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In this paper, a new algorithm to improve the accuracy of estimating diameter at breast height (DBH) for tree trunks in forest areas is proposed. First, the information is collected by a two-dimensional terrestrial laser scanner (2DTLS), which emits laser pulses to generate a point cloud. After extraction and filtration, the laser point clusters of the trunks are obtained, which are optimized by an arithmetic means method. Then, an algebraic circle fitting algorithm in polar form is non-linearly optimized by the Levenberg-Marquardt method to form a new hybrid algorithm, which is used to acquire the diameters and positions of the trees. Compared with previous works, this proposed method improves the accuracy of diameter estimation of trees significantly and effectively reduces the calculation time. Moreover, the experimental results indicate that this method is stable and suitable for the most challenging conditions, which has practical significance in improving the operating efficiency of forest harvester and reducing the risk of causing accidents.

In forestry, Light Detection and Ranging (LiDAR) devices are often used for remote sensing applications to record inventory parameters that can describe the state of forests. Besides traditional satellite laser scanning (e.g., ICESat-GLAS) [

A large number of experimental studies have confirmed the potential of TLS to successfully extract the DBH as mentioned. All of these have investigated the tree trunk diameter with three-dimensional terrestrial laser scanners (e.g., Faro LS 800, Riegl LMSZ420i, Leica HDS6000). As DBH is defined as the diameter 1.3 m above the finished grade at the end of the trunk, a horizontal slice with a thickness at a height of 1.3 m above the representative ground point is cut from a high resolution 3D point cloud in the usage of 3D terrestrial laser scanners. Then an adjusting circle is fit into the 2D projection of the points of that slice to estimate the DBH as well as location, and high level tree features [

A standard pattern recognition method with a Hough-transformation was applied by Aschoff and Spieker [

Others methods have been developed to match laser data as circles for estimating a trunk diameter. Those geometric fitting approaches aim at minimizing the error between the sum of the squares of the distances of laser points and the radius of the fitted circle. There exist various numerical algorithms to find the circle that best fits a given set of measured laser data pairs. The problem of solving the equation of a circle is restated by Wang [

However, a major concern in geometric fitting is that the minimization algorithms require iterative and computationally intensive numeric schemes. Thus the algorithm estimating the DBH fits an algebraic equation to represent a circle. Corresponding algebraic fitting methods such as the Kasa algorithm are non-iterative and thus faster than geometric fitting as reported in [

Nevertheless, their performances strongly depend, among other factors, on the choice of the initial laser data of the 2D laser scanner (2DLS). When a single 2DLS laser pulse is sent out and reflected by an object surface within the range of the scanner, the elapsed time between emission and reception of the laser pulse serves to calculate the distance between the object and the 2DLS [

However, a systematic study of the factors which influence the accuracy of information extracted from laser data DBH estimation algorithms is still lacking, even though the need for such analyses is already formulated at quite an early stage. To solve this problem, this paper investigates the possibility of using enhanced algorithms with polar parameters to estimate the diameter of tree trunks by using 2DLS data. This work applies the algebraic fit method to linearly fit the discretely distributed laser points as a circle to form the initial guess. Then the Levenberg-Marquardt scheme is selected to minimize the algebraic distances from the contour points to the resulting circle nonlinearly. After cluster extraction and filtering, this hybrid algorithm uses the arithmetic mean method based on multiple scans to adjust the original laser points for obtaining a higher accuracy in the diameter estimation. From the comparison results, this proposed method improves the accuracy of DBH estimation and effectively reduces the calculation time, which is also affected weakly by the harsh environment puzzling the drivers and suitable for the challenging conditions in forestry.

The rest of this paper is as follows:

For continuous accurate measurements rapidly, a LMS511-pro type 2D laser scanner produced by the SICK Company (Waldkirch, Germany) is used as the essential sensor to build the system for measuring the DBH parameter of living-trees in forest areas. The measurement data corresponding to the surrounding contour scanned by the LMS511-pro is output in hexadecimal format to form the raw point cloud via the Ethernet interface at the rate of 100 Hz. A computer having a conventional Windows 7 operating system installed is applied to link with the 2D laser scanner and analyze the measurement data, which are stored exclusively for post-processing. In the PC, the actual data acquisition and analytical software is programmed with M language to set the operating parameters of the laser scanner and handle the laser data in offline model by using Matlab 2012b.

