# The Influence of Cross-Section Thickness on Diameter at Breast Height Estimation from Point Cloud

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Plots and Field Measurements

#### 2.2. Data Processing

## 3. Results

#### 3.1. DBH Estimations

#### 3.2. DBH Estimation Errors

_{SH}in Table 2). Contrastingly, the errors of beech DBH estimation were not normally distributed for more than half of the tested cross-section thicknesses (p

_{SH}in Table 2).

^{−6}). Meanwhile, beech DBH estimations were unbiased for 50, 60, and 70 cm cross-sections (p-values of Student’s t-test 0.16, 0.65, and 0.08, respectively).

_{W}in Table 2) was not constant across cross-section thickness (Levene’s test for homogeneity, p-values < 0.001). Homogeneity of variance was rejected for both species and cross-sections 10–100 cm thick (Levene’s test for homogeneity, p-value = 2.6 × 10

^{−15}and 0.02 for beech and oak, respectively), whereas Levene’s test failed to reject homogeneity of variance for both species and cross-sections < 10 cm thick (Levene’s test for homogeneity, p-value 1.0 and 0.996 for beech and oak, respectively).

^{−16}). The pairwise t-test confirmed the trend visible on Figure 6. DBH estimation biases from cross-sections up to 10 cm were not significantly different for both species under study (Table A3 and Table A4, Figure A39).

_{SH}in Table 3). The influence of cross-section thickness on MSE

_{W}was significant for both species under study (permutation one-way repeated measures ANOVA, p-values < 2.2 × 10

^{−16}).

_{W}approximately followed the trend of the bias absolute values (Table 2). MSE

_{W}of beech DBH estimation slightly decreased with cross-section thickness up to 50 cm and increased relatively fast with thicker cross-sections. MSE

_{W}of oak DBH estimation slightly decreased with increasing cross-section thickness. The differences between most beech DBH estimation accuracies for cross-sections up to 10 cm were not statistically significant (Table A5). Moreover, all accuracies of oak DBH estimation for cross-sections up to 10 cm were not significantly different among them (Table A6, Figure A40).

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Cross-Section Thickness (cm) | European Beech | Sessile Oak | ||||||
---|---|---|---|---|---|---|---|---|

Min | Max | Avg | Std | Min | Max | Avg | Std | |

1 | 79 | 3132 | 709.8 | 581.9 | 161 | 2492 | 539.4 | 424.3 |

2 | 151 | 6244 | 1424.4 | 1165.1 | 343 | 4996 | 1081.9 | 847.5 |

3 | 212 | 9457 | 2135.4 | 1750.6 | 532 | 7476 | 1614.8 | 1266.0 |

4 | 276 | 12,594 | 2843.8 | 2332.0 | 666 | 10,003 | 2158.6 | 1696.2 |

5 | 353 | 15,684 | 3556.0 | 2910.4 | 861 | 12,421 | 2697.8 | 2108.9 |

6 | 429 | 18,845 | 4267.6 | 3495.0 | 1066 | 14,946 | 3239.4 | 2531.5 |

7 | 506 | 21,971 | 4980.2 | 4075.1 | 1226 | 17,379 | 3779.2 | 2950.3 |

8 | 591 | 25,128 | 5692.3 | 4658.5 | 1398 | 19,867 | 4317.7 | 3372.7 |

9 | 668 | 28,249 | 6402.6 | 5239.9 | 1604 | 22,359 | 4860.9 | 3794.1 |

10 | 746 | 31,353 | 7111.3 | 5819.1 | 1794 | 24,780 | 5396.8 | 4205.1 |

20 | 1639 | 62,652 | 14,204.0 | 11,635.9 | 3534 | 49,611 | 10,800.2 | 8425.7 |

30 | 2507 | 93,705 | 21,302.8 | 17,430.6 | 5352 | 74,453 | 16,202.7 | 12,639.4 |

40 | 3359 | 124,978 | 28,391.9 | 23,225.7 | 7090 | 98,972 | 21,608.2 | 16,824.7 |

50 | 4171 | 155,980 | 35,447.9 | 28,989.3 | 8844 | 123,219 | 26,986.4 | 20,974.0 |

60 | 5044 | 187,014 | 42,466.5 | 34,734.4 | 10,659 | 147,211 | 32,351.9 | 25,092.0 |

70 | 5835 | 217,860 | 49,416.7 | 40,415.8 | 12,438 | 171,021 | 37,714.1 | 29,186.4 |

