Estimating the vegetation canopy height using micro-pulse photon-counting LiDAR data

Sheng Nie; Cheng Wang; Xiaohuan Xi; Shezhou Luo; Guoyuan Li; Jinyan Tian; Hongtao Wang

doi:10.1364/OE.26.00A520

1. Introduction

Vegetation canopy height is a key input parameter required for modeling vegetation biomass, which is very important for quantitatively monitoring the storage of carbon levels [1–3]. Therefore, it is necessary to rapidly and accurately estimate vegetation canopy height. Advances in LiDAR technology make it a reliable data source for vegetation canopy height retrieval [4–6]. There are three types of LiDAR systems according to the platform: terrestrial, airborne and space-borne LiDAR systems [7–9]. However, terrestrial and airborne LiDAR systems are only available for small extents due to the limited coverage and high acquisition costs [10–12]. In contrast, space laser altimetry is an ideal choice for studies of large extent [13, 14]. In fact, the Ice, Cloud and land Elevation Satellite (ICESat) mission, launched by National Aeronautics and Space Administration (NASA), has made significant contributions to measure ice sheet elevations and changes in elevation, obtain sea ice thickness and retrieve vegetation canopy height [15]. The Geoscience Laser Altimeter System (GLAS) onboard the ICESat, is the first earth observation space-borne LiDAR which can provide effective data for measuring earth’s vegetation characteristics [15]. However, the ICESat ceased operation in 2009. Its successor ICESat-2 will continue to provide global sampling of vegetation canopy height by using the Advanced Topographic Laser Altimeter System (ATLAS) [16–19].

Different from the GLAS low-repetition-rate, high-energy, waveform-digitizing LiDAR system, the ATLAS will employ a photon-counting laser instrument with high-repetition-rate, low-energy, single-photon-sensitive detectors [20–22]. Specifically, the ATLAS will emit pulses with much lower energy and higher repetition rate, which will lead to a denser spatial sampling and small ground footprint diameter compared with GLAS system [16, 23, 24]. Additionally, unlike the GLAS analog waveform system, the ATLAS will employ the photon-counting LiDAR sensor [25–28]. Due to the change from GLAS analog waveform system to the ATLAS photon-counting system, new data processing techniques are required to automatically detect canopy and ground surfaces, and thereafter accurately estimate vegetation canopy height. However, there are currently several problems that remain unsolved in vegetation canopy height retrieval using the photon-counting LiDAR data. Among them, the primary challenge exists in the effective detection of signal photons from massive noise photons caused by solar background, system dark current and atmospheric scattering [29–31]. These noise photons are randomly and widely distributed (above and within the canopy, and below the true ground surface), which greatly affected the detection of signal photons. Therefore, an effective noise filtering algorithm is essential to differentiate signal photons from noise photons.

To date, several noise filtering algorithms have been developed by previous studies for efficiently handling noise in photon-counting LiDAR data [32–35]. These methods were proposed based on the fact that noise photons are sparsely and randomly distributed, while signal photons have a more clustered distribution [35]. Thus the density of signal photon is much higher than that of noise photons. These current noise filtering algorithms can be further divided into three categories: image processing, localized statistics, and density clustering based algorithms [28]. Image processing based algorithms are achieved by interpolating point clouds into raster images, and then image processing methods are adopted to reduce noises and retrieve canopy height [29, 30]. The localized statistics based methods calculate the feature parameters using localized spatial statistical analysis, and then set corresponding thresholds of feature parameters to differentiate signal photons from noise photons [28, 31, 32, 34, 36, 37]. In the density clustering-based methods, raw photon-counting LiDAR data are classified into noise photons and signal photons using a density clustering algorithm [33, 35]. Among all types of noise filtering algorithms, image processing based algorithms have a limitation in removing noise photons because some useful information may be lost due to the interpolation from point clouds to raster image. The density clustering based algorithms usually fail to effectively filter out noise photons in vegetated environments with steep relief [33]. Furthermore, the surface spectral reflectance, atmospheric conditions, and solar incidence angle spatially vary in the along-track direction, leading to the inconsistency of point density, which may also greatly affect the performance of the density clustering based algorithms [34]. The localized statistics-based algorithms have therefore been the most widely employed algorithms in differentiating signal photons from noise photons over vegetated areas. However, the previous localized statistics-based algorithms have some deficiencies. Specifically, these algorithms didn’t consider the influence due to the inconsistency of noise photon density, and the edge effect. Therefore, a new localized statistics-based algorithm is required for better filtering out the noise photons in complex vegetated environments.

