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Accurate vehicle localization in forest environments is still an unresolved problem. Global navigation satellite systems (GNSS) have well known limitations in dense forest, and have to be combined with for instance laser based SLAM algorithms to provide satisfying accuracy. Such algorithms typically require accurate detection of trees, and estimation of tree center locations in laser data. Both these operations depend on accurate estimations of tree trunk diameter. Diameter estimations are important also for several other forestry automation and remote sensing applications. This paper evaluates several existing algorithms for diameter estimation using 2D laser scanner data. Enhanced algorithms, compensating for beam width and using multiple scans, were also developed and evaluated. The best existing algorithms overestimated tree trunk diameter by

Accurate estimation of tree trunk diameter is important both for traditional remote sensing applications and for advanced automation solutions in forestry. The main focus for remote sensing in forestry has generally been on describing properties and locations of trees. Features of relevance for forest related products and the operations related to forest management have been prioritized. Predictions of tree trunk attributes for entire forest areas are valuable for optimization of wood supply and for planning forest operations [

Forest machines used for fully mechanized cut-to-length (CTL) harvesting are technically advanced, with for instance automatic mechanical measuring of stem diameters and lengths during harvest. This information is processed in real-time optimization algorithms to support value maximizing cutting of stems into logs. Moreover, the information is transferred from the machines and used in central systems for managing wood supply of forest industries. The trend is towards even more advanced operation through, for instance, automation of crane functions [

Recent progress suggests new interesting possibilities to combine such automatically generated local maps with airborne laser scanning (ALS). Through ALS, high precision geographical information is available for large areas. Height models of tree crowns and ground are created from ALS data, and tree crown segmentation algorithms can be applied to produce global tree maps with complete coverage. Several variables related to crown shape and size, for example stem volume [

In this article, we focus on the use of terrestrial 2D laser scanners for estimation of tree diameter. Such scanners provide scan lines in a typically horizontal plane, and have been used to estimate diameter and also location of the centerpoint of trees [

Other studies report on the usage of terrestrial 3D laser scanners. The algorithms often require a high resolution 3D point cloud, and are based on a variety of techniques such as the Hough transform [

The objectives of this study were to (1) compare several existing algorithms with new algorithms compensating for beam width; (2) to evaluate how the errors depend on tree trunk diameter and distance to the scanner; and (3) to evaluate various methods for using multiple laser scans. The paper is organized as follows. Section 2 describes the experiments, and in Section 3 existing and new diameter estimation algorithms are described. In Section 4, an evaluation of all described algorithms is presented. Section 5 contains a discussion of the results, and Section 6 finalizes with conclusions of the study.

Three existing algorithms for tree trunk diameter estimation (DEA) using a 2D laser scanner were evaluated. To improve the algorithms, we developed and evaluated two methods compensating for laser beam width, and two methods using multiple scans. This resulted in fourteen combinations in total. For the experiment, a SICK LMS 221 laser scanner was used. The angular resolution of the laser scanner was 0.25^{°}, the field of view 100^{°}, and the measurement range 80 m. Each laser beam had a width of 0.6^{°} (ca. 14 cm at 10 m range).

Nine tree trunk sections with diameters in the range of 6–50 cm were used for the experiment (

To identify trees in the laser scans, clusters of laser points fulfilling the following condition were extracted [_{i}_{max}_{max}^{°} wide sector centered at the middle laser beam were considered. In Jutila

Once the clusters were identified for the 170 samples, the algorithms for tree trunk diameter estimation were applied to the identified clusters. In the following section, the evaluated existing algorithms, and suggested improvements are described in detail. All algorithms use a cluster consisting of _{1}, _{1})_{n},_{n}

Three existing diameter estimation algorithms are evaluated (CF, TD, and VA). A suggested compensation for beam width resulted in an additional four algorithms (CFAA, CFEA, TDEA, and VAEA). Furthermore, all seven algorithms were used with multiple scans in two ways (MR and MD), giving a total of 14 algorithms that were evaluated. In the remainder of this section, existing algorithms and suggested improvements are described in detail.

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_{c}^{2} + (_{c}^{2} = ^{2} by restating the problem as a linear least square problem. In this way, radius _{c}, y_{c}

For the laser scanner used in the experiments, the width of each laser beam is 0.6^{°}. This means that the actual angle at which reflection occurs can be ^{°} off the nominal angle. Due to the width of the beam, an object will always be covered by at least three beams, regardless of its size, as illustrated in

Since the beam is wider than the spacing between two beams, the center of the outermost beam will normally be outside the tree, leading to an overestimation of the diameter. To compensate for this, we developed enhanced versions of all algorithms, called

For the VA algorithm, the edge point adjustment is computed as follows (algorithm VAEA) (compare with

For the CF algorithm, the edge point adjustment is done by moving the two outermost points towards the center of the cluster by an angle (algorithm CFEA).