80 | 6607 | 248,505 | 56,321.5 | 46,093.0 | 14,244 | 194,517 | 43,059.1 | 33,246.2 |

90 | 7438 | 278,968 | 63,189.8 | 51,725.1 | 16,033 | 217,687 | 48,398.0 | 37,261.4 |

100 | 8213 | 309,329 | 69,978.5 | 57,314.7 | 17,813 | 239,948 | 53,712.1 | 41,186.0 |

Cross-Section Thickness (cm) | European Beech | Sessile Oak | ||||||
---|---|---|---|---|---|---|---|---|

Min | Max | Avg | Std | Min | Max | Avg | Std | |

1 | 8.09 | 61.59 | 28.07 | 11.97 | 16.93 | 40.42 | 30.64 | 5.56 |

2 | 8.04 | 61.47 | 28.06 | 11.98 | 17.00 | 40.65 | 30.64 | 5.57 |

3 | 8.08 | 61.49 | 28.07 | 11.99 | 17.04 | 40.64 | 30.64 | 5.56 |

4 | 7.91 | 61.59 | 28.06 | 12.00 | 17.01 | 40.70 | 30.64 | 5.57 |

5 | 7.87 | 61.52 | 28.08 | 12.01 | 16.92 | 40.63 | 30.65 | 5.59 |

6 | 8.00 | 61.37 | 28.06 | 11.99 | 16.82 | 40.47 | 30.64 | 5.57 |

7 | 8.01 | 61.66 | 28.06 | 11.99 | 16.99 | 40.58 | 30.65 | 5.57 |

8 | 8.13 | 61.58 | 28.08 | 11.99 | 16.99 | 40.72 | 30.63 | 5.56 |

9 | 8.02 | 61.56 | 28.06 | 11.99 | 16.91 | 40.72 | 30.65 | 5.56 |

10 | 8.09 | 61.60 | 28.08 | 12.00 | 16.82 | 40.53 | 30.66 | 5.56 |

20 | 8.43 | 61.39 | 28.10 | 11.96 | 17.04 | 40.55 | 30.67 | 5.53 |

30 | 8.49 | 61.49 | 28.15 | 11.92 | 17.10 | 40.75 | 30.71 | 5.52 |

40 | 8.59 | 61.51 | 28.23 | 11.85 | 17.26 | 40.67 | 30.72 | 5.48 |

50 | 8.68 | 61.43 | 28.31 | 11.76 | 17.59 | 40.83 | 30.76 | 5.47 |

60 | 8.63 | 61.56 | 28.42 | 11.68 | 17.71 | 40.91 | 30.80 | 5.46 |

70 | 8.97 | 61.61 | 28.53 | 11.57 | 18.10 | 40.79 | 30.87 | 5.43 |

80 | 8.83 | 61.70 | 28.63 | 11.50 | 18.18 | 41.09 | 30.95 | 5.39 |

90 | 8.82 | 61.72 | 28.77 | 11.41 | 18.44 | 40.97 | 31.00 | 5.37 |

100 | 8.95 | 61.80 | 28.89 | 11.33 | 18.87 | 41.27 | 31.08 | 5.36 |

## Appendix B

**Figure A1.**Linear regression of measured on estimated DBH (cm) for European beech 1-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A2.**Linear regression of measured on estimated DBH (cm) for European beech 2-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A3.**Linear regression of measured on estimated DBH (cm) for European beech 3-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A4.**Linear regression of measured on estimated DBH (cm) for European beech 4-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A5.**Linear regression of measured on estimated DBH (cm) for European beech 5-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A6.**Linear regression of measured on estimated DBH (cm) for European beech 6-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A7.**Linear regression of measured on estimated DBH (cm) for European beech 7-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A8.**Linear regression of measured on estimated DBH (cm) for European beech 8-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A9.**Linear regression of measured on estimated DBH (cm) for European beech 9-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A10.**Linear regression of measured on estimated DBH (cm) for European beech 10-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A11.**Linear regression of measured on estimated DBH (cm) for European beech 20-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A12.**Linear regression of measured on estimated DBH (cm) for European beech 30-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A13.**Linear regression of measured on estimated DBH (cm) for European beech 40-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A14.**Linear regression of measured on estimated DBH (cm) for European beech 50-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A15.**Linear regression of measured on estimated DBH (cm) for European beech 60-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A16.**Linear regression of measured on estimated DBH (cm) for European beech 70-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A17.**Linear regression of measured on estimated DBH (cm) for European beech 80-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A18.**Linear regression of measured on estimated DBH (cm) for European beech 90-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A19.**Linear regression of measured on estimated DBH (cm) for European beech 100-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

