@Article{box_dimension1,
AUTHOR = {Arseniou, Georgios and MacFarlane, David W. and Seidel, Dominik},
TITLE = {Measuring the Contribution of Leaves to the Structural Complexity of Urban Tree Crowns with Terrestrial Laser Scanning},
JOURNAL = {Remote Sensing},
VOLUME = {13},
YEAR = {2021},
NUMBER = {14},
ABSTRACT = {Trees have a fractal-like branching architecture that determines their structural complexity. We used terrestrial laser scanning technology to study the role of foliage in the structural complexity of urban trees. Forty-five trees of three deciduous species, Gleditsia triacanthos, Quercus macrocarpa, Metasequoia glyptostroboides, were sampled on the Michigan State University campus. We studied their structural complexity by calculating the box-dimension (Db) metric from point clouds generated for the trees using terrestrial laser scanning, during the leaf-on and -off conditions. Furthermore, we artificially defoliated the leaf-on point clouds by applying an algorithm that separates the foliage from the woody material of the trees, and then recalculated the Db metric. The Db of the leaf-on tree point clouds was significantly greater than the Db of the leaf-off point clouds across all species. Additionally, the leaf removal algorithm introduced bias to the estimation of the leaf-removed Db of the G. triacanthos and M. glyptostroboides trees. The index capturing the contribution of leaves to the structural complexity of the study trees (the ratio of the Db of the leaf-on point clouds divided by the Db of the leaf-off point clouds minus one), was negatively correlated with branch surface area and different metrics of the length of paths through the branch network of the trees, indicating that the contribution of leaves decreases as branch network complexity increases. Underestimation of the Db of the G. triacanthos trees, after the artificial leaf removal, was related to maximum branch order. These results enhance our understanding of tree structural complexity by disentangling the contribution of leaves from that of the woody structures. The study also highlighted important methodological considerations for studying tree structure, with and without leaves, from laser-derived point clouds.},
DOI = {10.3390/rs13142773}
}

@Book{box_dimension2,
title={The fractal geometry of nature},
publisher={Freeman},
author={Mandelbrot, Benoit B.},
year={1983}
}

@Article{box_dimension3,
author = {Saarinen, Ninni and Calders, Kim and Kankare, Ville and Yrttimaa, Tuomas and Junttila, Samuli and Luoma, Ville and Huuskonen, Saija and Hynynen, Jari and Verbeeck, Hans},
title = {Understanding 3D structural complexity of individual Scots pine trees with different management history},
journal = {Ecology and Evolution},
volume = {11},
number = {6},
pages = {2561-2572},
keywords = {box dimension, forest ecology, ground-based LiDAR, growth and yield, silviculture, terrestrial laser scanning, tree structure},
doi = {https://doi.org/10.1002/ece3.7216},
abstract = {Abstract Tree functional traits together with processes such as forest regeneration, growth, and mortality affect forest and tree structure. Forest management inherently impacts these processes. Moreover, forest structure, biodiversity, resilience, and carbon uptake can be sustained and enhanced with forest management activities. To assess structural complexity of individual trees, comprehensive and quantitative measures are needed, and they are often lacking for current forest management practices. Here, we utilized 3D information from individual Scots pine (Pinus sylvestris L.) trees obtained with terrestrial laser scanning to, first, assess effects of forest management on structural complexity of individual trees and, second, understand relationship between several tree attributes and structural complexity. We studied structural complexity of individual trees represented by a single scale-independent metric called “box dimension.” This study aimed at identifying drivers affecting structural complexity of individual Scots pine trees in boreal forest conditions. The results showed that thinning increased structural complexity of individual Scots pine trees. Furthermore, we found a relationship between structural complexity and stem and crown size and shape as well as tree growth. Thus, it can be concluded that forest management affected structural complexity of individual Scots pine trees in managed boreal forests, and stem, crown, and growth attributes were identified as drivers of it.},
year = {2021}
}