To acquire abundant tree features with adequate resolution from the laser cloud measurements taken in the forest, the scanning angular resolution of the LMS511-pro is set to its minimum value 0.1667°. Then the maximum scanning angle is set to 100° and maximum scanning distance is 32 m. Therefore, the measurement result of LMS511-pro laser scanner is a right ahead semicircle in the front of the device, while its centre is the scanner’s location, the radius is 32 m and the scanning degree is 100° in a range from 40° to 140°. The electronics of the LMS511-pro are directly powered by a 24 V lithium battery. In order to recording the corresponding visual information, a Fluke TI55 type infrared thermal camera with images of 640 × 480 pixels resolution is mounted on the side of the laser scanner. This device can obtain both RGB visible and infrared thermal images simultaneously and regularly. Visible images reflect the visual reality and infrared thermal images record the temperature of the environment. Because of the complicated surroundings in a forest, it is difficult to detect targets guided by any single information source. When it is dark or misty in the forest, it becomes difficult to distinguish the objects in the RGB images without information about temperature, whereas after a period of extensive cooling (e.g., after a long period of rain or early in the morning), the infrared images are less detailed in representing the background due to the low thermal levels compared with visible images. In this situation, the fusion of the visible and thermal image on a single display could enhance the fused images’ clarity and capture more abundant information about the reality. Therefore, an algorithm based on a Contourlet transform and a pulse coupled neural network (PCNN) is used to generate the mutual complementary blending images (the detail description can be found in [

The measurement equipment includes sensor equipment fixed on the tripod platform as well as the data acquisition PC and lithium batteries providing 24 V for the system. The experiment is used in a birch forest.

To measure the DBH of living-trees in a real forestry environment, outdoor experiments were carried out in birch forest located in the Peking Olympic Park. In our experiments, the 2D laser scanner is fixed on a tripod with telescopic legs as seen in

The raw laser data scanning result.

The corresponding visual information of the forest area: a visible image (

In order to increase the target quantity, a further outside and indoor simulation is performed to reveal the influence of the distance and diameter on the diameter estimation error. For each abovementioned birch, the 2DTLS scanned all eight targets at a distance ranging from 2 m to 12.2 m every 0.6 m to the tree. Then, thirteen tree trunk sections with diameters in the range of 9–35 cm and lengths in the range of 40–49 cm are used in the indoor experiment. They are also placed at distances from the 2DTLS varying between 2 m and 12.1 m in 0.3 m steps. The diameter range and length of the trunks are recorded in

The thirteen tree trunks and the indoor experimental scene.

Tree species, diameter range and length of the trunk sections scanned in the experiment.

Species | Diameter Range (mm) | Length (mm) |
---|---|---|

Weeping willow ( |
173.6–178.2 | 470.8 |

Weeping willow ( |
264.2–279.4 | 401.4 |

Weeping willow ( |
310.9–347.5 | 433.2 |

Weeping willow ( |
243.2–250.4 | 427.1 |

False acacia ( |
225.8–227.2 | 429.6 |

False acacia ( |
147.8–148.4 | 452.4 |

False acacia ( |
296.2–310.5 | 416.1 |

False acacia ( |
235.8–256.4 | 482.6 |

Abele ( |
259.0–266.2 | 411.5 |

Abele ( |
158.4–160.8 | 416.1 |

Abele ( |
197.2–198.1 | 420.5 |

Abele ( |
294.4–316.1 | 429.4 |

Silver birch ( |
99.4–101.8 | 408.8 |

As the measurement data is processed in increasing order of the bearing angle from 40° to 140° with the chosen angular resolution, a vector _{i}_{i}_{i}_{i}_{i}_{i}_{i}_{+1}. As shown in

The schematic of the difference calculation for clustering the raw laser data.