Apart from the noise removal, the separation of ground photons and canopy photons is also an essential step to recover canopy and ground surfaces, and thereafter accurately estimate canopy height. For conventional discrete-return LiDAR systems, there are many point classification algorithms to separate ground returns from canopy returns [38–40]. However, the photons yielded from photon-counting systems are shown in a profile along track, which is basically different from conventional LiDAR point clouds. In this case, new point classification algorithms are required for separating ground photons from canopy photons. Moreover, existing methods largely distinguish ground photons from canopy photons based on the moving curve fitting algorithm [28]. However, the moving curve fitting algorithm has limitations in distinguishing ground returns from canopy returns in complex forest ecosystems [28]. Therefore, an effective photon classification algorithm is essential to better separate ground photons from canopy photons.

Overall, there are several challenges in estimating vegetation canopy height from photon-counting LiDAR data. To address the aforementioned issues, this paper proposed an automatic approach for better estimating vegetation canopy height using photon-counting laser altimeter data. There are three key steps to fulfill this objective. Firstly, a new localized statistics-based algorithm was proposed to filter out noise photons. Secondly, the ground photons were separated from canopy photons using an effective photon classification algorithm, and then the canopy-top and ground surfaces were determined. Finally, vegetation canopy height was accurately estimated based on canopy-top and ground surfaces. Additionally, the applicability of our vegetation height estimation approach was tested to two types of simulated ICESat-2 data, and retrieved canopy heights were validated using canopy height models (CHM) derived from airborne discrete-return LiDAR data.

2. Materials

Two types of simulated ICESat-2 data were used in this paper. The first one is the Sigma Space LiDAR data, which were used for evaluating the performance of new noise removal algorithm. The second source of simulated ICESat-2 data is from the MATLAS data, which were used to test the applicability of photon classification algorithms.

2.1 Sigma Space LiDAR data

To evaluate the performance of new noise removal algorithm, two Sigma Space LiDAR data sets were collected in early October 2009. This is a micro-pulse photon-counting LiDAR sensor, which operates at 532 nm with a high repetition rate of 100 KHz [28, 41–43]. The first data set is located in the Pine Barren regions of Silas Little and Cedar Bridge in New Jersey. This is a heavily forested, flat, and sandy area comprising of mainly pitch pine (Pinus rigida), shortleaf pine (Pinus echinata), Eastern black oak (Quercus velutina), white oak (Quercus alba), post oak (Quercus stellata), chestnut oak (Quercus prinus), scarlet oak (Quercus coccinea), and blackjack oak (Quercus marilandica). The forest canopy cover in this area is 75-80% [28]. The second data set was acquired over the Smithsonian Environmental Research Center (SERC) forest. This area is mainly dominated by mature secondary upland forest but also a part of floodplain forests. The upland forest has many tree species, including the ‘tulip poplar’, several oaks (Quercus spp.), beech (Fagus grandifolia), and several hickories (Carya spp), red maple (Acer rubrum), sour gum (Nyssa sylvatica), American hornbeam (Carpinus caroliniana), spicebush (Lindera benzoin), and paw-paw (Asimina triloba). The floodplain forest is largely dominated by ash (Fraxinus spp), American sycamore (Platanus occidentalis), and American elm (Ulmus Americana). This experiment site has an extremely high canopy cover of greater than 95% [28].