We also developed a second beam-width correction method for CF, called

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Since a laser scanner generates several scans per second (typically with a frequency of around 20 Hz), it is possible to combine multiple scans even for mobile applications. All algorithms have been evaluated for two ways of using multiple scans (MS):

To summarize, we have three base algorithms (CF, TD, VA). Each one of these can be combined with beam width compensation (CFAA, CFEA, TDEA, VAEA). Finally these seven algorithms can be combined with the two different methods for fusing several scans (MR and MD), leading to a total of 14 algorithms that are evaluated (see

The error values were evaluated for systematic bias (over- or underestimations) by using 1-sample T-tests to analyze if the mean value was significantly separated from zero within treatments.

Diameter estimation accuracy was evaluated as absolute error and as absolute percentage error. Absolute error was calculated as the absolute value of the difference between estimated and observed diameter. Absolute percentage error was calculated as the absolute error divided by the observed diameter and then multiplied by 100.

To evaluate the effect of beam width compensation and multiple scans, the data was analyzed by use of analysis of covariance (ANCOVA). The full factorial model contained three fixed factors: diameter estimation algorithm (DEA; CF, TD & VA), Beam width compensation (BWC; Yes & No), and Multiple scans method (MS; MD & MR). Thus, this ANCOVA model evaluated the resulting combinations of the three factors’ levels (

Additionally, a separate two-way ANCOVA model was used for analyzing the additional beam width compensation method used uniquely for the CF algorithm (AA). Thus, within CF, a full factorial model with beam width compensation (EA, AA & No) and multiple scans method (MD & MR) was used (

A general linear model (GLM) was used for analyzing the ANOVA models (Minitab 16, Minitab Inc., State College, PA, USA). When needed, the dependent variable data were transformed to natural logarithms (Ln) to meet the the statistical tests’ assumptions of normality and homoscedasticity. During the GLM procedure, pairwise differences were analyzed with Tukey’s simultaneous test of means. When significant effects from covariates in ANCOVA analyses were found, the relationships were established by use of linear regression analysis. The critical level of significance was set to 5%.

The 14 algorithms described in Section 3 were tested and evaluated on clusters representing 170 trees. The number of points in each cluster (

The optimal beam-width correction angle ^{°} to 0.4^{°} with 0.0029^{°} step (5^{−}^{5} radians), and choosing the ^{°}, and 0.22^{°} for CFEA and CFAA (^{°} for TDEA and VAEA, and 0.02^{°} for CFEA and CFAA. This suggests that the optimal value is very independent of the subsampling, and that the same optimal values would be estimated if using a separate data set for optimization.

As described in Section 3.3, multiple scan were used in two ways. Combining diameter estimations from more than one scan with the MD method reduced both mean and standard deviation for the diameter estimation error (dotted lines in

The absolute value of the Ln-transformed error in diameter estimation was significantly decreased (

The absolute percentage error in diameter estimation displayed a response identical to the absolute error (^{2}-adj) in the absolute error data, and 55.8% in the absolute percentage error data. The main effect of BWC contributed with most (

For the CF algorithm, two different methods of BWC were tested, out of which the EA method provided smaller mean errors and standard deviations than the AA method (

Since the multiple scans methods did not influence the errors, the following analysis are conducted on estimation with only one of the multiple scans methods (MD). Without angle correction, all algorithms systematically overestimated the diameter (

The ANCOVAs showed that the absolute percentage estimation error is influenced by tree trunk diameter. When analyzing the effects on one treatment combination (VAEA MD), it is shown that the absolute percentage error decreases with increasing tree trunk diameter and increases with increased distance (^{2}-adj; for untransformed and Ln-transformed absolute percentage error, respectively). Similarly, the distance to the tree as single predictor explains only 15% and 12%, respectively, of the observed variation.

The experiment was not designed to evaluate the effect of tree species (bark texture), but allowed nevertheless for such an indicative analysis. Thus, for trees with diameters between 15 and 20 cm there were a reasonable (albeit unbalanced) number of observations for different species (95 birch, 213 aspen, and 72 pine). For this subsample, the tree species replaced the multiple scans factor in the general ANCOVA model. The analysis of the Ln transformed absolute errors and absolute percentage errors yielded basically the same results as previously: significant effects of DEA, BWC, the interaction between DEA and BWC, and distance to tree (

The VA and TD methods gave very similar results with 39% and 40% error respectively. By compensating for beam width (TDEA, VAEA), the error was reduced to ca. 12%. These two methods gave the best result in our study. The same effect was observed for all other methods as well; using beam width correction reduced the error by at least 70%. The algorithm based on circle fitting (CF) did not perform well at all, giving 156% error on average. The algorithm was also very sensitive to noise in the data. If the points did not form well-behaved arcs, the diameter was overestimated significantly. CFEA and CFAA were a bit less sensitive than CF in this respect, as can be seen in