Then the values of vector are compared with the depth threshold ∆_{max}_{min}_{max}

Using Equation (2) is certainly effective and sufficient for extracting laser clusters of targeted trunks from the point cloud in a forest with a few bare living-trees. However, the laser beam may be reflected by uninteresting things such as branches, stones or the ground in a more complex environment, which causes measurement errors in the point cloud. Thereby, the incorrect points clustered from the raw laser cloud should be filtered out with some detective criteria to obtain the actual trunk clusters. Here the filtering is performed by testing the curvature of each cluster, which describes the diameter of the tree. If the feature width and the curvature inspection satisfy the constraints simultaneously, the clusters will be accepted as trunk features of living trees. The curvature values are calculated for each individual point

By using the curvatures of each point, the curvature of the whole cluster is calculated as follows:

In the equation, _{min}_{min}_{max}_{max}

The clustering and filtering result of the experiment in polar form.

According to the working principle of 2D laser scanners, the distance value of a laser beam is influenced by the reflectance of objects and the returned energy of the laser beam. In the actual process of a single continuous measurement, the laser reflection ability of various objects is not only directly affected by the coarseness and color of objects, but also influenced by the incidence angle and laser beam spot size.

With the discrepancy of reflectivity and the change of the laser speckle, the size of the laser energy obtained by the measurement instrument is different in the same laser beam as time goes by. Therefore, the measuring value of the same laser beam are also disturbed by fluctuating errors like the temporal extension. This is the main factor affecting the measuring accuracy of a laser scanner in the application for DBH estimation. To confirm the range of the error, a white board is located in 2 m distance from center of the laser scanner and perpendicular to the 24-th laser beam. The measured distances for 100 scans are obtained to establish the relationship between multiple scans of an object and the corresponding frequency of occurrence as follows.

Relation histogram of the measured values

As shown in _{i}

After extracting and optimizing the trunk features from the point cloud, the trunk clusters are ready for the DBH estimation with the circle fitting algorithm. There exist a number of different methods to fit a circle and estimate its parameters [

Another issue is that the accuracy of diameter estimation in the mentioned studies is severely influenced by the initial guess. If the initial guess is picked at random or disturbed by noise, the chance of divergence may be very high [

For estimating the diameter with the new hybrid method, it is necessary to assume that the cross section of the living-tree is an ideal circle and there are at least three laser points in polar form located on the living-tree.

Similarly, we assume that the vector _{i}_{i}_{i}_{i}_{x}_{y}_{i}

To obtain an initial guess for the circle center, the cost function

This equation can be solved by setting:

Simplify Formula (9) to get the initial parameters of the fitting circle:

Once the initial guess for the circle center is ensured, we need to improve the circle for some definition of best fit against the points set. Using an iterative method for nonlinear least squares problems such as the Levenberg-Marquardt estimator based on the geometry distance between the points and the circle is a wise choice [

To improve the circle fitting with an independent variable _{i}_{i}_{i}_{i}_{i}

Thus this general optimization problem can be solved by finding _{min}

Providing that the function

As regards

Similarly the Hessian of

This shows that _{lm}

The resulting normal equations for the Levenberg-Marquardt perturbation are:

The stopping criteria for the algorithm should reflect that at a global minimizer, thus the LM algorithm terminates when at least one of the following conditions is met:

The magnitude of the gradient of ^{T}_{1}:

The error ^{T}f_{2}:

The relative change in the magnitude of _{lm}_{3}:

A maximum number of iterations _{max} is completed safeguard against an infinite loop: K ≥ _{max}.

Otherwise, iterations terminate when the iteration count exceeds a pre-specified limit. In our experiment, _{max} is set to 1000 and the initial threshold δ_{1} = δ_{2} = 10^{−4}, δ_{3} = 10^{−5} consequently, faster convergence can be expected. The optimized estimation of the DBH and other trunks’ parameters in the horizontal plane can be calculated via this hybrid circle fit algorithm. For detailed explanations of the LM method, readers should refer to [

Finally, the overall data analysis flow of the equipment for the measurement and calculation of the tree parameters is shown in

The analysis flow of DBH estimation with 2DTLS data for the harvesting head.

