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Fig. 1. The location of our study area in pink (Våler municipality) in Norway (top left; made with Natural Earth), a zoomed in view of the 253 plot locations in blue (top right; made with Esri World Imagery), and a circular cross-section of the point cloud obtained from near the perimeter of a single plot coloured by height (bottom; made with own data).

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Fig. 2. The number of detected and undetected field-measured European aspens by height (left), diameter at breast height (centre), and volume (right) from our study area in Våler, Norway.

Table 1. Definitions of the binary classification measures used in this work. The Bayesian estimate of FDRtree (base rate p) is defined using the expected value and estimated by the mean of the distribution obtained directly by simulating samples from the false discovery rate and true positive rate distributions. Note that Cohen’s Kappa is primarily included for illustrative purposes, although its use in low prevalence classification is discouraged (Foody 2020).
Primary metrics Frequentist approach Bayesian approach (Jeffreys prior)
FNRtree

FNRvolume
FPRtree

TPRtree

FDRtree (sample)

FDRvolume (sample)
FDRtree (base rate p)

Secondary metrics
F1-score
User’s accuracy
Producer’s accuracy
Overall accuracy
Cohen’s Kappa
Matthews correlation coefficient
FDR = False discovery rate, FN = False negative, FNR = False negative rate, FP = False positive, TN = True negative, TP = True positive, and TPR = True positive rate.
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Fig. 3. The effect of different ratios of European aspen to other tree species from our study area in Våler, Norway resulting from synthetic minority oversampling technique (SMOTE) with various degrees of over- and undersampling on the F1-score of European aspens. The over- and undersampling values in this figure ranged from 2 to 24 in steps of 2 (following criteria from the R package performanceEstimation). Oversampling values go from 2 to 24 from right to left for each undersampling value.

Table 2. Tree-level confusion matrices from random forest with five-fold plot-level cross-validation for all segmented trees and only canopy-reaching trees (trees within four meters from the highest laser echo in each plot). We show count-based and volume-based results (in m3) with 95% posterior credible intervals in parentheses. Results from our study area in Våler, Norway.
All trees (count-based)
Predicted class
European aspen Other Sum FNR
Observed class European aspen 15 40 55 73% (60­­–83)
Other 7 5393 5400  
Sum 22 5433  
FDR 32% (16–52)  
All trees (volume-based)
Predicted class
European aspen Other Sum FNR
Observed class European aspen 9.5 11.1 20.6 54% (38–71)
Other 4.3 1613.6 1617.9  
Sum 13.8 1624.7  
FDR 31% (11–51)  
Canopy-reaching trees (count-based)
Predicted class
European aspen Other Sum FNR
Observed class European aspen 11 20 31 65% (47–79)
Other 3 1973 1976  
Sum 14 1993  
FDR 21% (7–46)  
Canopy-reaching trees (volume-based)
Predicted class
European aspen Other Sum FNR
Observed class European aspen 7.0 8.5 15.5 55% (35–75)
Other 1.7 1048.2 1049.9  
Sum 8.7 1056.7  
FDR 20% (0–43)
FDR = False discovery rate, FNR = False negative rate.
Table 3. Several standard metrics shown from random forest with five-fold plot-level cross-validation for all segmented trees and only canopy-reaching trees (trees within four meters from the highest laser echo in each plot) with count-based and volume-based results from our study area in Våler, Norway.
F1-score
European aspen 		User’s accuracy European aspen Producer’s accuracy European aspen Overall accuracy Cohen’s Kappa Matthews correlation coefficient
All trees (count-based) 0.39 0.68 0.27 0.99 0.39 0.43
All trees (volume-based) 0.55 0.69 0.46 0.99 0.55 0.56
Canopy-reaching trees (count-based) 0.49 0.79 0.35 0.99 0.48 0.52
Canopy-reaching trees (volume-based) 0.58 0.80 0.45 0.99 0.57 0.60
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Fig. 4. Variable-importance measures for the 20 best features to separate European aspen from non-aspen species for all trees and only canopy-reaching trees from our study area in Våler, Norway. A green font colour represents ALS-derived features, while a blue font colour represents spectral features. Abbreviations: / = division of two image bands, R = Red, G = Green, B = Blue, NIR = near-infrared, NDVI = normalised difference vegetation index, I = intensity, H = height, P = percentile, SD = standard deviation, XY = XY-plane, f = first and only echoes, pcum = cumulative percentage of returns in the xth layer.

Table 4. Re-analysis of ten previous publications on tree species classification from remotely sensed data in Fennoscandia where European aspen was included as a class. For comparison, our count-based results from this study are displayed in red but not included in the median and mean calculations. Assuming a 1% base rate (meaning that European aspen represents 1% of all tree species in an area), we display the false negative and false discovery rates (the latter being strongly affected by the selected base rate) of these publications and our results in this study with their 95% posterior credible intervals in parentheses.
Author(s) N other N European aspen European aspen (%) FNR FDR (sample) FDR (1% BR)
Erikson 2004 777 14 1.8% 30% (10–55) 38% 52% (31–72)
Kulikova et al. 2007 34 14 29% 17% (3–39) 14% 86% (59–96)
Ørka et al. 2007 203 21 9% 75% (55–90) 44% 88% (70–97)
Viinikka et al. 2020 528 178 25% 11% (7–16) 8% 73% (61–82)
Mäyrä et al. 2021 448 82 15% 13% (6–21) 6% 56% (33–73)
Kuzmin et al. 2021 63 28 31% 19% (7–35) 15% 88% (73–95)
Hardenbol et al. 2021 383 104 21% 4% (1–9) 3% 45% (19–68)
Korpela et al. 2022 2405 167 6% 23% (17–30) 16% 57% (47–66)
Bjørnbet 2024 431 48 10% 62% (48–75) 50% 91% (86–95)
Toivonen et al. 2024 33 164 31 0.1% 77% (61–89) 80% 28% (16–46)
Median 439 39 8% 21% 16% 65%
Mean 3844 69 18% 33% 27% 66%
This work (all trees) 5400 55 1% 72% (60–83) 32% 33% (16–52)
This work (canopy-reaching trees) 1976 31 1.5% 65% (47–79) 21% 32% (10–57)
ALS = Airborne laser scanning, BR = Base rate, CIR = Colour-infrared, FDR = False discovery rate, FNR = False negative rate, HS = Hyperspectral imagery, MS = Multispectral imagery, RS = Remote sensing.