The photon density of Sigma Space LiDAR data is higher than the expected density of ICESat-2 data. Thus the Sigma Space LiDAR data must been randomly down-sampled to generate simulated ICESat-2 data. These simulated ICESat-2 data sets are available from the NASA Goddard ICESat-2 website (http://icesat.gsfc.nasa.gov/icesat2/). As the simulated ICESat-2 data generated from Sigma Space LiDAR data have been manually classified into noise photons and noise photons, these data sets can be regarded as reference classification data sets for evaluating the performance of the new proposed noise removal algorithm. However, we cannot obtain the airborne LiDAR data corresponding to the Sigma Space LiDAR data, thus another simulated ICESat-2 data (MATLAS data) were used to test the photon classification algorithm.

In this article, the flight lines over the Pine Barrens are represented as Cedar-2 and Cedar-4. Data sets over the SERC forest are referred as SERC-1, SERC-3, and SERC-5. There are there different noise levels for each transect, including “0.5 MHz”, “2 MHz” and “5 MHz,” representing nighttime acquisitions, late daytime acquisitions with clear sky, and daytime acquisitions with a hazy atmosphere, respectively.

2.2 MATLAS data

MATLAS is another simulated ICESat-2 data acquired for evaluating the performance of photon classification algorithms. The MATLAS data simulates the expected performance of ICESat-2’s ATLAS instrument, and is generated from the Multiple Altimeter Beam Experimental Lidar (MABEL) data [44–46], which is an airborne simulator of ATLAS and specifically developed by NASA’s Goddard Space Flight Center to pre-validate the ICESat-2 mission [47–49]. MABEL flights were carried out on NASA’s ER-2 High Altitude Airborne Science Aircraft (http://www.nasa.gov/centers/armstrong/aircraft/ER-2/index.html). The MABEL data were acquired using a photon-counting LiDAR with a pulse width of ~2 ns, and a variable pulse repetition frequency (PRF) of 5-25 kHz [49].

The MATLAS data were generated by adjusting the density of MABEL data corresponding to ATLAS instrument model design cases. Specifically, each MATLAS transect was produced from the corresponding MABEL transect in following five steps according to the ICESat-2 science team [26]. Firstly, the trajectory of MABEL data was simplified to simulate the ATLAS trajectory. Secondly, the spatial resolution of MABEL data was reduced from 2 m to 14 m to keep consistent with the ATLAS data. Thirdly, photons in MABEL data for were classified into signal and noise classes. Fourthly, signal photons in the MABLE data were subsampled to match the expected ATLAS signal photon density. Finally, noise levels were adjusted if simulated background noise levels exceed that of the MABEL data, while retaining the observed spatial variability of solar background noise caused by changing surface reflectance along the flight line.

This study collected two MATLAS data sets on the NASA Goddard ICESat-2 website (http://icesat.gsfc.nasa.gov/icesat2/). The first one was acquired over the East Coast site, which is a temperate, hilly area with extremely high vegetation cover of greater than 90%. Another is located in a heavily forested, temperate, montane West Coast site. The canopy cover of West Coast site is approximately 90%. In this article, the flight line over the East Coast is represented as EC in short. The transect over the West Coast forest is referred as WC.

2.3 Airborne LiDAR data

To assess the accuracy of our new proposed approach for estimating canopy height from photon-counting LiDAR data, the results obtained from MATLAS data have been compared with airborne discrete-return LiDAR data, which were collected for the same flight paths using the multi-sensor instrument NASA-Goddard’s LiDAR, Hyperspectral, and Thermal Imager (G-LiHT) [50]. Both the digital terrain model (DTM) and canopy height model (CHM) along the flight transects have already been generated from airborne LiDAR data by the G-LiHT science team (http://gliht.gsfc.nasa.gov/). Both the DTM and CHM have a same resolution of 1 m. The DTM was used to evaluate the performance of the adapted photon classification algorithm, and CHM was adopted to validate the accuracy of canopy height estimates.