## Appendix C

**Figure A20.**Linear regression of measured on estimated DBH (cm) for sessile oak 1-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A21.**Linear regression of measured on estimated DBH (cm) for sessile oak 2-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A22.**Linear regression of measured on estimated DBH (cm) for sessile oak 3-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A23.**Linear regression of measured on estimated DBH (cm) for sessile oak 4-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A24.**Linear regression of measured on estimated DBH (cm) for sessile oak 5-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A25.**Linear regression of measured on estimated DBH (cm) for sessile oak 6-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A26.**Linear regression of measured on estimated DBH (cm) for sessile oak 7-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A27.**Linear regression of measured on estimated DBH (cm) for sessile oak 8-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A28.**Linear regression of measured on estimated DBH (cm) for sessile oak 9-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A29.**Linear regression of measured on estimated DBH (cm) for sessile oak 10-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A30.**Linear regression of measured on estimated DBH (cm) for sessile oak 20-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A31.**Linear regression of measured on estimated DBH (cm) for sessile oak 30-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A32.**Linear regression of measured on estimated DBH (cm) for sessile oak 40-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A33.**Linear regression of measured on estimated DBH (cm) for sessile oak 50-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A34.**Linear regression of measured on estimated DBH (cm) for sessile oak 60-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A35.**Linear regression of measured on estimated DBH (cm) for sessile oak 70-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A36.**Linear regression of measured on estimated DBH (cm) for sessile oak 80-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A37.**Linear regression of measured on estimated DBH (cm) for sessile oak 90-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

**Figure A38.**Linear regression of measured on estimated DBH (cm) for sessile oak 100-cm cross-section (a, regression slope; r, correlation coefficient; RSE, residual standard error).

## Appendix D

**Table A3.**p-Values of pairwise comparison between DBH estimation bias for European beech from different cross-section thickness.

w | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |

2 | 0.441 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

3 | 0.963 | 0.442 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

4 | 0.532 | 0.937 | 0.513 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

5 | 0.706 | 0.182 | 0.684 | 0.231 | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

6 | 0.500 | 0.961 | 0.500 | 0.996 | 0.218 | - | - | - | - | - | - | - | - | - | - | - | - | - |

7 | 0.501 | 0.965 | 0.442 | 0.930 | 0.137 | 0.956 | - | - | - | - | - | - | - | - | - | - | - | - |

8 | 0.791 | 0.288 | 0.808 | 0.323 | 0.867 | 0.252 | 0.164 | - | - | - | - | - | - | - | - | - | - | - |

9 | 0.513 | 0.965 | 0.455 | 0.996 | 0.138 | 0.963 | 0.963 | 0.160 | - | - | - | - | - | - | - | - | - | - |

10 | 0.761 | 0.230 | 0.711 | 0.293 | 0.963 | 0.270 | 0.234 | 0.867 | 0.148 | - | - | - | - | - | - | - | - | - |

20 | 0.106 | 0.006 | 0.093 | 0.025 | 0.230 | 0.011 | 0.006 | 0.121 | 0.011 | 0.188 | - | - | - | - | - | - | - | - |

30 | 0.003 | 0.003 | 0.003 | 0.003 | 0.009 | 0.003 | 0.003 | 0.006 | 0.003 | 0.003 | 0.003 | - | - | - | - | - | - | - |

40 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - | - | - | - | - | - |

50 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - | - | - | - | - |

60 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - | - | - | - |

70 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - | - | - |

80 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - | - |

90 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | - |

100 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 | 0.003 |

**Table A4.**p-Values of pairwise comparison between DBH estimation bias for sessile oak from different cross-section thickness.

w | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |

2 | 0.967 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

3 | 0.973 | 0.960 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

4 | 0.898 | 0.957 | 0.976 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

5 | 0.957 | 0.805 | 0.824 | 0.805 | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

6 | 0.947 | 0.957 | 0.986 | 0.960 | 0.775 | - | - | - | - | - | - | - | - | - | - | - | - | - |

7 | 0.805 | 0.733 | 0.805 | 0.715 | 0.926 | 0.657 | - | - | - | - | - | - | - | - | - | - | - | - |

8 | 0.520 | 0.561 | 0.599 | 0.701 | 0.466 | 0.705 | 0.306 | - | - | - | - | - | - | - | - | - | - | - |

