# SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds

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## Abstract

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## 1. Introduction

#### 1.1. Related Work

#### 1.1.1. Methods in Computational Forestry producing QSMs of the Branching Structure

#### 1.1.2. Methods in Computer Vision producing QSMs of the Branching Structure

#### 1.1.3. Further Open Source Tree Modelling Software and Point Cloud Processing Libraries

#### 1.2. Relevance of the Presented Work in the State of the Art

#### 1.3. Structure of the Manuscript

## 2. Software—SimpleTree

**Figure 1.**A QSM modelling with SimpleTree of a P. avium cloud:

**(a)**the input cloud coloured by the second principal component [47];

**(b)**over 4500 cylindrical output features are coloured by the diameter of the represented AGB component;

**(c)**secondary derived output features, i.e., single branches, are coloured differently;

**(d)**the branching order of the underlying tree component is coloured differently;

**(e)**an abstract representation of the crown [54].

**Methodname**(a, b) is here-on a wild-card for a method with name

**Methodname**, utilizing input parameters a and b. The dialogues utilized for user input of parameters include useful standard parameters, but to improve the results given by SimpleTree functionalities those standard parameters usually need to be adjusted to the point cloud quality.

#### 2.1. Filter and Clustering Routines

**Curvature Filtering**(min1, max1, min2, max2, min3, max3)

**Figure 3.**Usage of curvature filtering routine. Outlier points, i.e., non woody material points, are coloured red transparent.

**Intensity Filtering**(min, max)

**Crop Sphere | Crop Box**(radius)

#### 2.2. Tree Modeling

**Stem Point Detection**[10] ()

**Voxel-Grid**(0.02) filtered input cloud. If the eigenvalues ${\lambda}_{1}$, ${\lambda}_{2}$ and ${\lambda}_{3}$ fulfil user-hidden thresholds, the point is accepted as a preliminary detected stem point. On these points

**Euclidean Clustering**(0.05, 1, 100) is performed and the output is marked as further detected stem-points. By a simple buffering operation (buffer width = 0.05 m) with the original cloud, the original cloud can be enriched with stem point information. Downscaling and up-scaling was not used in [10] and is now included to improve runtime performance.

**Spherefollowing Method**[10,12] (sphereMultiplier, epsClusterStem, epsClusterBranch, epsSphere, minPtsRansacStem, minPtsRansacBranch, minPtsClusterStem, minPtsClusterBranch, minRadiusSphereStem, minRadiusSphereBranch)

**Euclidean Clustering**($epsClusterStem$, 5 ,$minPtsClusterStem$) into i clusters ${P}_{i}$. The number of returned clusters is set to five, as this is the maximum expected number of cross sectional areas located on a sphere surface. Each cluster represents a cross-sectional area of the stem/branch. A circle is fitted with the Random Sample Consensus (RANSAC) [85,86] algorithm into ${P}_{i}$, if the number of points in ${P}_{i}$ exceeds $minPtsRansacStem$, and with the more robust but less accurate median method proposed in Hackenberg et al. [12] otherwise. The center point of the circle, the center point of the sphere and the circle radius are chosen as cylinder parameters. The circle is enlarged with $sphereMultiplier$ and transformed to a three dimensional sphere. The procedure is repeated recursively until no more cross sectional areas can be found.

**Parameter Optimization**(iterations, criterion, seeds)

**Spherefollowing Method**uses ten input parameters. To enable an automatic search for optimal parameters, initial parameters have to be set by the user. Then a multi-threaded parameter search starts. In each iteration step $seeds$ new parameter sets are created. For one creation each parameter is chosen from a normal distribution centred around the parameter value from the last iteration. For each set a tree model is build. The average euclidean distance from the point cloud to the model is computed. If this distance is smaller than the last found optimal distance, the method stores the distance and the parameter set. If after one iteration the distance improvement is smaller than $criterion$, the search is stopped. If the number of iterations exceeds $iteration$, the search stops. The best parameter set is printed out after completion.