3. Methodologies

3.1 Noise photon removal

In this paper, an effective algorithm based on the localized statistical analysis was proposed to filter out noise photons. The new noise filtering algorithm consists of two main steps: coarse de-noising and fine de-noising (Fig. 1).

Fig. 1 The flow chart of new noise removal algorithm.

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1) Coarse de-noising
Coarse de-noising is a process to roughly filter out noise photons and approximately determine the position of signal photons. A method based on elevation frequency histogram was introduced to roughly reduce noises according to the study of Moussavi et al. [28]. This coarse de-noising method was performed as follows: Firstly, the elevation frequency histogram was built by setting an elevation bin size of 1 m. Secondly, the standard deviation was calculated based on the elevation frequency histogram, and finally, we approximately determined the location of signal photons with a three-standard deviation cut-off. This coarse de-noising method can remove the highest and lowest noise photons. However, coarse de-noising failed to remove these noise photons near the canopy and ground surfaces, which greatly affected the retrieval of vegetation canopy height. Therefore, it is necessary to further eliminate the noise photons.
2) Fine de-noising
Fine de-noising is a process of removing remaining noise photons on the basis of coarse de-noising. A fine de-noising method based on localized statistics analysis was proposed to further eliminate the noise photons. The new proposed method consists of four key steps.
The first is to calculate the point density of each photon, which is defined as the number of photons in the neighborhood of each photon. The computational formula was given in Eq. (1). As the photon-counting LiDAR data distributed in the XZ profile (X is the along-track dimension and Z is the elevation dimension), and the average distance between photons along X (X-distance) was quite different from that along Z (Z-distance), an ellipse neighborhood rather than a circle neighborhood was adopted to calculate the photon density according to the previous studies [28,33]. The ellipse characteristics was determined based on the ratio of X-distance and Z-distance. In this study, the semi major axis and semi minor axis were set to 35 m and 3 m, respectively. Additionally, there may be no photons in part of their neighborhoods when these photons are located at the border region. In this case, the point density of photons within the border region are much smaller than that of photons located in non-border region, which may greatly affect the effective removal of noise photons. Therefore, it is necessary to consider the edge effect. To reduce the edge effect, data filling was conducted using the photons in adjacent area. In specific, the photons located in the border region were first detected and selected. Then these detected photons were mirrored according to the Eq. (2). Finally, data filling was conducted using the mirror photons.
$\begin{array}{l} \forall ψ_{i} (x_{i}, z_{i}) \in G, 1 \leq i \leq k; D_{i} = {ψ (x, z) | (^{x - x_{i}) 2} / a^{2} + (^{z - z_{i}) 2} / b^{2} \leq 1} \\ D e n s i t y_{i} = n (D_{i}) \end{array}$ $\begin{array}{l} x_{m i r r o r} = 2 x_{b o r d e r} - x_{p} \\ z_{m i r r o r} = z_{p} \end{array}$
where $D_{i}$ represents all the points in the neighborhood of photon $(x_{i}, z_{i})$ , $D e n s i t y_{i}$ is the point density of ith photon, ( $x_{p}, z_{p}$ ) are the coordinates of the point located in the border region, ( $x_{m i r r o r}, z_{m i r r o r}$ ) are the coordinates of the mirror point, $x_{b o r d e r}$ is the X coordinate of the border line.
The second step is to calibrate and normalize the photon density. Due to the different environments in the along-track direction, especially varying atmospheric conditions and surface characteristics, the noise photon density along track may be quite different. This inconsistent noise photon density greatly limits the performance of noise removal algorithms. To be specific, some noise photons may be misclassified to signal photons, while some other signal photons cannot be correctly detected. Therefore, it is necessary to reduce the effect of inconsistent noise photon density. We calibrated the photon density by using an adjusting factor to effectively reduce this effect. The calibrated photon density is given in Eq. (3). Additionally, the photon density was also normalized according to the Eq. (4).
$D e n C o r r_{i} = \frac{D e n s i t y_{i}}{λ_{i}}$ $γ_{i} = \frac{D e n C o r r_{i}}{\max (D e n C o r r_{i})}$
where $λ_{i}$ is the adjusting factor, which stands for the average point density of these noise photons that have the same X position with the ith photon point. $D e n C o r r_{i}$ is the calibrated density of ith photon, $γ_{i}$ is the normalized point density of the ith photon, which is defined as the ith calibrated point density divided by the maximum calibrated point density among all photons.
The third step is to build photon density frequency histogram. It is well known that the density of signal photon is much higher than that of noise photons, and the photons with low density can be regarded as noise photons [35]. In this case, a photon density threshold must be first set to separate the signal photons from noise photons. In this paper, the photon density threshold was set based on the photon density frequency histogram. Photons with normalized density less than the threshold, were classified as noise photons and subsequently removed from the raw photon-counting LiDAR data. This step can remove the majority of noise photons. However, there were some isolated noise photons left that needed to be eliminated.
The final step is to further remove the isolated noise photons by building a localized elevation frequency histogram. The localized elevation frequency histogram was first built by setting an elevation bin size and along-track bin size. Then an elevation threshold was set based on the localized elevation frequency histogram to further eliminate isolated noise photons below the ground surface and above the canopy surface.