The trunk feature extraction process presented in the previous section was programmed in MATLAB. All of the calculation results such as radius, location of the trunks and distances between adjacent trunks could be displayed on a human-computer interface for the researchers’ use.

In the experiment, there were eight fitted circles representing living-trees chosen to estimate the trunk parameters in this proposed method in contrast with manual work. Supposing the measurement base point the origin of laser scanner in the polar form, the fitting results of the trunk point cloud (red points) are shown as the blue circles in

The parameters of the trunk could be extracted from the point cloud with the new fitting algorithm, as shown in

The fitting results of the trunk with laser clouds acquired by 2DTLS.

Parameters of the trunks acquired by different methods and the corresponding error.

Sample | Manual | New Algorithm | Error | |||||
---|---|---|---|---|---|---|---|---|

Center Location (mm) | Radius (mm) | Center Location (mm) | Radius (mm) | Central Angular Deflection (degree) | Central Distance Deflection (mm) | Radial Absolute Error (mm) | Radial Relative Error (%) | |

Tree first | (−275.4, 1986.1) | 96.89 | (−273.5, 1987.9) | 97.611 | 0.061 | 1.557 | 0.721 | 0.744 |

Tree second | (20.2, 1984.3) | 78.21 | (18.6, 1973.5) | 75.534 | 0.043 | 10.829 | 2.676 | 3.421 |

Tree third | (288.6, 1990.6) | 54.22 | (285.3, 1972.6) | 53.233 | 0.00057 | 4.276 | 0.987 | 1.821 |

Tree fourth | (−9260.3, 8302.7) | 146.315 | (−9249.3, 8285.7) | 155.331 | 0.024 | 19.562 | 9.016 | 6.162 |

Tree fifth | (−3200.5, 8282.5) | 134.205 | (−3190.5, 8282.5) | 130.082 | 0.060 | 3.604 | 4.123 | 3.072 |

Tree sixth | (2722.9, 8335.1) | 127.61 | (2727.7, 8328.0) | 131.496 | 0.044 | 5.307 | 3.886 | 3.045 |

Tree seventh | (3913.9, 7502.5) | 143.82 | (3922.9, 7492.7) | 146.877 | 0.084 | 4.544 | 3.057 | 2.126 |

Tree eighth | (8802.7, 8172.0) | 156.52 | (8812.3, 8170.1) | 148.545 | 0.038 | 5.709 | 7.976 | 5.096 |

The manual measurement values of the central location and radius of the trunk were also given in the 1st and 2nd column of

To evaluate the effect of circle fitting optimization and beam improvement with multiple scans, the proposed algorithm was analyzed in a series of computer tests by comparing the results with those obtained with other methods. As competitors, two triangle diameter estimation (TDE) methods described in [

To verify the feasibility of the proposed circle detection algorithm, Gaussian noises with mean 0 and standard deviation 5 (mm) were also added to the trunk clusters in the radar slice plane detected by scanners, which were approximately the same as the observed noise distribution in sensors. The Gaussian noises were also independent among trials. Several contrast parameters were selected to verify high accuracy of diameter estimation with the new algorithm proposed in this paper as shown in

Experimental result of new algorithm compared with related works.

Parameter | TDE | LSF | F-R | PRP | CFAA-MS | New Method |
---|---|---|---|---|---|---|

Average radial absolute error (mm) | 13.976 | 8.341 | 5.761 | 6.599 | 5.894 | 3.655 |

Max error of radius (mm) | 26.089 | 13.078 | 11.469 | 12.716 | 10.805 | 8.579 |

Average radial relative error (%) | 12.125 | 7.486 | 4.707 | 5.683 | 5.253 | 2.893 |