**Allometric improvement**(a, b, fac, minRad)

**Parameter Optimization**, the minimum radius can be automatically computed.

**Crown Computation**(α)

**Figure 5.**Different crown models for a Prunus avium:

**(a)**the convex hull;

**(b)**the α hull with $\alpha =0.2$;

**(b)**the α hull with $\alpha =0.1$.

#### 2.3. Point Cloud Processing

**Merge**()

**Figure 6.**Alignment of a P. avium cloud [12] of winter 2012 to the cloud of of the same tree after pruning in winter 2013:

**(a)**red cloud (2012) and green cloud (2013) are automatically initial aligned;

**(b)**red and green cloud are the same as in

**(a)**, the yellow cloud (2012) is a manually rotated version of the red cloud;

**(c)**the final result - the green cloud is the target cloud and the red one the manually aligned cloud and the yellow cloud the ICP improved version of the red cloud;

**(d)**the final result from another point of view.

#### 2.4. Output Data

**Cloud To Model Distance**

**Single Value Tree Parameters**

**Complete Cylinder Model**

## 3. Software—Comparison Method Raumonen et al. (2013)

**Allometric improvement**was used in a second statistical improvement instead of the taper improvement. Parameters a and b were directly computed per model within the Matlab code with the standard Matlab NLS fitting routine.

**Figure 8.**The variation of the sample means as a function of sample size. The standard deviation and the difference of minimum and maximum sample means are given as percentages to the mean of the distribution.

## 4. Data Sets

#### 4.1. E. fordii

#### 4.2. P. massoniana

#### 4.3. Q. petraea

#### 4.4. Eucalyptus Leucoxylon, Eucalyptus Microcarpa and Eucalyptus Tricarpa

## 5. Results

**Parameter Optimization**(iteration, 0.0001, 81). In six different runs iteration was set to 0, 1, 2, 4, 6 and 8. The

**Spherefollowing Method**(1.8, 0.035, 0.015, 0.025, 500, 1111200, 12, 3, 0.07, 0.03) was additionally improved with the

**Allometric improvement**(240.559, 2.72, 2.5, 0.0025) in the optimization routine. The average standard deviation of the AGB volume prediction per tree in ${m}^{3}$ of five model runs with a fixed number of iteration was calculated first (Figure 9(a)).

**Parameter Optimization**(...) the overestimation for twelve Q. petraea trees is $\sim 1\%$, the error stabilizes at a maximum of $\sim 5\%$ with at least four iterations of the

**Parameter Optimization**(...).

**Parameter Optimization**(...), the ERROR_REL is $\sim 3\%$, leaving an estimated $\sim 2\%$ of total biomass undetected. The accuracy of the AGB volume prediction is with one iteration yet unstable, as the average value for the standard deviation of one tree modelling is $\sim 0.03{m}^{3}$, while it can be reduced to $\sim 0.01{m}^{3}$ with at least one more iteration.

**Figure 9.**Impact on the number of iterations during parameter search on:

**(a)**the average standard deviation of the volume prediction on tree level;

**(b)**the average total relative error of the biomass prediction on complete data set level;

**(c)**the ${R}_{adj.}^{2}$ of the model predicting ground truth biomass from TLS derived biomass;

**(d)**the CCC between ground truth and TLS predicted biomass.

**Figure 10.**Visualization of the modelling of a Q. petraea

**(a)**the input cloud;

**(b)**the model with unoptimized parameters;

**(c)**the model with optimized parameters (six iterations).

**Parameter Optimization**(≥4, 0.0001, 81) the majority of AGB is successfully detected. There seems to be a systematic error of $\sim 5\%$ overestimation in the modelling of the $Q.petraea$. The prediction accuracy on tree level is quantified by a ${R}_{adj.}^{2}$ value of $\sim 0.85$. The systematical error results in a reduction of the CCC to $\sim 0.9$ though, as the overestimation of five percent is hidden by the fact that not all branches are detected with only one iteration, where the CCC reaches its maximum of $\sim 0.93$.