@Article{box_dimension4,
author = {Seidel, Dominik},
title = {A holistic approach to determine tree structural complexity based on laser scanning data and fractal analysis},
journal = {Ecology and Evolution},
volume = {8},
number = {1},
pages = {128-134},
keywords = {competition, complexity, fractal analysis, LiDAR, management, shape, structure, three-dimensional, tree architecture},
doi = {https://doi.org/10.1002/ece3.3661},
abstract = {Abstract The three-dimensional forest structure affects many ecosystem functions and services provided by forests. As forests are made of trees it seems reasonable to approach their structure by investigating individual tree structure. Based on three-dimensional point clouds from laser scanning, a newly developed holistic approach is presented that enables to calculate the box dimension as a measure of structural complexity of individual trees using fractal analysis. It was found that the box dimension of trees was significantly different among the tested species, among trees belonging to the same species but exposed to different growing conditions (at gap vs. forest interior) or to different kinds of competition (intraspecific vs. interspecific). Furthermore, it was shown that the box dimension is positively related to the trees’ growth rate. The box dimension was identified as an easy to calculate measure that integrates the effect of several external drivers of tree structure, such as competition strength and type, while simultaneously providing information on structure-related properties, like tree growth.},
year = {2018}
}

@Article{box_dimension5,
author = {Seidel, Dominik and Annighöfer, Peter and Stiers, Melissa and Zemp, Clara Delphine and Burkardt, Katharina and Ehbrecht, Martin and Willim, Katharina and Kreft, Holger and Hölscher, Dirk and Ammer, Christian},
title = {How a measure of tree structural complexity relates to architectural benefit-to-cost ratio, light availability, and growth of trees},
journal = {Ecology and Evolution},
volume = {9},
number = {12},
pages = {7134-7142},
keywords = {box-dimension, fractal analysis, Germany, Indonesia, light availability, plant architecture, productivity},
doi = {https://doi.org/10.1002/ece3.5281},
abstract = {Abstract Aboveground tree architecture is neither fully deterministic nor random. It is likely the result of mechanisms that balance static requirements and light-capturing efficiency. Here, we used terrestrial laser scanning data to investigate the relationship between tree architecture, here addressed using the box-dimension (Db), and the architectural benefit-to-cost ratio, the light availability, and the growth of trees. We detected a clear relationship between Db and the benefit-to-cost ratio for the tested three temperate forest tree species (Fagus sylvatica L., Fraxinus excelsior L., and Acer pseudoplatanus L.). In addition, we could also show that Db is positively related to the growth performance of several tropical tree species. Finally, we observed a negative relationship between the strength of competition enforced on red oak (Quercus rubra L.) trees and their Db. We therefore argue that Db is a meaningful and integrative measure that describes the structural complexity of the aboveground compartments of a plant as well as its relation to structural efficiency (benefit-to-cost ratio), productivity, and growing conditions (competition or availability of light).},
year = {2019}
}

@Article{growth_parameter1,
AUTHOR = {Hackenberg, Jan and Spiecker, Heinrich and Calders, Kim and Disney, Mathias and Raumonen, Pasi},
TITLE = {SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds},
JOURNAL = {Forests},
VOLUME = {6},
YEAR = {2015},
NUMBER = {11},
PAGES = {4245--4294},
ABSTRACT = {An open source tool named SimpleTree, capable of modelling highly accurate cylindrical tree models from terrestrial laser scan point clouds, is presented and evaluated. All important functionalities, accessible in the software via buttons and dialogues, are described including the explanation of all necessary input parameters. The method is validated utilizing 101 point clouds of six different tree species, in the main evergreen and coniferous trees. All scanned trees have been destructively harvested to get accurate estimates of above ground biomass with which we assess the accuracy of the SimpleTree-reconstructed cylinder models. The trees were grouped into four data sets and for each one a Concordance Correlation Coefficient of at least 0.92 (0.92, 0.97, 0.92, 0.94) and an total relative error at most ~8 % (2.42%, 3.59%, –4.59%, 8.27%) was achieved in the comparison of the model results to the ground truth data. A global statistical improvement of derived cylinder radii is presented as well as an efficient optimization approach to automatically improve user given input parameters. An additional check of the SimpleTree results is presented via comparison to the results of trees reconstructed using an alternative, published method.},
DOI = {10.3390/f6114245}
}

