{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T18:17:32Z","timestamp":1767982652184,"version":"3.49.0"},"reference-count":56,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Victorian Government\u2019s Powerline Bushfire Safety Program R&amp;D fund, Powercor, Sylvanus and CSIRO Data61"}],"content-domain":{"domain":["www.mdpi.com"],"crossmark-restriction":true},"short-container-title":["Remote Sensing"],"abstract":"<jats:p>Generating accurate digital tree models from scanned environments is invaluable for forestry, agriculture, and other outdoor industries in tasks such as identifying fall hazards, estimating trees\u2019 biomass and calculating traversability. Existing methods for tree reconstruction rely on sparse feature identification to segment a forest into individual trees and generate a branch structure graph, limiting their application to easily separable trees and uniform forests. However, the natural world is a messy place in which trees present with significant heterogeneity and are frequently encroached upon by the surrounding environment. We present a general method for extracting the branch structure of trees from point cloud data, which estimates the structure of trees by adapting the methods of structural topology optimisation to find the optimal material distribution to interpolate the input data. We present the results of this optimisation over a wide variety of scans, and discuss the benefits and drawbacks of this novel approach to tree structure reconstruction. Our method generates detailed and accurate tree structures, with a mean Surface Error (SE) of 15 cm over 13 diverse tree datasets.<\/jats:p>","DOI":"10.3390\/rs15010172","type":"journal-article","created":{"date-parts":[[2022,12,29]],"date-time":"2022-12-29T02:52:21Z","timestamp":1672282341000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["Tree Reconstruction Using Topology Optimisation"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8932-018X","authenticated-orcid":false,"given":"Thomas","family":"Lowe","sequence":"first","affiliation":[{"name":"Robotics and Autonomus Systems Group, CSIRO Data61, Pullenvale, QLD 4069, Australia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8878-9012","authenticated-orcid":false,"given":"Joshua","family":"Pinskier","sequence":"additional","affiliation":[{"name":"Robotics and Autonomus Systems Group, CSIRO Data61, Pullenvale, QLD 4069, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2022,12,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Trochta, J., Kr\u010dek, M., Vr\u0161ka, T., and Kr\u00e1l, K. (2017). 3D Forest: An application for descriptions of three-dimensional forest structures using terrestrial LiDAR. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0176871"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"763","DOI":"10.1007\/s00371-014-0977-7","article-title":"Hybrid tree reconstruction from inhomogeneous point clouds","volume":"30","author":"Aiteanu","year":"2014","journal-title":"Vis. Comput."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Du, S., Lindenbergh, R., Ledoux, H., Stoter, J., and Nan, L. (2019). AdTree: Accurate, detailed, and automatic modelling of laser-scanned trees. Remote Sens., 11.","DOI":"10.20944\/preprints201907.0058.v2"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Livny, Y., Yan, F., Olson, M., Chen, B., Zhang, H., and El-Sana, J. (2010, January 15\u201318). Automatic reconstruction of tree skeletal structures from point clouds. Proceedings of the ACM SIGGRAPH Asia 2010, Seoul, Republic of Korea.","DOI":"10.1145\/1882262.1866177"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Li, H., Zhang, X., Jaeger, M., and Constant, T. (2010, January 12\u201313). Segmentation of forest terrain laser scan data. Proceedings of the 9th ACM SIGGRAPH Conference on Virtual-Reality Continuum and its Applications in Industry, Seoul, Republic of Korea.","DOI":"10.1145\/1900179.1900188"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1109\/JSTARS.2016.2565519","article-title":"Segmentation of individual trees from TLS and MLS data","volume":"10","author":"Zhong","year":"2016","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"2403","DOI":"10.1007\/s11676-021-01303-1","article-title":"Point-cloud segmentation of individual trees in complex natural forest scenes based on a trunk-growth method","volume":"32","author":"Liu","year":"2021","journal-title":"J. For. Res."