**Allometric Improvement**(240.559, 2.72, 2.5, 0.0025) was analyzed (see Figure 11). The twelve Q. petraea were modelled one time with the statistical improvement and one time without. Each modelling run of the complete data set took ∼10 min. The parameters a and b were computed from the non improved data set, $fac$ was estimated by visual inspection of the same plot (Figure 11(a)). The $minRadius$ was set in a manner, that the tip of the branches had a minimum diameter of half a centimetre (Figure 11(c)), Figure 11(d)).

**Allometric Improvement**(...) leads to a value of 0.85. The overestimation of ∼25.89% is reduced to ∼2.42% with the improvement. The CCC rises from 0.45 to 0.92 (Figure 11(e), Figure 11(f)).

**Spherefollowing Method**(3, 0.035, 0.025, 0.02, 200, 1111200, 3, 5, 0.07, 0.05). In one run with

**Allometric Improvement**(137.498, 2.62, 2.5, 0.0025) inside the

**Parameter Optimization**(6, 0.0001, 81) search (Figure 12(b), Figure 12(d), Figure 12(f)) and one time without those improvements (Figure 12(a), Figure 12(c), Figure 12(e)). In the comparison to the ground truth data the ${R}_{adj.}^{2}$ was improved from 0.81 to 0.95, the ERROR_REL reduced from 34.63% to 3.59% and the CCC improved from 0.65 to 0.97. The calculation with the

**Parameter Optimization**(...) took ∼3.5 h, the other ∼10 min.

**Spherefollowing Method**(1.5, 0.03, 0.02, 0.02, 10, 10, 3, 3, 0.07, 0.025). In one computation the

**Allometric Improvement**(95.551, 2.5, 2, 0.015–0.025) inside the

**Parameter Optimization**(6, 0.0001, 81) search was performed, a second run excluded those improvements.

**Allometric Improvement**(...) was set to a value derived from the automatic parameter search to prevent the smaller branches treated as twigs (Figure 13(a)). Additionally, an NLS model of the form

**Parameter Optimization**(...) took ∼2 h, the other ∼10 min.

**Figure 11.**Effect of the allometric improvement on Q. petraea:

**(a)**the fitted model based on the unimproved data;

**(b)**the fitted model based on the improved data;

**(c)**the model visualization without the improvement;

**(d)**the model visualization with the improvement;

**(e)**AGB estimation without the improvement;

**(f)**AGB estimation with the improvement.

**Figure 12.**Effect of the allometric improvement and the automatic parameter search on P. massoniana:

**(a)**the fitted model based on the unimproved data;

**(b)**the fitted model based on the improved data;

**(c)**the model visualization without the improvement;

**(d)**the model visualization with the improvement;

**(e)**AGB estimation without the improvement;

**(f)**AGB estimation with the improvement.

**Figure 13.**Effect of the allometric improvement and the automatic parameter search on E. fordii:

**(a)**the fitted model based on the unimproved data;

**(b)**the fitted model based on the improved data;

**(c)**the model visualization without the improvement;

**(d)**the model visualization with the improvement;

**(e)**AGB estimation without the improvement;

**(f)**AGB estimation with the improvement.

**Figure 14.**Effect on different statistical radii adjustments in the Raumonen et al. approach [49] for:

**(a)**Q. petraea;

**(b)**P. massoniana;

**(c)**E. fordii.

**Parameter Optimization**(6, 0.0001, 81) utilizing the same parameter set for all 65 trees in the

**Spherefollowing Method**(3.0, 0.1, 0.1, 0.045, 200, 1200, 3, 3, 0.1, 0.1). Parameters a and b were considered poor in the allometric improvement, as the NLS model did not show high quality as other allometric models did (Figure 15).

