# Annual Shoot Segmentation and Physiological Age Classification from TLS Data in Trees with Acrotonic Growth

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## Abstract

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## 1. Introduction

## 2. Description of the Annual Shoot Segmentation Model

- The segment that is the elementary element of a skeleton defined by 3D coordinates of its starting and ending points and by its unique identifier.
- The skeleton’s axes (axes${}_{Sk}$) are a linear assemblage of connected segments starting from a branching point (or at the tree base for the trunk) and ending at a tip of the skeleton (i.e., a segment without a child segment).

- data preparation prior to annual shoot segmentation (steps 1 to 4)
- annual shoot segmentation (steps 5 and 6)
- annual shoot classification into physiological ages (step 7)

#### 2.1. Data Preparation Prior to Annual Shoot Segmentation (Steps 1 to 4)

**Step 1.**By default, a skeleton is composed of only segments, and, the axes${}_{Sk}$ have to be retrieved from a hierarchy among the segments and the geometry of the skeleton. To do so, the hierarchy among connected segments (i.e., parent/child relationships) is first computed for the entire skeleton (Figure 2, Step 1).

**Step 2.**Segments are then grouped into axes${}_{Sk}$ using an iterative hierarchical process so that an axis always follow the longest path from its starting point to a branch tip (Figure 2, Step 2). Starting with the segment (S${}_{init}$) wtih the smallest z value (i.e., the trunk basis), the child segment that bears the longest branched system (longest in terms of the cumulative length) among all child segments (S${}_{children}$) is assumed to belong to the parent segment’s axis${}_{Sk}$. This process continues until no S${}_{children}$ are found (i.e., the axis tip is reached), and the process restarts with a new S${}_{init}$ being an unclassified child of an already classified segment.

**Step 3.**Once axes${}_{Sk}$ are segmented, the skeleton is smoothed in order to improve further axis length computation. To do so, the segment tip and base of the axes${}_{Sk}$ are displaced in order to reduce the deviation between three successive axis segments (see Figure 3 for an illustration). This step is performed iteratively until no additional modifications are conducted.

**Step 4.**After skeleton smoothing, the geodesic distance of each axis${}_{Sk}$ segment tip relative to the axis${}_{Sk}$ base is computed, as is the number of child axes${}_{Sk}$ of each segment of the structure (Figure 2, Step 4).

**Figure 2.**Illustration of the entire workflow (seven steps) involved in the annual shoot segmentation and physiological age classification model. On the left, a complete list of steps and illustrations of some steps and substeps of the algorithm. On the right, screen shots of the skeleton of a real tree at the end of key steps showing the entire tree and, in some cases, the detail of the tree base. In the screen shots, the colours correspond to the axis ID (step 2), the segmented annual shoots before non-branches axes correction (step 6.3), the corrected annual shoot segmentation (step 6.4), and the physiological ages (step 7, PA1 in black, PA2 in red, PA3 in green, and PA4 in blue). Note that substeps 6.1, 6.2, and 6.3 are illustrated in more detail in Figure 4.

**Figure 3.**Illustration of the structure smoothing for three axis segments. If a modification is needed (i.e., the case illustrated at the bottom), the point that makes the junction between the second and third axis segments is moved to the averaged location between the base of the second and the tip of the third axis segment.

**Figure 4.**Illustration of the annual shoot segmentation along the trunk of an 8-year-old simulated tree composed of 105 segments. The input data (

**a**) consists of a set of segments (dots of a dashed line), here presented with a schematic representation of their child axes${}_{Sk}$ (with the axes${}_{Sk}$ in green being used in the L${}_{2}$ metric computation and those in red being excluded). Note that the annual shoots of the main axis are represented by a bicolour line for the purpose of clarity. The L${}_{2}$ metric of each segment is then computed (bar height in (

**b**)). The segments are then grouped into clusters based on their L${}_{2}$ metric, and the clusters are ranked by increasing order of L${}_{2}$ metric (bar height in (

**c**)). An evolutive threshold (black line in (

**c**)) is then used to identify the tips of the annual shoots (arrows in (

**c**). The output is the segmented annual shoots (shown in black and grey in (

**d**)). Note that the annual shoots located near the tree base are not segmented by the method as the trunk base is not branched (compare annual shoots in (

**d**) to those in (

**a**)). Note that the steps indicated on the left of the figure correspond to the steps illustrated in Figure 2.

#### 2.2. Annual Shoot Segmentation (Steps 5 and 6)

- acrotony occurs at least on the main axes of the tree structure
- -
- the longest lateral axes are close to the AS tip,
- -
- an AS ends immediately or shortly after the last branching point, and
- -
- annual shoots are composed of only one growth unit (i.e., there is no polycyclism) so that branching occurs close to the tip of the AS.

