#### 1.1.1. TLS Derived Volume Estimations

All methods presented in this subsection estimating the above ground volume of trees directly are considered to have the potential to predict biomass by including density analyses. Works focusing on the extraction of parameters like the DBH and height can also be used if accurate allometric models are available. In addition non forestry related tree modeling approaches are included to a minor extent, as these works can still have an impact in computational forestry if their accuracy is validated in future research.

Early approaches for the estimation of forestry parameters from terrestrial point clouds have already been carried out in 2003. Simonse

et al. [

7] first determined a digital terrain model (DTM) by selecting the lowest points from the input cloud and extracted according to the DTM a layer corresponding to the hight of 1.3 m. In this layer the authors fitted circles in stem sections with the application of a Hough transform. Ground truth comparison was applied to estimated tree positions. For most trees a difference of less than 20 cm to the reference data could been carried out. Comparison regarding the DBH resulted in a standard deviation of 2.8 cm.

In 2004, Thies

et al. [

8] used registered TLS data derived from three scan positions per tree to perform a more accurate stem modeling. Two stem of different tree species, namely

Fagus sylvatica (beech) and

Prunus avium (cherry), were modeled by fitting cylinders into the point cloud. The non-linear fitting method for estimating the cylinder parameters minimized the square sum of residuals to the cylinder surface. The beech stem was modeled with 75 overlapping cylinders with a length 0.5 m each. The cherry stem was modeled with 59 cylinders in total. Both stems could be modeled to the height of the first fork. A root mean square error (RMSE) of 1.7 cm of the fitted cylinders was calculated and also a ground truth comparison to DBH measurements was applied, showing a deviation of −1.3 cm and 0.6 cm for both trees respectively.

These publications represent two different trends in retrieving forestry parameters from TLS data applied during the last decade. Various works focus on single trees manually extracted to gain a high level of information. Others determine less accurate parameters, often just DBH and height, but cover a larger area of interest, e.g., hectare sized plots [

5].

Plotwise detection methods for forestry parameters are well reported within the literature:

Four plots were scanned by Bienert

et al. [

9] in both single and multiple scan mode. A DTM was extracted by using density variation along the

z-axis. By a clustering operation followed by a circle fitting routine trees were detected in a 10 cm thick slice 1.3 m above the DTM. Output data partially consisted of the relative coordinates of each tree. After isolating the detected trees, DBH and height were also estimated for each individual tree. A DBH comparison to manual collected reference data resulted in a standard deviation between 1.21 cm and 2.47 cm.

Moscal

et al. [

10] developed an algorithm called point cloud slicing (PCS) algorithm where DBH, height, basal area and volume of trees could be calculated. The data was collected in single scan mode and then transferred to the voxel domain. After generating a DTM, a slice at 1.3 m height was produced to estimate DBH by cylinder fitting applying the least squares method. Height was predicted as the difference between minimum and maximum

z-coordinates and volume was obtained by summing up the volumes of all voxels. Validation was accomplished by comparison to single tree measurement of DBH, stem location and tree height. TLS methods captured 91.17% of the variation of DBH, but on average only 57.27% of tree height was predicted.

Concerning modeling individual trees at a higher level of detail, various works have been reported in literature:

Pfeifer

et al. [

11] were the first authors found in literature to fit cylinders representing both stem and branches into multiple scan mode point clouds by non-linear least squares fitting. Single trees were extracted and cylinders fitted by five parameter determination. As proposed by Thies

et al. [

8], cylinders have been shifted backward and forward to get an approximate position of the next cylinder. NLS methods need accurate starting parameters, while nowadays being reported to be more accurate than Hough transforms [

12]. Stem and branches were only partially detected. Quality assessment was performed through visual inspection and also by the calculation of a RMSE of 1.8 cm between the cylinders and their allocated points.

Eysn

et al. [

13] modeled 120 trees in a 0.65 ha sized area using 34 scan positions. The individual scan positions were registered into a common coordinate system. Yet each scan was processed independently. Through the manual digitization of stem and branch axes in AUTOCAD software all scans were handled as a two dimensional range or intensity map. After this manual step an automatic computation of cylinder radii was applied. Validation was performed by investigating deviations between the model and their corresponding TLS point clouds applied on five randomly selected trees. The mean deviation was between 2 mm and 6 mm for these trees, with a standard deviation of 1 cm for one tree and 2 cm for the others.

Bayer

et al. [

14] used a manual skeletonization method on extracted point clouds of single trees in leaves. The tree skeleton served as a basis for further automatic computation of branch angles, branch length and branch bending. Furthermore, by using α-shapes [

15] on points allocated to a branch section the authors could calculate the space requirement of the branches by summing up the volumes of all tetrahedrons being part of the α-shape. Comparison with ground truth data was not applied. This work is mentioned, as further research on α shapes of branches might result in deeper knowledge about the photosynthesis potential of trees which is related to the growth of biomass.