Method | Error | R ^{2} _{adj.} | CCC |
---|---|---|---|

Raumonen et al. (2013) [49] | 8.80 | 0.97 | 0.98 |

SimpleTree | 7.24 | 0.91 | 0.95 |

**Figure 16.**Comparison of two different QSM methods between ground truth AGB and TLS derived AGB of the species:

**(a)**P. massoniana;

**(b)**Q. petraea;

**(c)**E. fordii;

**(d)**Eucalyptus spp.

## 6. Discussion

**Parameter Optimization**analysis with more than 100,000 modelling runs of Q. petraea).

**Allometric improvement**was introduced as a statistical improvement method to account for this problem. The average error for the Q. petraea models was reduced to 2% with this improvement, Hackenberg et al. [10] results showed here an ERROR_REL of 34%. Fitting an allometric function of the form of Equation (3) can also estimate the AGB of removed twigs, this can be observed for the E. fordii models.

**Allometric improvement**in the Raumonen et al. [49] code, a comparison between the taper and the allometric correction could be performed. For all three data sets, i.e., Q. petraea, P. massoniana and E. fordii clouds, the comparison revealed that the allometric approach seems to be superior to the taper corrections. For E. fordii the additive component to estimate the removed twigs was not utilized in the Raumonen et al. [49] modelling, a further improvement of the results could be expected by implementing this function.

**Allometric improvement**can still be problematic. For Q. petraea and P. massoniana clouds the minimum diameter was set to 0.5 cm in software SimpleTree, as here the cylinder models reached to the tip of twigs. The results proved this approach reasonable. In E. fordii clouds twig-points were removed during the de-noising procedures. A hard-coded threshold of 0.5 cm is therefore not desired. As the quality of the de-noised clouds representing the main branching structure of those trees is still considered high, the automatic search for this parameter was successful. In the Eucalyptus spp. clouds also twigs have been removed, but the cloud quality is poorer here. The point density is lower, noise points could not have been removed as efficiently and the double effect of small twigs due to imperfect co-registration of multiple scans was observed more often. Those reasons forced the optimization routine to find a minimum radius of 4 or 4.5 cm for the majority of trees. SimpleTree reconstructed results should in fact underestimate the ground truth volume for Eucapytus spp. due to the removal of twigs. We assume that the main reason in unexpected overestimation is an overestimated minimum radius.

**Sphere Following**method, while the Eucalyptus spp. data set was used for QSM [49] modelling in Calders et al. [9].

#### 6.1. The Benefit of Open Source

#### 6.2. The Benefit of QSMs

## 7. Outlook

## 8. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Appendix

## A. De-noising

**E. fordii**

**Voxel-Grid Filter**(0.005) was applied to the input cloud. Afterwards an intensity histogram was computed. All points with an intensity larger the histogram maximum plus a user-defined threshold (15) were deleted. With the

**Curvature Outlier Removal**(0,55,0,100,0,100) more needle hits were removed. With a

**Conditional Outlier Removal**(30, 4) isolated points were removed. By

**Euclidean Clustering**(0.02) procedure the tree was separated from remaining artefacts. The whole procedure took 16.5 min for all twelve trees.

**Intensity Outlier Removal**(∼110, 255),

**Euclidean Clustering**(∼0.02) and the

**Crop Sphere**(0.2–1) were used.

**P. massoniana**

**Voxel Grid Filtering**(0.005). Then needle hits were reduced with the

**Curvature Outlier Removal**(0, 45, 55, 100, 0, 45) The two last steps were a

**Statistical Outlier Removal**(30, 0.9) and an

**Euclidean Clustering**(0.02) routine. Running this pipeline took 42 min for all trees. Some large artefacts of other trees remained in the cloud. More automatic removal of noise points has resulted in an unacceptable loss of biomass information.