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"438","DOI":"10.1111\/2041-210X.13121","article-title":"Extracting individual trees from lidar point clouds using treeseg","volume":"10","author":"Burt","year":"2019","journal-title":"Methods Ecol. Evol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.14358\/PERS.78.1.75","article-title":"A new method for segmenting individual trees from the lidar point cloud","volume":"78","author":"Li","year":"2012","journal-title":"Photogramm. Eng. Remote Sens."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1080\/07038992.2017.1252907","article-title":"Layer stacking: A novel algorithm for individual forest tree segmentation from LiDAR point clouds","volume":"43","author":"Ayrey","year":"2017","journal-title":"Can. J. Remote Sens."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Heinzel, J., and Huber, M.O. (2018). Constrained spectral clustering of individual trees in dense forest using terrestrial laser scanning data. Remote Sens., 10.","DOI":"10.3390\/rs10071056"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1111\/phor.12247","article-title":"Scalable individual tree delineation in 3D point clouds","volume":"33","author":"Wang","year":"2018","journal-title":"Photogramm. Rec."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"326","DOI":"10.1016\/j.isprsjprs.2021.03.002","article-title":"Individual tree extraction from urban mobile laser scanning point clouds using deep pointwise direction embedding","volume":"175","author":"Luo","year":"2021","journal-title":"ISPRS J. Photogramm. Remote Sens."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Krisanski, S., Taskhiri, M.S., Aracil, S.G., Herries, D., and Turner, P. (2021). Sensor agnostic semantic segmentation of structurally diverse and complex forest point clouds using deep learning. Remote Sens., 13.","DOI":"10.3390\/rs13081413"},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Tagliasacchi, A., Delame, T., Spagnuolo, M., Amenta, N., and Telea, A. (2016, January 20\u201324). 3d skeletons: A state-of-the-art report. Proceedings of the Computer Graphics Forum, Berlin, Germany.","DOI":"10.1111\/cgf.12865"},{"key":"ref_16","first-page":"321","article-title":"Automatic Reconstruction of Skeletal Structures from TLS Forest Scenes","volume":"2","author":"Schilling","year":"2014","journal-title":"ISPRS Ann. Photogramm. Remote Sens. Spat. Inf. Sci."},{"key":"ref_17","first-page":"1","article-title":"Skeleton extraction from point clouds of trees with complex branches via graph contraction","volume":"37","author":"Jiang","year":"2020","journal-title":"Vis. Comput."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"491","DOI":"10.3390\/rs5020491","article-title":"Fast automatic precision tree models from terrestrial laser scanner data","volume":"5","author":"Raumonen","year":"2013","journal-title":"Remote Sens."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"606","DOI":"10.1109\/JSTARS.2017.2781132","article-title":"Lidar point clouds to 3-D urban models: A review","volume":"11","author":"Wang","year":"2018","journal-title":"IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.cag.2017.04.004","article-title":"Efficient tree modeling from airborne LiDAR point clouds","volume":"67","author":"Hu","year":"2017","journal-title":"Comput. Graph."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"19-es","DOI":"10.1145\/1289603.1289610","article-title":"Knowledge and heuristic-based modeling of laser-scanned trees","volume":"26","author":"Xu","year":"2007","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_22","unstructured":"Raumonen, D.P. (2022, October 16). TreeQSM. Available online: https:\/\/github.com\/InverseTampere\/TreeQSM."