@Article{growth_parameter2,
author = {Hackenberg, Jan and Bontemps, Jean-Daniel},
year = {2023},
month = {11},
pages = {},
title = {Improving quantitative structure models with filters based on allometric scaling theory},
volume = {15},
journal = {Applied Geomatics},
doi = {10.1007/s12518-023-00537-4}
}

@Article{TreeQSM,
AUTHOR = {Raumonen, Pasi and Kaasalainen, Mikko and Åkerblom, Markku and Kaasalainen, Sanna and Kaartinen, Harri and Vastaranta, Mikko and Holopainen, Markus and Disney, Mathias and Lewis, Philip},
TITLE = {Fast Automatic Precision Tree Models from Terrestrial Laser Scanner Data},
JOURNAL = {Remote Sensing},
VOLUME = {5},
YEAR = {2013},
NUMBER = {2},
PAGES = {491--520},
ABSTRACT = {This paper presents a new method for constructing quickly and automatically precision tree models from point clouds of the trunk and branches obtained by terrestrial laser scanning. The input of the method is a point cloud of a single tree scanned from multiple positions. The surface of the visible parts of the tree is robustly reconstructed by making a flexible cylinder model of the tree. The thorough quantitative model records also the topological branching structure. In this paper, every major step of the whole model reconstruction process, from the input to the finished model, is presented in detail. The model is constructed by a local approach in which the point cloud is covered with small sets corresponding to connected surface patches in the tree surface. The neighbor-relations and geometrical properties of these cover sets are used to reconstruct the details of the tree and, step by step, the whole tree. The point cloud and the sets are segmented into branches, after which the branches are modeled as collections of cylinders. From the model, the branching structure and size properties, such as volume and branch size distributions, for the whole tree or some of its parts, can be approximated. The approach is validated using both measured and modeled terrestrial laser scanner data from real trees and detailed 3D models. The results show that the method allows an easy extraction of various tree attributes from terrestrial or mobile laser scanning point clouds.},
DOI = {10.3390/rs5020491}
}

@Article{treegraph1,
author = {Wilkes, Phil and Shenkin, Alexander and Disney, Mathias and Malhi, Yadvinder and Bentley, Lisa Patrick and Vicari, Matheus Boni},
title = {Terrestrial laser scanning to reconstruct branch architecture from harvested branches},
journal = {Methods in Ecology and Evolution},
volume = {12},
pages = {2487-2500},
keywords = {architecture, branch, canopy, LiDAR, quantitative structure models, reconstruction, structure, terrestrial laser scanning},
doi = {https://doi.org/10.1111/2041-210X.13709},
abstract = {Abstract Quantifying whole branch architecture is critical to understanding tree function, for example, branch surface area controls woody gas exchange. Yet, due to measurement difficulty, branch architecture of small diameter branches (e.g. <10 cm ) is modelled, subsampled or ignored. Methods that use terrestrial laser scanning (TLS) are now being widely applied to analyse tree and plot-level tree architecture; however, resolving small diameter branches in-situ remains a challenge. Currently, it is suggested that accurate reconstruction of small diameter branches can only be achieved by harvest and measurement in controlled conditions. Here we present a new TLS workflow for rapid and accurate reconstruction of complete branch architecture from harvested branches. The workflow sets out scan configuration, post-processing (including a novel reflectance filter) and fitting of quantitative structure models (QSM) to reconstruct topologically coherent branch models. This is demonstrated on 595 branches (scanned indoors to negate the impact of wind) and compared with 65 branches that were manually measured (i.e. with measuring tape and callipers). Comparison of a suite of morphological and topological traits reveals a good agreement between TLS-derived metrics and manual measurements where RMSE (\%RMSE) for total branch length = 0.7 m (10\%), volume = 0.09 L (43\%), surface area = 0.04 m2 (26\%) and N tips = 6.4 (35\%). Scanning was faster and invariant to branch size compared with manual measurements which required significantly more personnel time. We recommend measuring a subsample of tip widths to constrain the QSM taper function as the TLS workflow tends to overestimate tip width. The workflow presented here allows for a rapid characterisation of branch architecture from harvested branches. Increasing the number of branches analysed (e.g. many branches from a single tree or branches from many species globally) could allow for a comprehensive analysis of the ‘missing link’ between the leaves and larger diameter branches.},
year = {2021}
}