**Crop Spheres**(0.1–1) and

**Euclidean Clustering**(0.02) on the automatic output.

**Q. petraea**

**Voxel Grid Filter**(0.005). Afterwards a

**Statistical Outlier Removal**(30, 0.5) was performed, followed by an

**Euclidean Clustering**(0.02). The last two steps were repeated one time to further reduce the noise. The complete de-noising took 28.6 min for all trees.

**Crop Spheres**(0.1-1) and

**Euclidean Clustering**(0.02) on the automatic output.

**Eucalyptus leucoxylon, Eucalyptus microcarpa and Eucalyptus tricarpa**

**Curvature Outlier Removal**(0, 55, 0, 100, 0, 100) was used in a first step, followed by an

**Euclidean Clustering**(0.06–0.12). Remaining leaf artefacts were manually deleted with

**Crop Spheres**(0.1–1). The procedure took two hours for all 65 clouds.

## B. Result tables

ID | AGB _{GT} (kg) | AGB_{Hackenberg et al.} (kg) | AGB_{Raumonen et al.} (kg) |
---|---|---|---|

Q1 | 458 | 410 | 469 |

Q2 | 311 | 347 | 422 |

Q3 | 595 | 656 | 756 |

Q4 | 518 | 497 | 537 |

Q5 | 413 | 481 | 488 |

Q6 | 468 | 488 | 543 |

Q7 | 366 | 373 | 544 |

Q8 | 633 | 589 | 674 |

Q9 | 582 | 609 | 657 |

Q10 | 412 | 453 | 588 |

Q11 | 452 | 447 | 533 |

Q12 | 590 | 581 | 719 |

ID | AGB _{GT} (kg) | AGB_{Hackenberg et al.} (kg) | AGB_{Raumonen et al.} (kg) |
---|---|---|---|

E1 | 284 | 234 | 225 |

E2 | 236 | 277 | 207 |

E3 | 268 | 237 | 215 |

E4 | 303 | 330 | 281 |

E5 | 521 | 424 | 375 |

E6 | 156 | 147 | 134 |

E7 | 256 | 229 | 202 |

E8 | 412 | 453 | 376 |

E9 | 443 | 398 | 341 |

E10 | 524 | 490 | 447 |

E11 | 361 | 363 | 293 |

E12 | 315 | 309 | 285 |

ID | AGB _{GT} (kg) | AGB_{Hackenberg et al.} (kg) | AGB_{Raumonen et al.} (kg) |
---|---|---|---|