},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Fan, G., Nan, L., Dong, Y., Su, X., and Chen, F. (2020). AdQSM: A New Method for Estimating Above-Ground Biomass from TLS Point Clouds. Remote Sens., 12.","DOI":"10.3390\/rs12183089"},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1899","DOI":"10.1007\/s00158-018-2055-7","article-title":"Topology optimization of conductive heat transfer problems using parametric L-systems","volume":"58","author":"Ikonen","year":"2018","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"103874","DOI":"10.1016\/j.mechmachtheory.2020.103874","article-title":"Topology optimization of stiffness constrained flexure-hinges for precision and range maximization","volume":"150","author":"Pinskier","year":"2020","journal-title":"Mech. Mach. Theory"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"397","DOI":"10.1016\/j.precisioneng.2018.10.008","article-title":"Topology optimization of leaf flexures to maximize in-plane to out-of-plane compliance ratio","volume":"55","author":"Pinskier","year":"2019","journal-title":"Precis. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1016\/j.mechmachtheory.2017.12.017","article-title":"Topology optimisation of bridge input structures with maximal amplification for design of flexure mechanisms","volume":"122","author":"Clark","year":"2018","journal-title":"Mech. Mach. Theory"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"2100086","DOI":"10.1002\/aisy.202100086","article-title":"From Bioinspiration to Computer Generation: Developments in Autonomous Soft Robot Design","volume":"4","author":"Pinskier","year":"2022","journal-title":"Adv. Intell. Syst."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"650","DOI":"10.1089\/soro.2017.0058","article-title":"Design and Development of a Topology-Optimized Three-Dimensional Printed Soft Gripper","volume":"5","author":"Zhang","year":"2018","journal-title":"Soft Robot."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6605","DOI":"10.1016\/S0045-7825(01)00252-3","article-title":"Design of multiphysics actuators using topology optimization - Part I: One-material structures","volume":"190","author":"Sigmund","year":"2001","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1007\/s00158-019-02442-0","article-title":"Topology optimization of fluidic pressure-loaded structures and compliant mechanisms using the Darcy method","volume":"61","author":"Kumar","year":"2020","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.jcp.2017.08.008","article-title":"Topology optimisation of micro fluidic mixers considering fluid-structure interactions with a coupled Lattice Boltzmann algorithm","volume":"349","author":"Munk","year":"2017","journal-title":"J. Comput. Phys."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhang, H.K., Zhou, J., Fang, W., Zhao, H., Zhao, Z.L., Chen, X., Zhao, H.P., and Feng, X.Q. (2022). Multi-functional topology optimization of Victoria cruziana veins. J. R. Soc. Interface, 19.","DOI":"10.1098\/rsif.2022.0298"},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Bends\u00f8e, M.P., and Sigmund, O. (2003). Topology Optimization: Theory, Methods, and Applications, Springer.","DOI":"10.1007\/978-3-662-05086-6"},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Zhang, X., and Zhu, B. (2018). Topology Optimization of Compliant Mechanisms, Springer.","DOI":"10.1007\/978-981-13-0432-3"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1031","DOI":"10.1007\/s00158-013-0978-6","article-title":"Topology optimization approaches: A comparative review","volume":"48","author":"Sigmund","year":"2013","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"613","DOI":"10.1007\/s00158-015-1261-9","article-title":"Topology and shape optimization methods using evolutionary algorithms: A review","volume":"52","author":"Munk","year":"2015","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1007\/s00158-013-0912-y","article-title":"Level-set methods for structural topology optimization: A review","volume":"48","author":"Maute","year":"2013","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_39","unstructured":"Yuta, T. (2022, October 16). PANSFEM. Available online: https:\/\/github.com\/PANFACTORY\/PANSFEM2."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s00158-010-0594-7","article-title":"Efficient topology optimization in MATLAB using 88 lines of code","volume":"43","author":"Andreassen","year":"2011","journal-title":"Struct. Multidiscip. Optim."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"238","DOI":"10.1002\/nme.1064","article-title":"Achieving minimum length scale in topology optimization using nodal design variables and projection functions","volume":"61","author":"Guest","year":"2004","journal-title":"Int. J. Numer. Methods Eng."