@Article{treegraph2,
 author = {Wanxin Yang and Phil Wilkes and Matheus B. Vicari and Kate Hand and Kim Calders and Mathias Disney},
 doi = {10.1002/rse2.399},
 issn = {2056-3485},
 journal = {Remote Sensing in Ecology and Conservation},
 month = {6},
 title = {Treegraph: tree architecture from terrestrial laser scanning point clouds},
 year = {2024},
}

@misc{blanco2014nanoflann,
  title        = {nanoflann: a {C}++ header-only fork of {FLANN}, a library for Nearest Neighbor ({NN}) with KD-trees},
  author       = {Blanco, Jose Luis and Rai, Pranjal Kumar},
  howpublished = {\url{https://github.com/jlblancoc/nanoflann}},
  year         = {2014}
}

@manual{coder2021,
  title        = {Tree Anatomy Manual: Twigs},
  author       = {Coder, Kim D.},
  year         = {2021},
  month        = {May},
  organization = {University of Georgia Warnell School of Forestry \& Natural Resources},
  address      = {Athens, GA},
  note         = {Publication WSFNR-21-41C},
}

@article{real_twig_forestry,
    author = {Morales, Aidan and MacFarlane, David W},
    title = {Reducing tree volume overestimation in quantitative structure models using modeled branch topology and direct twig measurements},
    journal = {Forestry: An International Journal of Forest Research},
    pages = {cpae046},
    year = {2024},
    month = {10},
    issn = {0015-752X},
    doi = {10.1093/forestry/cpae046},
    url = {https://doi.org/10.1093/forestry/cpae046},
    eprint = {https://academic.oup.com/forestry/advance-article-pdf/doi/10.1093/forestry/cpae046/59482375/cpae046.pdf},
}

@article{FaNNI,
  author       = {Markku Åkerblom and Pasi Raumonen and Eric Casella and Mathias I. Disney and F. Mark Danson and Rachel Gaulton and Lucy A. Schofield and Mikko Kaasalainen},
  title        = {An algorithm to insert leaves into quantitative structure models of trees},
  journal      = {Interface Focus},
  year         = {2018},
  volume       = {8},
  number       = {2},
  pages        = {20170045},
  doi          = {10.1098/rsfs.2017.0045},
  publisher    = {The Royal Society},
  address      = {England},
  keywords     = {laser scanning, leaf distribution, leaf insertion, quantitative structure model, tree reconstruction},
  issn         = {2042-8898},
  eprint       = {20180216},
}

@article{path_fraction,
  author = {Smith, Duncan and Sperry, John and Enquist, Brian and Savage, V.m and McCulloh, Katherine and Bentley, Lisa},
  year = {2013},
  month = {09},
  pages = {},
  title = {Deviation from symmetrically self-similar branching in trees predicts altered hydraulics, mechanics, light interception and metabolic scaling},
  volume = {201},
  journal = {The New phytologist},
  doi = {10.1111/nph.12487}
}