9 | 0.775 | 0.657 | 0.660 | 0.607 | 0.899 | 0.717 | 0.969 | 0.305 | - | - | - | - | - | - | - | - | - | - |

10 | 0.575 | 0.599 | 0.599 | 0.558 | 0.694 | 0.597 | 0.805 | 0.317 | 0.845 | - | - | - | - | - | - | - | - | - |

20 | 0.218 | 0.265 | 0.311 | 0.203 | 0.326 | 0.159 | 0.326 | 0.067 | 0.470 | 0.679 | - | - | - | - | - | - | - | - |

30 | 0.017 | 0.008 | 0.047 | 0.014 | 0.014 | 0.017 | 0.017 | 0.008 | 0.014 | 0.085 | 0.158 | - | - | - | - | - | - | - |

40 | 0.017 | 0.005 | 0.023 | 0.005 | 0.017 | 0.005 | 0.014 | 0.005 | 0.023 | 0.047 | 0.042 | 0.617 | - | - | - | - | - | - |

50 | 0.008 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.017 | 0.065 | 0.138 | - | - | - | - | - |

60 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.011 | 0.029 | 0.032 | 0.187 | - | - | - | - |

70 | 0.005 | 0.008 | 0.005 | 0.005 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 | 0.008 | 0.011 | 0.020 | 0.011 | - | - | - |

80 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 | 0.008 | 0.005 | 0.005 | 0.011 | - | - |

90 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.050 | - |

100 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.005 | 0.008 |

## Appendix E

**Table A5.**p-Values of pairwise comparison between DBH estimation MSE

_{W}for European beech from different cross-section thickness.

w | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |

2 | 0.577 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

3 | 0.571 | 0.352 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

4 | 0.779 | 0.778 | 0.385 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

5 | 0.535 | 0.385 | 0.780 | 0.385 | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

6 | 0.802 | 0.772 | 0.399 | 0.903 | 0.296 | - | - | - | - | - | - | - | - | - | - | - | - | - |

7 | 0.596 | 0.982 | 0.411 | 0.802 | 0.334 | 0.820 | - | - | - | - | - | - | - | - | - | - | - | - |

8 | 0.112 | 0.024 | 0.339 | 0.044 | 0.671 | 0.013 | 0.027 | - | - | - | - | - | - | - | - | - | - | - |

9 | 0.370 | 0.130 | 0.780 | 0.161 | 0.937 | 0.119 | 0.094 | 0.555 | - | - | - | - | - | - | - | - | - | - |

10 | 0.211 | 0.127 | 0.399 | 0.110 | 0.576 | 0.056 | 0.096 | 0.970 | 0.596 | - | - | - | - | - | - | - | - | - |

20 | 0.044 | 0.013 | 0.091 | 0.030 | 0.315 | 0.021 | 0.046 | 0.475 | 0.279 | 0.519 | - | - | - | - | - | - | - | - |

30 | 0.006 | 0.006 | 0.010 | 0.006 | 0.041 | 0.006 | 0.006 | 0.013 | 0.010 | 0.027 | 0.024 | - | - | - | - | - | - | - |

40 | 0.010 | 0.006 | 0.080 | 0.010 | 0.135 | 0.006 | 0.006 | 0.106 | 0.070 | 0.182 | 0.234 | 0.904 | - | - | - | - | - | - |

50 | 0.711 | 0.863 | 0.565 | 0.776 | 0.530 | 0.780 | 0.835 | 0.370 | 0.508 | 0.474 | 0.321 | 0.091 | 0.017 | - | - | - | - | - |

60 | 0.098 | 0.110 | 0.049 | 0.151 | 0.068 | 0.114 | 0.130 | 0.062 | 0.100 | 0.059 | 0.046 | 0.010 | 0.006 | 0.013 | - | - | - | - |

70 | 0.017 | 0.027 | 0.013 | 0.041 | 0.030 | 0.013 | 0.017 | 0.017 | 0.017 | 0.010 | 0.010 | 0.006 | 0.010 | 0.006 | 0.006 | - | - | - |

80 | 0.006 | 0.010 | 0.013 | 0.006 | 0.006 | 0.006 | 0.010 | 0.006 | 0.013 | 0.006 | 0.006 | 0.006 | 0.010 | 0.006 | 0.006 | 0.006 | - | - |

90 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | - |

100 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 | 0.006 |

**Table A6.**p-Values of pairwise comparison between DBH estimation MSE

_{W}for sessile oak from different cross-section thickness.

w | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 |

2 | 0.820 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

3 | 0.978 | 0.854 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

4 | 0.891 | 0.958 | 0.891 | - | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