Dassot

et al. [

16] determined the skeletons of 42 trees manually with Polyworks software. After an automatic cylinder fitting routine utilizing 25 cm long skeleton segments as input data, wrongly fitted cylinders were identified and removed manually. Gaps in the resulting cylinder model were linearly interpolated. Comparison of the modeled volume to ground truth measurements revealed a relative error in the range of 10% for the stems and in the range of 30% for branches with a diameter larger than 7 cm. Buksch

et al. [

17,

18,

19] developed an automatic method to determine a tree skeleton using point cloud data. The authors generated an octree search structure [

20] of the input points. By using the neighborhood information of the octree cells a graph was extracted and contained cycles in the graph were removed. The resulting graph represented the tree skeleton. Goodness of fit evaluation was performed by calculating and depicting distances between the points and the predicted skeleton.

Xu

et al. [

21] found a way to calculate tree models by applying the Dijkstra algorithm [

22], which is normally used for the solution of shortest paths determination in way finding routines. Every point was linked with neighboring points resulting in a connected graph. Along this graph for every node the shortest path from a preselected root point was calculated with the Dijkstra algorithm. The lengths of these paths were quantized and clustered into bins. Then a skeleton was formed by connecting centroids of adjacent bins. This method was further applied by Livny

et al. [

23]. Both publications aim for computer vision modeled trees rather than on the estimation of forestry parameters. All three presented tree skeletonization methods work automatically and the skeletons can be used as input data in tree modeling algorithms relying on manual derived tree structures,

i.e., [

13,

14,

16].

Belton

et al. [

24] extracted evergreen trees manually from TLS raw data. By performing a principal component analysis (PCA) they were able to estimate parameters like the curvature of the surface represented by each points neighborhood. After clustering operations through a Gaussian mixture model [

25] utilizing these parameters leaf points were removed from the input point cloud. By connecting ellipses fitted in horizontal slices the tree skeleton was extracted. This skeleton was used as input data for a cylinder fitting routine. The volume of the tree was calculated by summing up the cylinders’ volumes. The authors compared the results (74 m

^{3}) to the estimated volume of an allometric function (34 m

^{3}).

Raumonen

et al. [

26] performed a PCA on small subsets of the point cloud. The eigenvectors were used to automatically extract skeleton lines of the underlying branch segments. Neighboring subsets belonging to the same skeleton line were merged to subpoint clouds representing branch sections. Into these sections cylinders were modeled. Validation with an artificial point cloud with known volume revealed a complete modeling of the stem and up to 90% of branches. In nowadays literature the method is commonly referred to as quantitative structure modeling (QSM).

Kaasalainen S.

et al. [

27] applied the QSM method to both real and artificial time-series. Five scanning campaigns covering two complete growth periods were carried out to analyze the biomass change of one

Acer platanoides. In a laboratory experiment a

Populus tremula branch was scanned four times additionally. Each time sub-branches had been cut off before new time stamp data was collected. The difference in volume change between the model and reference data was 20–40 mL (12% of the estimated total branch volume). For the

A. platanoides scans validation could not be performed at this high accuracy level, as no destructive reference data could be collected. An overall trend in both total branch length and total branch volume was detected.

Hackenberg

et al. [

5] used high quality TLS data derived from trees growing under controlled conditions. Their method utilized spheres to follow the complete branching structure of a tree. The spheres’ surfaces cut the tree point cloud, resulting in spatially unconnected sub-point-clouds representing the cross sectional areas of the branches. Into these sub point clouds circles where fitted and their radii were used as radii for preliminary fitted cylinders. These cylinders were enhanced with a non-linear least squares fitting routine. Comparison between the resulting models and the input point cloud revealed that the models did cover up to 99% of the tree with a fit quality in sub-millimeter accuracy.

Latest research reports that nowadays both presented approaches can be combined to build tree models including the thin branching structure on a larger scale:

Calders

et al. [

28] further developed the QSM method to work on plot level. A 40 m radius plot containing 75 Eucalyptus trees was covered with 5 scans. A semi automatic extraction of those trees allowed the modeling proposed by Raumonen

et al. [

26]. 65 tree models could be linked to ground truth data gained by destructive harvesting. Biomass of those trees was inferred from total volume estimates (QSM) and basic density. Comparison between ground truthed biomass and TLS derived biomass revealed a root mean squared error (RMSE) of 16.1%.

The following publications [

6,

29] give a comprehensive overview of articles concerning LiDAR-based computational forestry.