research-article

The Shape Space of 3D Botanical Tree Models

Authors:

Hedi TabiaAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 37, Issue 1

Article No.: 7, Pages 1 - 18

https://doi.org/10.1145/3144456

Published: 18 January 2018 Publication History

Abstract

We propose an algorithm for generating novel 3D tree model variations from existing ones via geometric and structural blending. Our approach is to treat botanical trees as elements of a tree-shape space equipped with a proper metric that quantifies geometric and structural deformations. Geodesics, or shortest paths under the metric, between two points in the tree-shape space correspond to optimal deformations that align one tree onto another, including the possibility of expanding, adding, or removing branches and parts. Central to our approach is a mechanism for computing correspondences between trees that have different structures and a different number of branches. The ability to compute geodesics and their lengths enables us to compute continuous blending between botanical trees, which, in turn, facilitates statistical analysis, such as the computation of averages of tree structures. We show a variety of 3D tree models generated with our approach from 3D trees exhibiting complex geometric and structural differences. We also demonstrate the application of the framework in reflection symmetry analysis and symmetrization of botanical trees.

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Index Terms

The Shape Space of 3D Botanical Tree Models
1. Computing methodologies
  1. Computer graphics
    1. Shape modeling
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 37, Issue 1

February 2018

167 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/3151031

Editor:
Kavita Bala
Cornell University

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Publication History

Published: 18 January 2018

Accepted: 01 September 2017

Revised: 01 September 2017

Received: 01 October 2016

Published in TOG Volume 37, Issue 1

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Wu DYang MLiu ZTu FLiu FCheng Z(2024)VRTree: Example‐Based 3D Interactive Tree Modeling in Virtual RealityComputer Graphics Forum10.1111/cgf.1525443:7Online publication date: 7-Nov-2024
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Wang GLaga HSrivastava A(2024)Elastic Shape Analysis of Tree-Like 3D Objects Using Extended SRVF RepresentationIEEE Transactions on Pattern Analysis and Machine Intelligence10.1109/TPAMI.2023.333452546:4(2475-2488)Online publication date: 1-Apr-2024
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Khanam TLaga HBennamoun MWang GSohel FBoussaid FWang GSrivastava A(2024)A Riemannian Approach for Spatiotemporal Analysis and Generation of 4D Tree-Shaped StructuresComputer Vision – ECCV 202410.1007/978-3-031-72855-6_19(326-341)Online publication date: 9-Nov-2024
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