Our results show that diameter of and distance to the trees influenced the estimation errors. This makes perfect sense since the combination of diameter and distance is directly correlated to how many laser beams hit the tree, and hence to accuracy. The smaller the tree and the further away, the fewer laser beams hit the tree. At distances larger than 19 m, the algorithms estimated approximately the same diameter (

All mentioned previous studies used substantially smaller datasets for evaluation, which may be one explanation to the different results compared to our study. Another plausible reason could be that the previous studies used a validation algorithm to filter out the best trees [

Estimation performance depends on the type of laser scanner. Previous studies [

When comparing real and estimated tree trunk diameter, it is crucial to know exactly where the laser beam hits the tree trunk, since tree trunks are well known for their taper [

We have evaluated several existing algorithms for estimating tree trunk diameter using a 2D laser scanner. The results show that algorithms based on circle fitting are sensitive to noise in the laser scans, and often give very large estimation errors. Two different algorithms based on viewing angle (TD and VA) give very similar result with around 40% error. Our suggested compensation for beam width results in a significant reduction down to 12% for the enhanced algorithms (TDEA and VAEA). In general, the observed errors for existing algorithms were higher in our study than in previously published research, but similar results were achieved when applying the same method to filter out data samples. A direct comparison is further complicated by the dependency on type of laser scanner, and on the amount and type of trees used for evaluation. Regarding influence of external factors, our study shows that the estimation error grows with increasing distance, in particular for trees with small diameter. In this study we considerably improved the tree trunk diameter estimation algorithms. Our enhanced algorithms may be used to improve SLAM generated local maps, which in combination with global ALS maps can be used for localization of forest machines. Improved diameter estimation is important also for several other forestry automation and remote sensing applications. Further efforts should focus on improved clustering and validation to extract laser points belonging to trees only, thereby improving the quality of data input to the estimation algorithms. Combining laser scanner with cameras is one possible approach that should be investigated towards these ends.

This work was partly funded by the European Commission (CROPS GA no 246252) and the Royal Swedish Academy of Agriculture and Forestry (KSLA; H11-0085-MEK, H11-0085-GBN).

The authors declare no conflict of interest.

The nine tree trunk sections that were used in the experiment.

Tree trunk diameter according to the TD algorithm using two right-angled triangles and the center point for the detected cluster.

Schematic view of three 0.6^{°} wide laser beams separated by 0.25^{°}. The outer edges of the beams are illustrated by dotted lines in red, blue, and green, with the center of each beam marked with a solid line. Regardless of size, an object will be covered by at least three beams, due to the width of the beams, as can be seen around the solid green line in the center.

Mean absolute percentage estimation error and standard deviation as a function of number of scans for 14 algorithms. The legend shows the order of the algorithms for 10 scans, since this is used in the analysis of the results. (

Absolute estimation error for varying beam width correction angle

Distribution of diameter estimation errors (positive error values = overestimation, negative values = underestimation) for the 7 algorithms, when applying the MD multiple scans method.

The estimation error decreases with increasing diameter (n = 170).

The estimation error increases with increasing distance. The size of the circles corresponds to the actual diameter of the trees (n = 170).

Tree species and diameter range for the nine tree trunk sections used in the experiment.

Goat willow ( |
42.2–49.6 |

European aspen ( |
7.6–8.5 |

European aspen ( |
17.2–19.2 |

Scots pine ( |
5.6–6.0 |

Scots pine ( |
11.5–13.4 |

Scots pine ( |
17.6–20.8 |

Silver birch ( |
16.5–18.3 |

Silver birch ( |
22.9–28.0 |

Silver birch ( |
31.5–34.4 |

Abbreviations.

DEA: | Diameter estimation algorithms |

VA: | Diameter estimation based on viewing angle |

TD: | Two triangle diameter estimation |

CF: | Circle fit |

BWC: | Beam width compensation |

EA: | Edge points adjusted |

AA: | All points adjusted |

MS: | Multiple scans |

MR: | Mean ranges |

MD: | Mean diameter |

Mean estimation error and standard deviation (SD) for all tested combinations of diameter estimation algorithm (DEA) and beam width compensation (BWC) methods, using the MD multiple scan methods with 10 scans. Within columns, different superscripted lowercase letters indicate significant differences (

CF | No | 168 | 22.1^{a,A} |
14.8 | 155.6^{a,A} |
188.9 |

EA | 170 | 3.7^{b,B} |
3.4 | 19.2^{b,B} |
16.9 | |

AA | 170 | 4.0^{B} |
4.3 | 21.3^{B} |
22.5 | |

| ||||||

VA | No | 170 | 5.8^{c} |
2.7 | 38.9^{c} |
35.8 |

EA | 170 | 2.2^{d} |
3.0 | 11.7^{d} |
13.9 | |

| ||||||

TD | No | 170 | 6.0^{c} |
2.7 | 40.0^{c} |
35.8 |

EA | 170 | 2.2^{d} |
3.0 | 11.8^{d} |
14.0 |