5 | 0.913 | 0.913 | 0.910 | 0.923 | - | - | - | - | - | - | - | - | - | - | - | - | - | - |

6 | 0.910 | 0.913 | 0.913 | 0.917 | 0.923 | - | - | - | - | - | - | - | - | - | - | - | - | - |

7 | 0.754 | 0.903 | 0.769 | 0.891 | 0.785 | 0.767 | - | - | - | - | - | - | - | - | - | - | - | - |

8 | 0.958 | 0.811 | 0.956 | 0.891 | 0.913 | 0.923 | 0.610 | - | - | - | - | - | - | - | - | - | - | - |

9 | 0.820 | 0.913 | 0.767 | 0.913 | 0.913 | 0.913 | 0.913 | 0.810 | - | - | - | - | - | - | - | - | - | - |

10 | 0.923 | 0.909 | 0.917 | 0.913 | 0.923 | 0.986 | 0.754 | 0.963 | 0.811 | - | - | - | - | - | - | - | - | - |

20 | 0.349 | 0.734 | 0.580 | 0.725 | 0.572 | 0.481 | 0.910 | 0.320 | 0.910 | 0.441 | - | - | - | - | - | - | - | - |

30 | 0.065 | 0.023 | 0.056 | 0.084 | 0.031 | 0.041 | 0.056 | 0.041 | 0.041 | 0.060 | 0.149 | - | - | - | - | - | - | - |

40 | 0.041 | 0.039 | 0.041 | 0.078 | 0.039 | 0.041 | 0.039 | 0.041 | 0.078 | 0.041 | 0.041 | 0.785 | - | - | - | - | - | - |

50 | 0.031 | 0.023 | 0.041 | 0.023 | 0.041 | 0.041 | 0.023 | 0.023 | 0.023 | 0.023 | 0.039 | 0.224 | 0.466 | - | - | - | - | - |

60 | 0.041 | 0.023 | 0.023 | 0.023 | 0.031 | 0.031 | 0.023 | 0.023 | 0.023 | 0.023 | 0.045 | 0.130 | 0.149 | 0.406 | - | - | - | - |

70 | 0.083 | 0.031 | 0.031 | 0.041 | 0.051 | 0.045 | 0.031 | 0.041 | 0.023 | 0.041 | 0.103 | 0.221 | 0.349 | 0.548 | 0.903 | - | - | - |

80 | 0.121 | 0.070 | 0.060 | 0.045 | 0.084 | 0.112 | 0.078 | 0.065 | 0.045 | 0.088 | 0.178 | 0.308 | 0.483 | 0.636 | 0.913 | 0.807 | - | - |

90 | 0.180 | 0.150 | 0.084 | 0.162 | 0.149 | 0.178 | 0.164 | 0.150 | 0.141 | 0.138 | 0.224 | 0.481 | 0.610 | 0.785 | 0.913 | 0.913 | 0.917 | - |

100 | 0.278 | 0.300 | 0.239 | 0.279 | 0.296 | 0.284 | 0.349 | 0.278 | 0.229 | 0.278 | 0.447 | 0.736 | 0.810 | 0.891 | 0.923 | 0.913 | 0.978 | 0.926 |

