Research Paper
Accuracy of tree diameter estimation from terrestrial laser scanning by circle-fitting methods

https://doi.org/10.1016/j.jag.2017.07.015Get rights and content

Highlights

  • The highest accuracy was achieved with the optimal circle method.

  • The Monte Carlo method was not significantly different from the optimal circle method in multi-scan mode.

  • The minimum bounding box method was more accurate than the maximum distance method in multi-scan mode.

  • The maximum distance method was more suitable than the minimum bounding box method in single-scan mode.

  • The centroid method proved to be the least suitable circle-fitting method.

Abstract

This study compares the accuracies of diameter at breast height (DBH) estimations by three initial (minimum bounding box, centroid, and maximum distance) and two refining (Monte Carlo and optimal circle) circle-fitting methods The circle-fitting algorithms were evaluated in multi-scan mode and a simulated single-scan mode on 157 European beech trees (Fagus sylvatica L.). DBH measured by a calliper was used as reference data. Most of the studied circle-fitting algorithms significantly underestimated the mean DBH in both scanning modes. Only the Monte Carlo method in the single-scan mode significantly overestimated the mean DBH. The centroid method proved to be the least suitable and showed significantly different results from the other circle-fitting methods in both scanning modes. In multi-scan mode, the accuracy of the minimum bounding box method was not significantly different from the accuracies of the refining methods The accuracy of the maximum distance method was significantly different from the accuracies of the refining methods in both scanning modes. The accuracy of the Monte Carlo method was significantly different from the accuracy of the optimal circle method in only single-scan mode. The optimal circle method proved to be the most accurate circle-fitting method for DBH estimation from point clouds in both scanning modes.

Introduction

High-density point clouds from terrestrial laser scanning (TLS) open up new possibilities for accurate measurement of tree parameters and detailed three-dimensional modelling of forest stands. New TLS devices are small and lightweight; therefore, they can be easily used in a forest environment.

Trunks of all diameters can be detected and measured in high-density TLS point clouds. Studies have been carried out with a focus on deriving diameter at breast height (DBH), tree height (Király and Brolly, 2007; Liang and Hyyppä, 2013), and plot basal area (Seidel and Ammer, 2014). Point clouds completely cover the trees and canopy. This fact allows researchers to derive the shape and size of the tree crown (Moorthy et al., 2011), crown volume (Fernández-Sarría et al., 2013), and tree biomass (Kankare et al., 2013, Saarinen et al., 2017) from TLS data. Analysis of the amount and spatial distribution of reflected laser beams can be used in gap analysis (Ramirez et al., 2013) and estimation of leaf area index (Culvenor et al., 2014).

The prospective applications of TLS in forestry include 3D modelling of trees (Hackenberg et al., 2014), 3D modelling of tree root systems (Smith et al., 2014), and derivation of forest canopy fuel properties (García et al., 2011). Multi-temporal TLS of a forest stand was used to evaluate the influence of skidding operations on soil disturbance (Koreň et al., 2015).

DBH is one of the most important parameters required for forest inventory. Callipers or girth tapes are used to measure DBH in forest practices. TLS data offers new opportunities to derive tree diameter not only at breast height but potentially at any height above ground.

Trunk circumference is usually represented by a circle. The position and diameter of the circle are estimated by circle-fitting algorithms from a spatial cluster of points. Other geometric approaches approximate tree sections with cylinders (Brolly and Király, 2009), free-form curves (Pfeifer and Winterhalder, 2004), polygons (Wezyk et al., 2007) or skeletonization (Pál, 2008). Procedures based on three-dimensional rasters (Moskal and Zheng, 2012), Hough transformation (Aschoff and Spiecker, 2004) and morphological analysis (Maas et al., 2008) are under development.

Circle-fitting methods for deriving DBH from point clouds are based on horizontal cross-sectional slices. Horizontal cross-sectional slices of a point cloud are created at a given height above the ground. The thickness of the horizontal cross section is chosen according to the density of a point cloud to include the sufficient number of points needed for a reliable identification of trunks and measurement of their DBH. Cross-sections of individual trunks are identified by spatial clustering. Spatial clusters are also used for noise filtering. Spatial clusters with a low number of points are excluded from the subsequent data processing.

The accuracy of DBH estimated from a TLS point cloud is influenced by the technical parameters and settings of the scanner, scanning mode, positioning of the scanner, and data processing techniques. Most previous works studied the accuracy of one preferred DBH estimation algorithm. The results of these studies are difficult to compare because experiments were carried out in different forest stands and point clouds were processed by different methods. In our study, the accuracy of DBH estimation using different circle-fitting algorithms has been analysed in the same point cloud.

The aim of this work was to compare the results of DBH estimation using five circle-fitting methods from cross-sections of a TLS point cloud of European beech (Fagus sylvatica L.). The circle-fitting methods were evaluated by bias, precision, and accuracy of DBH estimation in a multi-scan and a single-scan mode. The results of DBH estimation by five algorithms have been statistically tested. Our findings provide deeper insight into the performance of the studied circle-fitting algorithms.

Section snippets

Research plot and field measurements

The research plot was established on the property of the University Forest Enterprise of the Technical University in Zvolen, central Slovakia. The research plot (Fig. 1) was located in a monoculture of European beech (Fagus sylvatica L.). The size of the research plot was 50 × 50 m. The forest stand was 80 years old with 160 beech trees, four European hornbeams (Carpinus betulus L.) and one European silver (Abies alba Mill.). To eliminate the influence of tree species on the results, only DBH

DBH estimation

The number of points recorded by a terrestrial laser scanner on a trunk is influenced by several factors: scanning density, the distance from the scanner, the number of scans of the tree, the scanning angle, shadowing by trees, low vegetation and terrain. The merged point cloud consisted of 592 million points. The point cloud was reduced to 499 million points by the 58 m × 58 m box filter. A cross-section of the heights 1.28–1.32 m above the ground in the filtered point cloud contained 570,594

Discussion

The accuracy of DBH estimation has also been addressed by other authors (Antonarakis, 2011; Brolly and Király, 2009; Pueschel et al., 2013; Tansey et al., 2009). In most cases, methods of tree DBH estimation from TLS data were compared by bias and root mean square error of DBH estimation. An overview of studies focused on DBH estimation from TLS point clouds was given by Pueschel et al. (2013). DBH bias reported by authors varied from underestimation of −1.5 cm to overestimation greater than 4 

Conclusions

This study provides insight into the performance and properties of circle-fitting methods. Circle-fitting methods proved to be effective algorithms for tree diameter estimation from TLS data. The Monte Carlo and the optimal circle methods are especially attractive due to easy implementation and high accuracy of DBH estimation in the multi-scan and the single-scan modes.

The initial estimations of DBH with the minimum bounding box and maximum distance methods were significantly more accurate than

Acknowledgement

This work was supported by the Scientific Grant Agency of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the Slovak Academy of Sciences under the grant VEGA 1/0881/17.

References (28)

  • N. Chernov et al.

    Least squares fitting of circles

    J. Math. Imaging Vision

    (2005)
  • D.S. Culvenor et al.

    Automated in-situ laser scanner for monitoring forest leaf area index

    Sensors

    (2014)
  • M.J. Ducey et al.

    Adjusting for nondetection in forest inventories derived from terrestrial laser scanning

    Canad. J. Remote Sens.

    (2013)
  • J. Hackenberg et al.

    Highly accurate tree models derived from terrestrial laser scan data: a method description

    Forests

    (2014)
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