RMSE | 15.671 | 8.913 | 6.748 | 7.277 | 6.465 | 4.464 |

STD | 7.580 | 3.358 | 3.757 | 3.277 | 2.839 | 2.742 |

R-square | 0.161 | 0.729 | 0.844 | 0.819 | 0.857 | 0.932 |

Time consumption (ms) | 0. 019 | 6.296 | 488.622 | 288.789 | 9.771 | 4.745 |

As shown in

For testing the measurement effectiveness of each algorithm further, the proposed algorithm was compared with a few others in a series of statistic parameters. The Root Mean Square error (RMSE) of the absolute errors of estimated diameter in this algorithm was close to 4.5 mm, which was the smallest among all methods. The value of RMSE in this paper showed the obvious improvement by 71.5% compared with TDE and by 30.9% corresponding to CFAA-MS, which suggested a higher fitting precision of this chosen estimated model and a better prediction ability for laser data. What’s more, the minimum value of the Standard Deviation (STD) for the estimated diameter errors obtained by this proposed method indicated that the error distribution was not very discrete. In a sense, this measuring system could deal with the worst case scenario corresponding to very noisy laser data. Thus it indicated that this algorithm was suitable for the most challenging conditions and was more stable and robust than others in this paper.

Next, the coefficient of determination of regression squares (R-square) was applied to demonstrate the superiority of our new algorithm over the main existing algorithms. This parameter was decided by the sum of squares of the regression (SSR) divided by the total sum of squares (SST), which was through the change of the data to represent the fitting effect. By the above expression, the normal value of R-square was distributed in the certain range of [0, 1]. The numerical result in this new algorithm obtained a maximal value approximating 1, which suggested that the equation of this circle fitting method had stronger diameter estimation ability compared with the others. Also the estimation errors were weakly affected by distances and poses of the object and the fitting result for diameters was more stable and accurate. Lastly,

A further experiment dealing with the influencing factors on the estimation error was performed. The errors were mainly caused by the resolution, specular energy errors of the laser device and the approximation errors of the fitting algorithm. The error also was impacted by the distance between the base point of the laser scanner and the device. In addition, the distance was positively related to the size of the circles corresponding to the actual diameter of the trees. To confirm the significant factors, the paper was simplified with removing insignificant factors if they did not have any significant main or interaction effect. Then the iterations, the tree trunk diameter and its distance from the scanner were entered as core-variates affecting the error, which would be analyzed further.

To reveal the influence of the number of repeated laser scans on the absolute error of diameter estimation, an experiment was performed with the abovementioned trees 1 to 8. Those birches were encircled with coarse white bark at a height of 1.3 m above the ground, which made the reflectivity of scanned trees increase up to 100%. This eliminated the influence of different reflectivity on the diameter estimation. Then the 2DTLS acquired the laser scanning data of all trees for 100 consecutive trials. Consequently, the point clouds were distributed around the outline of trunk at a slight difference, which was caused by the fluctuating error as seen in the abovementioned analysis. According to Equation (7), the target clusters scanned at different times were applied to form an optimized cluster, which represented the mean value of several scans. For each tree, the number of multiple scans changed from 1 to 100, which was defined as the repetition number. As a consequence, there were 100 optimized laser data being generated to calculate the absolute errors for DBH estimation of one tree.

The variation tendency between the absolute estimation error and the number of repeat is displayed in

The relationship between the number of repeat and the absolute error of diameter estimation for all trees.

A specific section analysis of the others suggested that the errors increased to the peaks of the curve at different number. Trees 1, 3 and 6 gave a maximum error value between 11 and 13, while the other trees (4, 5 and 8) reached the peak value in the range of 6 to 8. Only the 7th tree gave the maximum at 20. Then, all curves of error and repeated number decreased to the smallest error threshold at a similar range between 20 and 25, including the second tree. In spite of different changes (Tree 4 and 8 rose, but the trees 1, 3, 5 and 7 fluctuated over a small range), the error curves tended to smooth after about 45 except for the 6th tree, which continued to decline until 70 and then tended to be stable, so according to the experimental results, it could be seen that 20 repeats had reduced the laser fluctuating error, which would effectively improve the accuracy of diameter estimation. As a result of considering that the scanning frequency of 2DTLS was set as 100 Hz, taking 20 scans to calculate the average just consumed 0.2 s in measuring process, which met the requirements of the real-time and accuracy for the measuring system in forestry harvesters. Therefore, it could be concluded that the design of this repeat number was optimal in terms of minimization of estimated errors and the actual forestry vehicle applications.