3.2 Separation of ground photons and canopy photons

The ground photons must be separated from canopy photons to recover the canopy and ground surfaces, and thereafter estimate vegetation canopy height. Conventional airborne LiDAR classification algorithms are not available for the photon-counting LiDAR data due to the difference between photon-counting and conventional LiDAR data. In this case, we adapted the progressive triangular irregular network (TIN) densification (PTD), which was proposed by Axelsson [51], making it applicable to separate ground photons from canopy photons. Similar to the PTD method, the adapted point classification method iteratively densifies an initial segment line created from selected seed ground photons according to certain criteria. This method includes three key steps: parameter specification, seed point selection and initial segment line generation, and the iterative detection of ground returns. The overall flow chart of the algorithm is presented in Fig. 2.

Fig. 2 The flow chart of the adapted photon classification algorithm.

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1) Parameter specification
There are three key input parameters in this photon classification algorithm to be present, including: i) Maximum non-ground features size, a length threshold, is used to define the size of line segment; ii) Maximum angle $q$ , a slope threshold, is the maximum angle between each segment line and a line connecting a potential ground point with the closest seed ground point; iii) Maximum distance $d$ , a distance threshold, is the maximum distance from a potential ground point to the corresponding segment line during each iteration.
2) Seed point selection and initial segment line generation
Seed ground points are selected based on the assumption that the point with lowest elevation in each segment line belongs to the true ground surface. To select seed ground points, we should first determine the boundary of the given data set, and then define the size of line segment based on the largest non-ground features in the experiment site. These seed ground points are selected as an initial ground points. The remaining points, except the seed ground points, are labeled as default object measurements.
3) The iterative detection of ground photons
The potential ground photons were iteratively detected based on several rigorous rules. To be specific, the judgement process of potential ground photons was made as follows: in each iteration process, one unclassified point is regarded as the potential ground photon if two key parameters of this point do not exceed the given thresholds. The first one is the angle between the segment line and the line connecting the point with the closest ground point ( $A_{a n g l e}$ ); the second is the distance from the potential ground photon to the corresponding ground line ( $D_{d i s \tan c e}$ ), as shown in Fig. 3. This process is made iteratively and stops when no more potential ground photons are detected.

3.3 Canopy height retrieval

The defined ground points were interpolated to generate a 5 m resolution Digital Elevation Model (DEM), which represents the ground surface. Using this DEM, we can remove the influence of topography and obtain DEM-normalized photons.

Fig. 3 The schematic diagram of angle and distance measurements.

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According to the study of Moussavi et al. [28], canopy-top surface was defined as where the 95th percentile of above-ground photons exists, thus the vegetation canopy height was calculated by finding the elevation at which 95% of DEM-normalized non-ground photons exist in the sampling size of 14 m.