- an AS produced at year n can only bear an AS produced at year $n+1$

**Step 5.**For each segment of an axis${}_{Sk}$, a metric describing the length of its child axes${}_{Sk}$ is first computed. This metric corresponds to the length of the lateral axes${}_{Sk}$ of the segment plus the length of their respective child axes${}_{Sk}$. As this metric refers to the length of the child axes of order $BO+1$ and $BO+2$ ($BO$ being the branching order of the target segment), we refer to it as the secondary order length (L${}_{2}$ metric, Figure 4a,b). The L${}_{2}$ metric is used as it captures the lateral axes complexity better than the length of the main axis${}_{Sk}$ while reducing the importance of the skeleton quality variations when comparing two lateral axes${}_{Sk}$, e.g., when comparing the length of an axis${}_{Sk}$ located in a poorly reconstructed part of the skeleton (due to low point cloud density) to the length of a better-defined axis${}_{Sk}$.

**Step 6.1**. After computation of the L${}_{2}$ metric, segments are grouped into k clusters based on their L${}_{2}$ metric. This transformation allows us to group segments with similar L${}_{2}$ metric, which enables us to mitigate the effect of small differences in L${}_{2}$ when comparing two segments. This also allows us to apply a simple thresholding approach to segment annual shoots, which results in simpler and more robust AS segmentation than if it is based on the raw L${}_{2}$ metric. The clustering is performed using hierarchical aggregative clustering with Ward’s method [43,44] (Figure 4c), implemented in R in the

`hclust`function [45]. This method iteratively groups single observations by minimizing the within-group dispersion at each fusion. The resulting dendrogram is then pruned in order to maintain k clusters. In the model, the optimal k is defined as the minimal number of clusters so that every non-branched segment (i.e., with L${}_{2}$ = 0) is grouped into one single cluster. This approach was found to be more efficient than partitioning clustering methods (e.g., regression trees) for quickly isolating non-branched segments to produce a reasonably small k and was favoured over non-hierarchical clustering methods (e.g., k-means) as the latter usually performs better in multidimensional space. Clusters are then ranked based on their L${}_{2}$ so that $C1$ has an average L${}_{2}$ of 0 and $C2<C3<C4<\dots <Ck$ (Figure 4 compares cluster rank in c to L${}_{2}$ in b).

**Steps 6.2 and 6.3.**The clusters are then used as the basis for AS segmentation. In acrotony, lateral axes located at the tip of an AS are expected to be longer than those located near the base of the AS. At the same time, lateral axes that initiate near the base of the parent axis are older, so they are expected to have a larger L${}_{2}$ metric and, therefore, belong to a higher cluster. To accommodate these two nested patterns, an evolutive threshold (t) is used. It starts with a value ${t}_{0}=2$, and, moving from the axis tip to the axis base, a new AS tip is added to the segment ${S}_{i}$ if ${C}_{i}\ge {t}_{i}$ and ${C}_{i-1}<{t}_{i}$, and at the same time ${t}_{i}={t}_{i-1}+1$, $if{C}_{i}>{t}_{i}$ (see Figure 4c for an illustration).

- The AS are correctly segmented. This is usually the case for axes${}_{Sk}$ of small order (i.e., main branches and trunk). This is because large axes usually bear many child axes, which are usually well reconstructed by skeletonization methods and because branching accidents are relatively rare in axes of lower order.
- The AS are not segmented. This is typically the case for axes${}_{Sk}$ of higher order (i.e., short axes) that are usually not branched or poorly branched. This results in an AS longer than it should be (compare steps 6.4 to 6.3 in Figure 2).
- Oversegmentation (i.e., the addition of an AS that does not exists in reality) occurs. This results in an AS shorter than it should be, usually one segment long and mostly occurring at the tip of an annual shoot.

