohammed Bennamoun
, Guanjin Wang
, Ferdous Sohel
, Farid Boussaid
, Guan Wang
, Anuj Srivastava

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

1 Citation (Scopus)

Abstract

We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT) [21]. By solving the spatial registration in the SRVFT space, which is equipped with an L² metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.

Original language	English
Title of host publication	Computer Vision – ECCV 2024 - 18th European Conference, Proceedings
Editors	Aleš Leonardis, Elisa Ricci, Stefan Roth, Olga Russakovsky, Torsten Sattler, Gül Varol
Publisher	Springer Science + Business Media
Pages	326-341
Number of pages	16
ISBN (Print)	9783031728549
DOIs	https://doi.org/10.1007/978-3-031-72855-6_19
Publication status	Published - 2025
Event	18th European Conference on Computer Vision - MICO DMC s.r.l., Milan, Italy Duration: 29 Sept 2024 → 4 Oct 2024 https://eccv.ecva.net/Conferences/2024 (event homepage)

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	15125 LNCS
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	18th European Conference on Computer Vision
Abbreviated title	ECCV 2024
Country/Territory	Italy
City	Milan
Period	29/09/24 → 4/10/24
Other	The European Conference on Computer Vision (ECCV) is a biennial premier research conference in Computer Vision and Machine Learning, managed by the European Computer Vision Association (ECVA). It is held on even years and gathers the scientific and industrial communities on these areas. The first ECCV was held in 1990 in Antibes, France, and subsequently organized all over Europe. Paper proceedings are published by Springer Science + Business Media.
Internet address	https://eccv.ecva.net/Conferences/2024 (event homepage)

Funding

Funders	Funder number
ARC Australian Research Council	DP220102197, DP210102674, DP210101682

Access to Document

10.1007/978-3-031-72855-6_19

Cite this

Khanam, T., Laga, H., Bennamoun, M., Wang, G., Sohel, F., Boussaid, F., Wang, G., & Srivastava, A. (2025). A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures. In A. Leonardis, E. Ricci, S. Roth, O. Russakovsky, T. Sattler, & G. Varol (Eds.), Computer Vision – ECCV 2024 - 18th European Conference, Proceedings (pp. 326-341). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 15125 LNCS). Springer Science + Business Media. https://doi.org/10.1007/978-3-031-72855-6_19

Khanam, Tahmina ; Laga, Hamid ; Bennamoun, Mohammed et al. / A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures. Computer Vision – ECCV 2024 - 18th European Conference, Proceedings. editor / Aleš Leonardis ; Elisa Ricci ; Stefan Roth ; Olga Russakovsky ; Torsten Sattler ; Gül Varol. Springer Science + Business Media, 2025. pp. 326-341 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inproceedings{9a618551be3746e799bbcc10098e7e71,

title = "A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures",

abstract = "We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT) [21]. By solving the spatial registration in the SRVFT space, which is equipped with an L2 metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.",

keywords = "4D registration, 4D tree generation, Statistical analysis",

author = "Tahmina Khanam and Hamid Laga and Mohammed Bennamoun and Guanjin Wang and Ferdous Sohel and Farid Boussaid and Guan Wang and Anuj Srivastava",

note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.; 18th European Conference on Computer Vision, ECCV 2024 ; Conference date: 29-09-2024 Through 04-10-2024",

year = "2025",

doi = "10.1007/978-3-031-72855-6\_19",

language = "English",

isbn = "9783031728549",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Science + Business Media",

pages = "326--341",

editor = "Ale{\v s} Leonardis and Elisa Ricci and Stefan Roth and Olga Russakovsky and Torsten Sattler and G{\"u}l Varol",

booktitle = "Computer Vision {\textendash} ECCV 2024 - 18th European Conference, Proceedings",

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Khanam, T, Laga, H, Bennamoun, M, Wang, G, Sohel, F, Boussaid, F, Wang, G & Srivastava, A 2025, A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures. in A Leonardis, E Ricci, S Roth, O Russakovsky, T Sattler & G Varol (eds), Computer Vision – ECCV 2024 - 18th European Conference, Proceedings. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 15125 LNCS, Springer Science + Business Media, pp. 326-341, 18th European Conference on Computer Vision, Milan, Italy, 29/09/24. https://doi.org/10.1007/978-3-031-72855-6_19

A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures. / Khanam, Tahmina; Laga, Hamid; Bennamoun, Mohammed et al.
Computer Vision – ECCV 2024 - 18th European Conference, Proceedings. ed. / Aleš Leonardis; Elisa Ricci; Stefan Roth; Olga Russakovsky; Torsten Sattler; Gül Varol. Springer Science + Business Media, 2025. p. 326-341 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 15125 LNCS).

Research output: Chapter in Book/Conference paper › Conference paper › peer-review

TY - GEN

T1 - A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures

AU - Khanam, Tahmina

AU - Laga, Hamid

AU - Bennamoun, Mohammed

AU - Wang, Guanjin

AU - Sohel, Ferdous

AU - Boussaid, Farid

AU - Wang, Guan

AU - Srivastava, Anuj

N1 - Publisher Copyright: © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

PY - 2025

Y1 - 2025

N2 - We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT) [21]. By solving the spatial registration in the SRVFT space, which is equipped with an L2 metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.

AB - We propose the first comprehensive approach for modeling and analyzing the spatiotemporal shape variability in tree-like 4D objects, i.e., 3D objects whose shapes bend, stretch and change in their branching structure over time as they deform, grow, and interact with their environment. Our key contribution is the representation of tree-like 3D shapes using Square Root Velocity Function Trees (SRVFT) [21]. By solving the spatial registration in the SRVFT space, which is equipped with an L2 metric, 4D tree-shaped structures become time-parameterized trajectories in this space. This reduces the problem of modeling and analyzing 4D tree-like shapes to that of modeling and analyzing elastic trajectories in the SRVFT space, where elasticity refers to time warping. In this paper, we propose a novel mathematical representation of the shape space of such trajectories, a Riemannian metric on that space, and computational tools for fast and accurate spatiotemporal registration and geodesics computation between 4D tree-shaped structures. Leveraging these building blocks, we develop a full framework for modelling the spatiotemporal variability using statistical models and generating novel 4D tree-like structures from a set of exemplars. We demonstrate and validate the proposed framework using real 4D plant data.

KW - 4D registration

KW - 4D tree generation

KW - Statistical analysis

UR - https://www.scopus.com/pages/publications/85209591356

U2 - 10.1007/978-3-031-72855-6_19

DO - 10.1007/978-3-031-72855-6_19

M3 - Conference paper

AN - SCOPUS:85209591356

SN - 9783031728549

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 326

EP - 341

BT - Computer Vision – ECCV 2024 - 18th European Conference, Proceedings

A2 - Leonardis, Aleš

A2 - Ricci, Elisa

A2 - Roth, Stefan

A2 - Russakovsky, Olga

A2 - Sattler, Torsten

A2 - Varol, Gül

PB - Springer Science + Business Media

T2 - 18th European Conference on Computer Vision

Y2 - 29 September 2024 through 4 October 2024

ER -

Khanam T, Laga H, Bennamoun M, Wang G, Sohel F, Boussaid F et al. A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures. In Leonardis A, Ricci E, Roth S, Russakovsky O, Sattler T, Varol G, editors, Computer Vision – ECCV 2024 - 18th European Conference, Proceedings. Springer Science + Business Media. 2025. p. 326-341. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-031-72855-6_19

A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures

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A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped Structures

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Fine-grained Human Action Recognition with Deep Graph Neural Networks

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