},{"key":"ref_42","first-page":"212","article-title":"Topology Optimization and Prototype of a Multimaterial-Like Compliant Finger by Varying the Infill Density in 3D Printing","volume":"9","author":"Liu","year":"2021","journal-title":"Soft Robot."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"81","DOI":"10.1007\/BF01637664","article-title":"CONLIN: An efficient dual optimizer based on convex approximation concepts","volume":"1","author":"Fleury","year":"1989","journal-title":"Struct. Optim."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"660","DOI":"10.1016\/j.ijheatmasstransfer.2018.01.114","article-title":"On the non-optimality of tree structures for heat conduction","volume":"122","author":"Yan","year":"2018","journal-title":"Int. J. Heat Mass Transf."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"79712","DOI":"10.1109\/ACCESS.2021.3084954","article-title":"RayCloudTools: A Concise Interface for Analysis and Manipulation of Ray Clouds","volume":"9","author":"Lowe","year":"2021","journal-title":"IEEE Access"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1111\/2041-210X.12301","article-title":"Nondestructive estimates of above-ground biomass using terrestrial laser scanning","volume":"6","author":"Calders","year":"2015","journal-title":"Methods Ecol. Evol."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connexion with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_48","unstructured":"Ramezani, M., Khosoussi, K., Catt, G., Moghadam, P., Williams, J., Borges, P., Pauling, F., and Kottege, N. (arXiv, 2022). Wildcat: Online Continuous-Time 3D Lidar-Inertial SLAM, arXiv."},{"key":"ref_49","unstructured":"Wang, J. (2022, October 16). TreeSeparation. Available online: https:\/\/github.com\/Jinhu-Wang\/TreeSeparation."},{"key":"ref_50","unstructured":"Burt, A., and Peter, T. (2022, October 16). Jgrn307. Apburt\/Treeseg: V0.2.2. Available online: https:\/\/zenodo.org\/record\/4884923#.Y6wNfUxByHs."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"106277","DOI":"10.1016\/j.compag.2021.106277","article-title":"SimTreeLS: Simulating aerial and terrestrial laser scans of trees","volume":"187","author":"Westling","year":"2021","journal-title":"Comput. Electron. Agric."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"105052","DOI":"10.1109\/ACCESS.2022.3211072","article-title":"Virtual LiDAR Simulation as a High Performance Computing Challenge: Toward HPC HELIOS++","volume":"10","author":"Yermo","year":"2022","journal-title":"IEEE Access"},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"1014","DOI":"10.1038\/s41467-017-00995-6","article-title":"Wind loads and competition for light sculpt trees into self-similar structures","volume":"8","author":"Eloy","year":"2017","journal-title":"Nat. Commun."},{"key":"ref_54","doi-asserted-by":"crossref","first-page":"258101","DOI":"10.1103\/PhysRevLett.107.258101","article-title":"Leonardo\u2019s rule, self-similarity, and wind-induced stresses in trees","volume":"107","author":"Eloy","year":"2011","journal-title":"Phys. Rev. Lett."},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1016\/S0169-5347(02)00016-2","article-title":"Is bigger better in plants? The hydraulic costs of increasing size in trees","volume":"18","author":"Midgley","year":"2003","journal-title":"Trends Ecol. Evol."},{"key":"ref_56","first-page":"197","article-title":"The mechanical self-optimisation of trees","volume":"73","author":"Mattheck","year":"2004","journal-title":"WIT Trans. Ecol. Environ."}],"updated-by":[{"DOI":"10.3390\/rs15112739","type":"correction","label":"Correction","source":"publisher","updated":{"date-parts":[[2022,12,28]],"date-time":"2022-12-28T00:00:00Z","timestamp":1672185600000}}],"container-title":["Remote Sensing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/172\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,8,3]],"date-time":"2025-08-03T22:22:58Z","timestamp":1754259778000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2072-4292\/15\/1\/172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,12,28]]},"references-count":56,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2023,1]]}},"alternative-id":["rs15010172"],"URL":"https:\/\/doi.org\/10.3390\/rs15010172","relation":{"correction":[{"id-type":"doi","id":"10.3390\/rs15112739","asserted-by":"object"}]},"ISSN":["2072-4292"],"issn-type":[{"value":"2072-4292","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,12,28]]}}}