**Step 6.4**. After AS segmentation, each axis${}_{Sk}$ is tested for potential segmentation errors. This test is based on assumptions that the segmentation of the main axis${}_{Sk}$ (that starts at the tree base and ends at the tip of the skeleton) is perfect and that an AS produced at year n can only bear AS produced at year $n+1$. For each axis, the year of the first AS is compared to the bearer of the annual shoot, and three results can occur depending on the above cases:

- if $beare{r}_{year}-chil{d}_{year}-1=0$, the annual shoots of the axis are correctly segmented (case 1)
- if $beare{r}_{year}-chil{d}_{year}-1>0$, some annual shoots are not segmented (case 2)
- if $beare{r}_{year}-chil{d}_{year}-1<0$, some supernumerary segmentation occurred (case 3)

#### 2.3. Classification of Physiological Ages

**Step 7**. A physiological age is then assigned to each segmented AS based on its length. A previous attempt to automatically retrieve AS types (a concept derived from the concept of PA) from field measurements was based on a combination of topological information and morphological measurements [5]. Other research has shown that morphological and functional variables scale with the AS length [2,3]. Therefore, in the present study, we decided to use the AS length as input for PA classification as it can be applied directly to the AS segmented in a skeleton. PA assignment thus requires the user to provide length thresholds that will be used to make the distinction between two PA. More details on the method we used to retrieve these thresholds from field measurement is provided in Section 3.1.2.

## 3. Material and Methods

- at the tree and AS level using “perfect data”
- at the tree level using simulated TLS data

#### 3.1. Tree Sampling, Modeling, and Physiological Age Classification

#### 3.1.1. Sampled Trees and Architectural Measurements

#### 3.1.2. Physiological Age Classification from Manual Measurements

- mean value of the distribution: mu = 2 cm, 10 cm, 30 cm, and 50 cm
- standard deviation: sigma = 10
- the (optional) proportion of the data contained in each distribution (pi) is not provided

`kendall`and

`kruskal`functions from the agricolae R package [49].

#### 3.1.3. Architectural Model Calibration

#### 3.2. TLS Simulations

#### 3.3. Simulated TLS Data Skeletonization

#### 3.4. Comparisons of Modeled vs. Simulated Annual Shoots and Physiological Ages

#### 3.5. Improving the Reconstruction through Non-Reconstructed Axes Modeling

- Markov chains were used to determine branching probabilities in order to estimate pPA4 and position modeled PA4 axes along an AS (using parameters shown in Supplementary Materials Figure S1b)
- binomial distributions were used to generate random PA4 ASs (using parameters shown in Supplementary Materials Figure S1c)

#### 3.6. An Example from the Real World

#### 3.6.1. Tree Sampling and QSM Reconstructions

#### 3.6.2. A New Functionality of the Annual Shoot Segmentation Model

- Near the trimming point (i.e., at the crown center), which results in highly heliotrope branches (i.e., nearly vertical) borne via old branches.
- On the trunk bellow the crown, which results in a less vertical TR orientation and TRs that emerge on older branches compared to case one.

## 4. Results

#### 4.1. Physiological Ages Partitioning and Functional Attributes

#### 4.2. Testing the Algorithm against Perfect Data

#### 4.3. Testing the Algorithm against Skeletons Obtained from Simulated TLS Data

#### 4.4. Real-Life Example

## 5. Discussion

#### 5.1. Model Accuracy, Possible Applications, and Limitations

- the capacity of the QSM and skeletonization methods to capture all the finest details of the point cloud; and
- the stage of development that influences the branching pattern, especially due to the drift effect [1]. This would limit the applicability of this method to large trees that do not express acrotony anymore.

#### 5.2. On the Use of Distribution Mixture Models to Retrieve Annual Shoot Physiological Ages

#### 5.3. Toward a More Complex Model

## Supplementary Materials

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Illustration of the differences between the botanical term (

**left**) and the terms used to describe the skeleton components (

**right**). On the left, = corresponds to the annual shoot delimitation.

**Figure 5.**A tree simulated with the AmapSim model at 8, 12, and 15 years of age. The arrows indicate the location of the reiteration that occurs at age 10.

