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BayesForest: a data-driven generator of clonal tree morphologies

BayesForest is an algorithm for realistic modeling of morphological tree clones. Here the morphological clones are defined as trees similar (and not the same) at the tree-level structure with varying fine-scale structural detail.

The BayesForest algorithm is composed of several sub-algorithms ultimately connected to each other and constituting an algorithmic pipeline. The pipeline is highly flexible and each of the choices of the pipeline can be substituted when needed depending on efficiency or application.

BayesForest Toolbox is a Matlab-based programmable wrapper for running the pipeline, handling necessary data, and facilitating tree morphology exploration.

Essence

BayesForest produces clonal tree morphologies by iteratively minimizing a "distance" between empirical distributions of structural features of DATA and MODEL trees by varying parameters of the (stochastic) MODEL. The resulting best-fit MODEL tree has "optimal" parameter values that generate trees statistically similar to the DATA tree, but not exact copies of each other.

Main constituents

BayesForest is based upon five distinct parts:

1. Quantitative Structural Model (QSM): the DATA tree. We propose using Terrestrial Laser Scanning (TLS) for generating QSM — faster obtaining of the raw data and easier extraction of the model with geometry and topology defined (see the reconstruction algorithm in [1] and its validation in [2-5].

2. Stochastic Structural Model (SSM): the MODEL tree, an analytical tree growth model with (some) stochastic rules of growth. The usual application specific choice is a Functional-Structural Plant Model (FSPM) as in [6]; structural model with heuristic rules for growth (SHM or procedural model) is a better choice for more general purpose (as in [7]).

3. Structural data set U, that is a collection of structural features (empirical distributions) relating different physical dimensions as well as spatial location of various parts and segments of a tree with optional sorting by the topological order.

4. Measure of structural distance/dissimilarity D_S, that is a measure of proximity between any two data sets.

5. Optimization routine, that is a numerical procedure capable of finding a minimum of any given function (Newton algorithm, genetic algorithm etc.).

Algorithm outline

The connection between the main components is outlined in the main figure above.

Stage A: Preparation

Stage A is a preliminary phase, in which:

• QSM is reconstructed from the TLS point cloud from a real tree; geometrical and topological relationships are reconstructed too;
• QSM is processed to yield the structural data sets U_d.

Stage B: Main cycle

Stage B is an iterative optimization process, thus it is a cycle, in which:

• SSM is simulated for a given parameter set;
• structural data sets U_m are extracted from SSM;
• comparison is done between U_d and U_m by means of the distance;
• SSM parameters are adjusted and the cycle is repeated.

The optimization algorithm makes sure that the distance decreases in each iteration of the cycle. The exit from the cycle is attained when no improvement of the distance is possible. The minimum distance SSM is called "best-fit" SSM.

The best-fit SSM, being a stochastic model, can generate morphological clones, given different random sequences used in the SSM simulation.

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References

[1] Raumonen P, Kaasalainen M, Åkerblom M, Kaasalainen S, Kaartinen H, Vastaranta M, et al. Fast Automatic Precision Tree Models from Terrestrial Laser Scanner Data. Remote Sensing. 2013;5:491-520.

[2] Calders K, Newnham G, Burt A, Murphy S, Raumonen P, Herold M, et al. Nondestructive estimates of above-ground biomass using terrestrial laser scanning. Methods in Ecol Evol. 2015;6:198-208.

[3] Hackenberg J, Spiecker H, Calders K, Disney M, Raumonen P. SimpleTree - an efficient open source tool to build tree models from TLS clouds. Forests. 2015;6:4245-4294.

[4] Kaasalainen S, Krooks A, Liski J, Raumonen P, Kaartinen H, Kaasalainen M, et al. Change Detection of Tree Biomass with Terrestrial Laser Scanning and Quantitative Structure Modeling. Remote Sensing. 2014;6:3906-3922.

[5] Raumonen P, Casella E, Calders K, Murphy S, Åkerblom M, Kaasalainen M. Massive-scale Tree Modelling from TLS Data. ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences. 2015;II-3/W4:189-196.

[6] Ilya Potapov, Marko Järvenpää, Markku Åkerblom, Pasi Raumonen, Mikko Kaasalainen, Data-based stochastic modeling of tree growth and structure formation, Silva Fennica, 50, 2016. http://dx.doi.org/10.14214/sf.1413

[7] Ilya Potapov, Marko Järvenpää, Markku Åkerblom, Pasi Raumonen, Mikko Kaasalainen, Bayes Forest: a data-intensive generator of morphological tree clones, GigaScience, free online: https://doi.org/10.1093/gigascience/gix079.