## References

- Koreň, M.; Mokroš, M.; Bucha, T. Accuracy of tree diameter estimation from terrestrial laser scanning by circle-fitting methods. Int. J. Appl. Earth Obs. Geoinf.
**2017**, 63, 122–128. [Google Scholar] [CrossRef] - Cabo, C.; Ordóñez, C.; López-Sánchez, C.A.; Armesto, J. Automatic dendrometry: Tree detection, tree height and diameter estimation using terrestrial laser scanning. Int. J. Appl. Earth Obs. Geoinf.
**2018**, 69, 164–174. [Google Scholar] [CrossRef] - Kankare, V.; Puttonen, E.; Holopainen, M.; Hyyppä, J. The effect of TLS point cloud sampling on tree detection and diameter measurement accuracy. Remote Sens. Lett.
**2016**, 7, 495–502. [Google Scholar] [CrossRef] - Liu, C.; Xing, Y.; Duanmu, J.; Tian, X. Evaluating different methods for estimating diameter at breast height from terrestrial laser scanning. Remote Sens.
**2018**, 10, 513. [Google Scholar] [CrossRef] [Green Version] - Luoma, V.; Saarinen, N.; Kankare, V.; Tanhuanpää, T.; Vastaranta, M. Examining Changes in Stem Taper and Volume Growth with Two-Date 3D Point Clouds. Forests
**2019**, 10, 382. [Google Scholar] [CrossRef] [Green Version] - Pueschel, P.; Newnham, G.; Rock, G.; Udelhoven, T.; Werner, W.; Hill, J. The influence of scan mode and circle fitting on tree stem detection, stem diameter and volume extraction from terrestrial laser scans. ISPRS J. Photogramm. Remote Sens.
**2013**, 77, 44–56. [Google Scholar] [CrossRef] - Puletti, N.; Grotti, M.; Scotti, R. Evaluating the eccentricities of poplar stem profiles with terrestrial laser scanning. Forests
**2019**, 10, 239. [Google Scholar] [CrossRef] [Green Version] - Liu, G.; Wang, J.; Dong, P.; Chen, Y.; Liu, Z. Estimating individual tree height and diameter at breast height (DBH) from terrestrial laser scanning (TLS) data at plot level. Forests
**2018**, 8, 398. [Google Scholar] [CrossRef] [Green Version] - Gollob, C.; Ritter, T.; Wassermann, C.; Nothdurft, A. Influence of scanner position and plot size on the accuracy of tree detection and diameter estimation using terrestrial laser scanning on forest inventory plots. Remote Sens.
**2019**, 11, 1602. [Google Scholar] [CrossRef] [Green Version] - Heinzel, J.; Ginzler, C. A single-tree processing framework using terrestrial laser scanning data for detecting forest regeneration. Remote Sens.
**2019**, 11, 60. [Google Scholar] [CrossRef] [Green Version] - Pitkänen, T.P.; Raumonen, P.; Kangas, A. Measuring stem diameters with TLS in boreal forests by complementary fitting procedure. ISPRS J. Photogramm. Remote Sens.
**2019**, 147, 294–306. [Google Scholar] [CrossRef] - Srinivasan, S.; Popescu, S.C.; Eriksson, M.; Sheridan, R.D.; Ku, N.W. Terrestrial laser scanning as an effective tool to retrieve tree level height, crown width, and stem diameter. Remote Sens.
**2015**, 7, 1877–1896. [Google Scholar] [CrossRef] [Green Version] - Oveland, I.; Hauglin, M.; Giannetti, F.; Kjørsvik, N.S.; Gobakken, T. Comparing three different ground based laser scanning methods for tree stem detection. Remote Sens.
**2018**, 10, 538. [Google Scholar] [CrossRef] [Green Version] - Aijazi, A.K.; Checchin, P.; Malaterre, L.; Trassoudaine, L. Automatic detection and parameter estimation of trees for forest inventory applications using 3D terrestrial LiDAR. Remote Sens.
**2017**, 9, 946. [Google Scholar] [CrossRef] [Green Version] - Pyörälä, J.; Liang, X.; Saarinen, N.; Kankare, V.; Wang, Y.; Holopainen, M.; Hyyppä, J.; Vastaranta, M. Assessing branching structure for biomass and wood quality estimation using terrestrial laser scanning point clouds. Can. J. Remote Sens.
**2018**, 44, 462–475. [Google Scholar] [CrossRef] [Green Version] - Reddy, R.S.; Jha, C.S.; Rajan, K.S. Automatic Tree Identification and Diameter Estimation Using Single Scan Terrestrial Laser Scanner Data in Central Indian Forests. J. Indian Soc. Remote Sens.
**2018**, 46, 937–943. [Google Scholar] [CrossRef] - Wang, Y.; Pyörälä, J.; Liang, X.; Lehtomäki, M.; Kukko, A.; Yu, X.; Kaartinen, H.; Hyyppä, J. In situ biomass estimation at tree and plot levels: What did data record and what did algorithms derive from terrestrial and aerial point clouds in boreal forest. Remote Sens. Environ.
**2019**, 232, 111309. [Google Scholar] [CrossRef] - Yrttimaa, T.; Saarinen, N.; Kankare, V.; Liang, X.; Hyyppä, J.; Holopainen, M.; Vastaranta, M. Investigating the feasibility of multi-scan terrestrial laser scanning to characterize tree communities in southern boreal forests. Remote Sens.
**2019**, 11, 1423. [Google Scholar] [CrossRef] [Green Version] - Wang, P.; Gan, X.; Zhang, Q.; Bu, G.; Li, L.; Xu, X.; Li, Y.; Liu, Z.; Xiao, X. Analysis of parameters for the accurate and fast estimation of tree diameter at breast height based on simulated point cloud. Remote Sens.
**2019**, 11, 2707. [Google Scholar] [CrossRef] [Green Version] - Koreň, M.; Slančík, M.; Suchomel, J.; Dubina, J. Use of terrestrial laser scanning to evaluate the spatial distribution of soil disturbance by skidding operations. IForest
**2015**, 8, 386–393. [Google Scholar] [CrossRef] - Koreň, M. DendroCloud: Point Cloud Processing Software for Forestry, Version 1.50; Dendro Cloud: Zvolen, Slovakia, 2019; Available online: http://gis.tuzvo.sk/dendrocloud/download/dendrocloud_1_50.pdf (accessed on 30 July 2020).
- Benjamini, Y.; Hochberg, Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. J. R. Stat. Soc. Ser. B
**1995**, 57, 289–300. [Google Scholar] [CrossRef]