**Figure 6.**Scenes, sampling plan, and simulated scans for a row of ten 13-year-old trees. The scene of the row, i.e., the mesh created from the mtg files, from above (

**a**) and from the front (

**b**). In (

**a**,

**b**), the TLS positions are represented by the purple diamonds except for one scan position for which the tripod and TLS device as well as its lateral viewing angle are shown. The resulting point clouds for the entire row (

**c**) and the details for one tree (

**d**) are shown after applying the statistical outliers filter.

**Figure 7.**Comparison between the skeletons of a 10-year-old simulated tree extracted using the PypeTree (

**left**) and SimpleTree (

**right**) models. The whole tree (

**top**) and details of a branch (

**bottom**) with the segments shown in black and grey.

**Figure 8.**Manual measurement of annual shoots leaf area ((

**a**), $\tau $ = 0.746), leaf area:shoot volume ratio ((

**b**), $\tau $ = −0.809) and leaf area display ((

**c**), $\tau $ = −40.592) as a function of annual shoots length. The colours indicate the annual shoots’ physiological ages retrieved from the distribution mixture model (legend on the graph).

**Figure 9.**Distribution mixture of annual length to retrieve annual shoot physiological ages (PA). Four normal distributions (continuous curve) are fitted to the frequency distribution of annual shoot length (grey histograms) to build the distribution mixture model (dotted curve). The black triangles show the average value of each distribution, and the vertical lines show the position of intersections between two distributions used to retrieve PAs.

**Figure 10.**Total length of the annual shoots of each physiological age (PA) classified with the annual shoot segmentation model as a function of the the total length observed in the output file of the AMAPsim model for the corresponding PA; 110 trees were simulated at different ages ranging from 5 to 15 years (10 trees per age). The dotted line represent the 1:1 relation. The Mean Absolute Percentage Error (mape, %) and Mean Prediction Error (mpe) are indicated on the graphs.

**Figure 11.**Mean absolute error and mean absolute percentage error (±standard deviation) of individual annual shoot length segmented by the annual shoot segmentation model as a function of production year for each physiological age (PA). Note that the y axis scale is the same for both indicators and that annual shoot year = 1 corresponds to the current year annual shoot.

**Figure 12.**Evaluation of skeletonization and annual shoot segmentation in 110 simulated terrestrial laser scanning (TLS) scans of 110 simulated trees (5 to 15 years with 10 trees per age) reconstructed with two quantitative structural model (QSM) methods. Number of segmented annual shoot (

**a**) and total reconstructed length (

**b**) cumulated at the tree level. Evaluations were done against the real AS number and length observed in the output of the AMAPsim model. The dotted line represents the 1:1 relation. The Mean Absolute Percentage Error (mape, %) and Mean Percentage Error (mpe, %) are indicated on the graphs.

**Figure 13.**Evaluation of skeletonization and annual shoot segmentation in 110 simulated TLS scans of 110 simulated trees (5 to 15 years with 10 trees per age) reconstructed with two QSM methods. Number of segmented annual shoot (

**a**) and total annual shoot length (

**b**) in each physiological age (PA). Evaluations are done against the AS number and length observed in the output file of the AMAPsim model. The dotted line represents the 1:1 relation. The Mean Absolute Percentage Error (mape, %) and Mean Percentage Error (mpe, %) are indicated on the graphs.

**Figure 14.**Number and length of PA4 annual shoots and reconstructed total length after the addition of non-reconstructed PA4 using a simple architectural automaton. The number of annual shoot is evaluated for PA4 only (

**a**) or for all PA at the tree level (

**c**) as well as the total reconstructed length ((

**b**,

**d**), respectively). The Mean Absolute Percentage Error (mape, %) and Mean Percentage Error (mpe, %) are indicated on the graphs.

**Figure 15.**Skeletons of six red ashes from a trimming experiment obtained with the SimpleTree QSM model with segmented annual shoots (Segmented) and annual shoots classified into four physiological ages (Classified) using the parameters described in Table 1. In the classified annual shoot, TR (purple) corresponds to traumatic reiterations that occurred after tree trimming.

**Table 1.**Parameters of the four distributions that constitute the distribution mixture model: average value, standard error, proportion of data in the distribution, and the length thresholds that were used to classify annual shoots into physiological ages (PA).