P1 | 280 | 306 | 272 |

P2 | 113 | 111 | 113 |

P3 | 154 | 170 | 149 |

P4 | 139 | 161 | 140 |

P5 | 185 | 191 | 198 |

P6 | 211 | 215 | 214 |

P7 | 163 | 164 | 172 |

P8 | 38 | 43 | 42 |

P9 | 156 | 179 | 168 |

P10 | 183 | 176 | 175 |

P11 | 234 | 231 | 222 |

P12 | 122 | 100 | 101 |

## C. Abbreviations

AGB | Above Ground Biomass |

AI | Artificial Iintelligence |

ALS | Airborne Laser Scanning |

CCC | Concordance Correlation Coefficient |

CO${}_{2}$ | Carbon dioxide |

DBH | Diameter at Breast Height |

DBSCAN | Density Based Spatial Clustering of Applications with Noise |

DTM | Digital Terrain Model |

ERROR_REL | total RELative - ERROR |

FIFO | First In - First Out (queue) |

ICP | Iterative Closest Point |

LiDAR | Light Detection And Ranging |

NLS | Non-linear Least Squares |

PCA | Principal Component Analysis |

QSM | Quantitative Structural tree Models |

RANSAC | Random Sample Consensus |

RMSE | Root Mean Squared Error |

TLS | Terrestrial Laser Scanning |

VLS | Vehicle-based Laser Scanning |

Radius Outlier Removal | |

r | the radius for the ϵ-neighbourhood search |

k | the minimum number of points in range r |

Statistical Outlier Removal | |

k | the number of nearest neighbours used for |

computing mean and standard deviation of distances | |

sdMult | the standard deviation is multiplied by this factor and |

added and subtracted from the mean for a range | |

Voxel Grid Filtering | |

cellsize | the cell-size of a voxel in which all points are merged |

Curvature Filtering | |

minX/maxX | range parameter for the eigenvalue ${\lambda}_{X}$ |

Intensity Filtering | |

min/max | range parameter for the intensity |

Crop Sphere | |

radius | the radius of the deletion sphere |

Euclidean Clustering | |

clusterTolerance | the minimum distance between two clusters |

minPts | the minimum number of contained points for a cluster creation |

numCluster | the maximum number of returned clusters |

Euclidean Clustering | |

sphereMultiplier | the factor of enlargement in the circle to sphere transformation |

epsClusterStem | the cluster tolerance for stem points |

epsClusterBranch | the cluster tolerance for branch points |

epsSphere | the search size around the sphere surface |

minPtsRansacStem | the minimum number of stem points for RANSAC fit |

minPtsRansacBranch | the minimum number of branch points for RANSAC fit |

minPtsClusterStem | the minimum cluster size for stem points |

minPtsClusterBranch | the minimum cluster size for branch points |

minRadiusSphereStem | the minimum radius for a sphere build from stem points |

minRadiusSphereBranch | the minimum radius for a sphere build from branch points |

Allometric Improvement | |

a | parameter of NLS fit |

b | parameter of NLS fit |

fac | a is divided by $fac$ for a minimum radius value computation |

minRad | the minimum radius of a cylinder after the improvement |

Parameter Optimization | |

iterations | the maximum number of iterations |

criterion | the minimum improvement for a new iteration to start |

seeds | the number of random seeds of parameter sets per iterations |

Crown Computation | |

α | parameter for α-shape computation |

Iterative Closest Point | |

β | the rotation angle for the alignment of two clouds |

## D. Sphere Following Routine

**Figure C1.**A sphere utilized by the cylinder fitting routine extracting a sub point cloud on the sphere surface (figure taken from Hackenberg et al. [12]).

**Figure C2.**The fitted circle is used to generate a finite cylinder (figure taken from Hackenberg et al. [12]).

**Figure C3.**The circle is transformed to a sphere and the procedure is repeated (figure taken from Hackenberg et al. [12]).

**Figure C4.**The sphere-following algorithm reaches a branch junction:

**(a)**multiple clusters are located on the sphere surface;

**(b)**into each cluster a circle is fitted and transformed to a sphere.

#### D.1. Post Processing

**Figure C7.**Merging of successive cylinders :

**(a)**before the merge operation;

**(b)**after the merge operation.

**Figure C8.**Merging of successive cylinders :

**(a)**before the merge operation;

**(b)**after the merge operation.

**Figure C9.**The effect of the cylinder fitting improvement :

**(a)**one cylinder of the stem is bad fitted before the improvement;

**(b)**the same cylinder represents the stem form better after the improvement.

**Figure C10.**The effect of the radius median segment check :

**(a)**one cylinder of a branch is overestimated before the improvement;

**(b)**the cylinder’s radius is set to the median radius of it’s segment.

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**MDPI and ACS Style**

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.
https://doi.org/10.3390/f6114245

**AMA Style**

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(11):4245-4294.
https://doi.org/10.3390/f6114245

**Chicago/Turabian Style**

Hackenberg, Jan, Heinrich Spiecker, Kim Calders, Mathias Disney, and Pasi Raumonen.
2015. "SimpleTree —An Efficient Open Source Tool to Build Tree Models from TLS Clouds" *Forests* 6, no. 11: 4245-4294.
https://doi.org/10.3390/f6114245