**Figure 4.**Box-plots of number of points in each cross-section thickness. Red crosses indicate average and the red line connects averages of each cross-section thickness.

**Figure 5.**Scatter plots showing trees with their reference (y-axis) and estimated (x-axis) DBH. Color distinguish the cross-sections thickness. Lines above graphs are marginal density plots.

**Figure 6.**Box-plots of error of DBH estimation for each cross-section thickness separated by tree species. Red crosses indicate average and red line is connecting averages of each cross-section thickness. The line is clearly showing the increment of average (bias) from 10–100 cm thickness.

**Figure 7.**Orthogonal projection of 100 cm cross-sections of (

**a**) a leaning beech and (

**b**) a straight oak.

Plot Number | Date of Scanning | Tree Species | Number of Trees | DBH (cm) | |||
---|---|---|---|---|---|---|---|

Min | Max | Avg | Std | ||||

1 | 23 October 2012 | European beech | 121 | 9.1 | 62.3 | 28.4 | 11.9 |

2 | 4 July 2017 | Sessile oak | 43 | 17.9 | 42.5 | 37.8 | 5.6 |

Cross−Section Thickness w (cm) | European Beech | Sessile Oak | ||||||||
---|---|---|---|---|---|---|---|---|---|---|

Min | Max | ${\overline{\mathit{e}}}_{\mathit{w}}$ | ${\mathit{s}}_{\mathit{w}}$ | p_{SH} | Min | Max | ${\overline{\mathit{e}}}_{\mathit{w}}$ | ${\mathit{s}}_{\mathit{w}}$ | p_{SH} | |