Average | se | % Data | Range | |
---|---|---|---|---|

PA1 | 58.06 | 2.09 | 1.47 | 54.51+ |

PA2 | 20.76 | 14.42 | 34.31 | 13.24–54.51 |

PA3 | 6.96 | 3.38 | 38.11 | 3.7–13.24 |

PA4 | 1.8 | 1.24 | 26.1 | 0–3.7 |

**Table 2.**Morphological and functional variables as a function of the four annual shoot physiological ages (PA) created with the distribution mixture model. The groups (gr) correspond to pairwise comparisons using the Kruskal–Wallis test with ($\alpha $ = 0.05).

LA (cm${}^{2}$) | LAD (cm${}^{2}$.cm${}^{-1}$) | L:S (cm${}^{2}$.cm${}^{-3}$) | ||||
---|---|---|---|---|---|---|

Mean (±sd) | gr | Mean (±sd) | gr | Mean (±sd) | gr | |

PA1 | 2478 (±933.25) | a | 30.39 (±7.34) | d | 0.28 (±0.14) | d |

PA2 | 973.76 (±453.39) | b | 37.55 (±12.46) | c | 1.02 (±0.73) | c |

PA3 | 537.26 (±222.44) | c | 73.85 (±30.95) | b | 3.99 (±2.95) | b |

PA4 | 271.76 (±136.70) | d | 296.17 (±230.60) | a | 21.06 (±18.22) | a |

**Table 3.**Length and annual shoot number in six red ashes from a tree trimming experiment. The total (number or length) as well as the total for each classified annual shoot types are presented (ST1 to 4 and traumatic reiterations, TR).

Annual Shoot Length | ||||||

Total (m) | PA1 (m-%) | PA2 (m-%) | PA3 (m-%) | PA4 (m-%) | TR (m-%) | |

Heavy 1 | 42.02 | 3.72–8.89 | 17.26–40.08 | 6.78–16.14 | 4.19–9.97 | 10.07–23.96 |

Heavy 2 | 43.61 | 1.39–3.19 | 17.52–40.17 | 10.44–23.94 | 4.75–10.89 | 9.51–21.81 |

Medium 1 | 132.19 | 6.5–4.92 | 70.15–53.07 | 34.14–25.83 | 14.31–10.83 | 7.09–5.36 |

Medium 2 | 76.41 | 3.75–4.91 | 44.09–57.70 | 17.68–23.14 | 5.88–7.70 | 5.01–6.56 |

Control 1 | 153.76 | 18.73–12.18 | 76.28–49.61 | 45.06–29.31 | 13.69–8.90 | - |

Control 2 | 215.18 | 39.77–18.48 | 110.02–51.13 | 51.88–24.11 | 13.51–6.28 | - |

Number of Annual Shoot | ||||||

Total (n) | PA1 (n-%) | PA2 (n-%) | PA3 (n-%) | PA4 (n-%) | TR (n-%) | |

Heavy 1 | 243 | 8–3.29 | 62–25.51 | 70–28.81 | 83–34.15 | 20–8.23 |

Heavy 2 | 288 | 1–0.35 | 74–25.69 | 94–32.64 | 94–32.64 | 25–8.68 |

Medium 1 | 1098 | 9–0.81 | 280–25.50 | 366–33.33 | 426–38.80 | 17–1.54 |

Medium 2 | 455 | 5–1.20 | 151–33.20 | 160–35.16 | 130–28.57 | 9–1.98 |

Control 1 | 1021 | 29–2.84 | 262–25.66 | 435–42.61 | 295–28.89 | - |

Control 2 | 1349 | 66–4.89 | 412–30.54 | 535–39.65 | 336–24.91 | - |

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**MDPI and ACS Style**

Lecigne, B.; Delagrange, S.; Taugourdeau, O.
Annual Shoot Segmentation and Physiological Age Classification from TLS Data in Trees with Acrotonic Growth. *Forests* **2021**, *12*, 391.
https://doi.org/10.3390/f12040391

**AMA Style**

Lecigne B, Delagrange S, Taugourdeau O.
Annual Shoot Segmentation and Physiological Age Classification from TLS Data in Trees with Acrotonic Growth. *Forests*. 2021; 12(4):391.
https://doi.org/10.3390/f12040391

**Chicago/Turabian Style**

Lecigne, Bastien, Sylvain Delagrange, and Olivier Taugourdeau.
2021. "Annual Shoot Segmentation and Physiological Age Classification from TLS Data in Trees with Acrotonic Growth" *Forests* 12, no. 4: 391.
https://doi.org/10.3390/f12040391