However, the

The changes in the relationship between the distance and the estimation error.

A simple analysis explained that the trend of the average estimation error was increasing with increasing distance for most methods. The error curve using the TDE and LSF algorithms rose persistently with increasing distances in the distance range, as well as the curve computed with the PRP method except for the sudden huge error at some distances (3.8 m). For the FR method, the error was badly disturbed by noise and did not increase with distance until the end of the curve, but the relationship only explained 66.7% of the observed variation respectively except for the results calculated by the CFAA and the new algorithms. The new algorithm and the CFAA method had less change error with increasing the distance, in other words, the errors obtained by the two methods were affected weakly by the distance. The error curve of this proposed algorithm was smoother than the CFAA curve and had smaller values for most distances, which showed the higher accuracy and stability in estimating the diameters of trees with this algorithm. Therefore, this proposed method was suitable for the measuring tasks of the logging harvester operations when the cutting targets were distributed at different distances.

The estimation error decreased with increasing number of point hitting the tree, which was associated with the size of the circles.

In view of that the error curves was seriously noisy, a potential cause was that the average error in one distance was achieved by using tree trunks with different diameters. Thereby, a depth analysis was carried out to reveal the effects of diameter on the estimation error. To avoid the influence of distance on the error, only partial laser data at three distances (2 m, 2.6 m and 3.2 m) were chosen as independent observations. Meanwhile, the number of laser points hitting the tree corresponded to the actual diameter of the trees and distances. Thus, the parameter was designed as a single predictor to reveal the influence of the trunk diameters on the estimated errors. Finally, 29 sets of data were randomly selected to compute the estimation errors in different algorithms as shown in

In summary, a new algorithm to improve the accuracy of tree trunk diameter estimating in forest area is proposed in this paper. First, the measuring information is collected by laser using a 2D laser scanner and an infrared thermal imager. Then, after cluster extraction and filtration, the features of the trunk could be obtained from the raw laser point cloud. Further, by optimizing the laser data based on the arithmetic mean method, a new hybrid algorithm based on an algebraic circle fitting algorithm in polar form fused with a non-linear optimization principle in the Levenberg-Marquardt method is generally used to determine the radii and positions of the trees.

Compared with previous works published by other researchers, the experimental results show that the proposed measuring system accomplishes the trunk detection and diameter estimation of trees effectively with the minimum value in the average absolute error and average relative error, which indicates that the estimated diameters best fitted the observed diameter. Moreover, by analyzing the RMSE, STD and R-square, we found that this proposed method is suitable for the most challenging conditions and is more stable and robust than others while also showing reduced calculation times, which are practical significance in improving the operating efficiency of forest harvesters and reducing the risks of causing accidents.

Finally, this paper reveals the influence of the number of repeats on the estimation error. The experimental results indicate 20 times is the best value of this repeat number, which will reduce the laser fluctuation errors and effectively improve the accuracy of diameter estimation. Furthermore, according to our study of the effects of external factors (diameters and distances) on the estimation error, the hybrid algorithm performs well in improving the estimation effectiveness of tree trunk diameter. Thus the improved diameter estimation algorithm is important for forestry logging operations, localization and automation of forest machines, SLAM generation of local maps and so on. However, the current diameter estimation method is proposed on the basis of a static system. In the future, a dynamic diameter estimation combining a laser scanner with cameras will be studied in order to achieve real-time and rapid measuring results in the forest environment.

This study is financially supported by the 948 project supported by State Forestry Administration, China (Grant No. 2011-4-02).

All authors have made significant contributions to the paper. Jianlei Kong was involved in the data collection, experimental work and writing of the paper under the supervision of Jinhao Liu and Lei Yan. Xiaokang Ding contributed to the paper organization and technical writing of early versions of the manuscript. Jianli Wang refined the protocol algorithms, defined the experiment set-up and edited the paper. They also contributed in several rounds of critical revisions. All authors have contributed to the interpretation and discussion of the results and have read and approved the final version of the manuscript.

The authors declare no conflict of interest.