1 | −2.26 | 1.08 | −0.32 | 0.46 | 0.01 | −2.08 | −0.09 | −1.15 | 0.44 | 0.48 |

2 | −2.43 | 0.95 | −0.33 | 0.47 | <0.01 | −1.85 | −0.20 | −1.15 | 0.40 | 0.51 |

3 | −1.96 | 0.79 | −0.32 | 0.45 | 0.13 | −1.95 | −0.30 | −1.15 | 0.43 | 0.50 |

4 | −2.33 | 1.02 | −0.33 | 0.46 | <0.01 | −2.00 | −0.30 | −1.16 | 0.39 | 0.96 |

5 | −1.88 | 0.99 | −0.31 | 0.45 | 0.27 | −1.88 | −0.10 | −1.15 | 0.43 | 0.33 |

6 | −2.26 | 0.89 | −0.33 | 0.46 | 0.04 | −2.03 | −0.10 | −1.15 | 0.41 | 0.88 |

7 | −2.43 | 1.12 | −0.33 | 0.47 | <0.01 | −1.92 | −0.21 | −1.14 | 0.40 | 0.95 |

8 | −2.16 | 0.73 | −0.31 | 0.44 | 0.03 | −1.93 | −0.28 | −1.17 | 0.39 | 0.79 |

9 | −2.19 | 0.61 | −0.33 | 0.44 | 0.01 | −1.82 | −0.22 | −1.14 | 0.42 | 0.25 |

10 | −2.08 | 0.93 | −0.31 | 0.44 | 0.06 | −1.97 | 0.02 | −1.13 | 0.47 | 0.52 |

20 | −2.05 | 0.89 | −0.29 | 0.44 | 0.06 | −1.95 | −0.09 | −1.12 | 0.44 | 0.89 |

30 | −2.09 | 0.72 | −0.24 | 0.44 | <0.01 | −1.90 | −0.12 | −1.09 | 0.42 | 0.33 |

40 | −2.32 | 1.21 | −0.16 | 0.47 | <0.01 | −1.83 | −0.20 | −1.07 | 0.42 | 0.25 |

50 | −2.33 | 1.97 | −0.08 | 0.58 | <0.01 | −1.86 | −0.19 | −1.03 | 0.46 | 0.08 |

60 | −2.20 | 2.97 | 0.03 | 0.72 | <0.01 | −1.75 | −0.18 | −0.99 | 0.47 | 0.09 |

70 | −1.96 | 4.21 | 0.14 | 0.87 | <0.01 | −2.28 | 0.20 | −0.92 | 0.56 | 0.83 |

80 | −2.34 | 5.29 | 0.24 | 1.04 | <0.01 | −2.85 | 0.33 | −0.85 | 0.63 | 0.13 |

90 | −2.30 | 5.72 | 0.38 | 1.17 | <0.01 | −3.19 | 0.65 | −0.79 | 0.69 | 0.06 |

100 | −2.54 | 6.05 | 0.50 | 1.33 | <0.01 | −3.54 | 0.97 | −0.71 | 0.77 | 0.01 |

_{SH}, p-value of the Shapiro-Wilk test of DBH estimation errors normality.

**Table 3.**DBH estimation accuracy. Conditional formatting ranges from lowest (green) to highest (red).

Cross-Section Thickness w (cm) | European Beech | Sessile Oak | ||||
---|---|---|---|---|---|---|

MSE_{W} | RMSE_{W} | p_{SH} | MSE_{W} | RMSE_{W} | p_{SH} | |

1 | 0.31 | 0.56 | <0.01 | 1.51 | 1.23 | <0.01 |

2 | 0.32 | 0.57 | <0.01 | 1.48 | 1.22 | 0.02 |

3 | 0.3 | 0.55 | <0.01 | 1.51 | 1.23 | 0.01 |

4 | 0.32 | 0.57 | <0.01 | 1.48 | 1.22 | 0.03 |

5 | 0.3 | 0.55 | <0.01 | 1.49 | 1.22 | 0.02 |

6 | 0.32 | 0.57 | <0.01 | 1.49 | 1.22 | 0.02 |

7 | 0.32 | 0.57 | <0.01 | 1.46 | 1.21 | 0.08 |

8 | 0.29 | 0.54 | <0.01 | 1.5 | 1.23 | 0.01 |

9 | 0.3 | 0.54 | <0.01 | 1.47 | 1.21 | 0.01 |

10 | 0.29 | 0.54 | <0.01 | 1.5 | 1.22 | 0.01 |

20 | 0.28 | 0.53 | <0.01 | 1.44 | 1.2 | 0.01 |

30 | 0.25 | 0.5 | <0.01 | 1.35 | 1.16 | <0.01 |

40 | 0.25 | 0.5 | <0.01 | 1.32 | 1.15 | <0.01 |

50 | 0.34 | 0.58 | <0.01 | 1.26 | 1.12 | 0.01 |

60 | 0.51 | 0.71 | <0.01 | 1.19 | 1.09 | <0.01 |

70 | 0.77 | 0.88 | <0.01 | 1.16 | 1.08 | <0.01 |

80 | 1.13 | 1.06 | <0.01 | 1.1 | 1.05 | <0.01 |

90 | 1.51 | 1.23 | <0.01 | 1.08 | 1.04 | <0.01 |

100 | 2 | 1.41 | <0.01 | 1.08 | 1.04 | <0.01 |

_{SH}, p-value of the Shapiro-Wilk test of DBH estimation square errors normality.

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Koreň, M.; Hunčaga, M.; Chudá, J.; Mokroš, M.; Surový, P.
The Influence of Cross-Section Thickness on Diameter at Breast Height Estimation from Point Cloud. *ISPRS Int. J. Geo-Inf.* **2020**, *9*, 495.
https://doi.org/10.3390/ijgi9090495

**AMA Style**

Koreň M, Hunčaga M, Chudá J, Mokroš M, Surový P.
The Influence of Cross-Section Thickness on Diameter at Breast Height Estimation from Point Cloud. *ISPRS International Journal of Geo-Information*. 2020; 9(9):495.
https://doi.org/10.3390/ijgi9090495

**Chicago/Turabian Style**

Koreň, Milan, Milan Hunčaga, Juliana Chudá, Martin Mokroš, and Peter Surový.
2020. "The Influence of Cross-Section Thickness on Diameter at Breast Height Estimation from Point Cloud" *ISPRS International Journal of Geo-Information* 9, no. 9: 495.
https://doi.org/10.3390/ijgi9090495