3.4 Performance evaluation and accuracy validation

In this paper, the new noise filtering algorithm was applied to Sigma Space LiDAR data of varying noise levels, and both qualitative and quantitative analysis were conducted. The qualitative analysis was made by visual inspection. Additionally, three statistical indicators, including recall $R$ , precision $P$ and comprehensive evaluation index $F$ , were adopted to quantitatively evaluate the performance of new noise removal algorithm. $R$ is the ratio of true signal points that are successfully detected to all true signal points. $P$ is the fraction of true signal points that are correctly detected from all the detected signal points, and $F$ is the harmonic mean of recall and precision. These three indicators were calculated using reference classification data according to Eqs. (5)-(7).

R = \frac{T P}{T P + F N}

P = \frac{T P}{T P + F P}

F = \frac{2 P R}{P + R}

where

T P

,

F P

, and

F N

represent the numbers of true positives (hit), false positives (false alarm) and false negatives (miss), respectively. To be more specific, true positives stand for true signal photons that are correctly detected, false positives represent the noise photons that are misclassified as signal photons, and false negatives represent the true signal photons that are not correctly detected.

To further test the applicability of our new noise filtering algorithm, this study conducted the comparison between our noise filtering algorithm (noise removal algorithm 1, or NR algorithm 1 for short) and two other commonly used noise filtering algorithms. One is the noise filtering algorithm based on localized statistics analysis proposed by the study of Moussavi et al. [28], this method is denoted as NR algorithm 2. Another is an adaptive density-based algorithm proposed by the study of [33], this method is referred as NR algorithm 3.

The adapted point classification algorithm (photon classification algorithm 1, or PC algorithm 1) was tested to MATLAS data, and both the elevations of ground photons and ground surface interpreted from ground photons were evaluated against the independent airborne discrete-return LiDAR data. Two statistical variables, coefficient of determination (R²) and root-mean-squared error (RMSE) were used to evaluate the performance of photon classification algorithms. Additionally, the adapted point classification method was also compared with another photon classification algorithm (PC algorithm 2), which is proposed based on moving curve fitting by the study of Moussavi et al. [28].

To validate the accuracy of the canopy heights estimated from the MATLAS data, we compared canopy height estimates using reference heights, which were calculated as the 95th percentile of CHM derived from airborne discrete-return LiDAR data. Moreover, our approach for vegetation height estimation (height estimation method 1, or HE method 1) was also compared with the vegetation height estimation method (HE method 2) proposed by the study of Moussavi et al. [28]. In their method, the NR algorithm 2 was used to filter out noise photons, and ground photons were separated from canopy photons using the PC algorithm 2.

4. Results and discussion

4.1 Noise removal

The qualitative analysis results were shown in Figs. 4-11, and the results indicate that both the NR algorithm 2 and NR algorithm 3 usually failed to remove these noise photons in the border region and detect the signal photons in the areas where the noise photon density was inconsistent along track. In contrast, our method performed much better than both the NR algorithm 2 and NR algorithm 3 in filtering out the noise photons.

Fig. 4 Simulated ICESat-2 data (reference classification data) over the Cedar-2 flight line with a background noise rate of 5 MHz.

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Fig. 5 The noise removal result using NR algorithm 1 over the Cedar-2 flight line with a background noise rate of 5 MHz.

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Fig. 6 The noise removal result using NR algorithm 2 over the Cedar-2 flight line with a background noise rate of 5 MHz.

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Fig. 7 The noise removal result using NR algorithm 3 over the Cedar-2 flight line with a background noise rate of 5 MHz.

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Fig. 8 Simulated ICESat-2 data (reference classification data) over the SERC-1 flight line with a background noise rate of 5 MHz.

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Fig. 9 The noise removal results using NR algorithm 1 over the SERC-1 flight line with a background noise rate of 5 MHz.

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Fig. 10 The noise removal results using NR algorithm 2 over the SERC-1 flight line with a background noise rate of 5 MHz.

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Fig. 11 The noise removal results using NR algorithm 3 over the SERC-1 flight line with a background noise rate of 5 MHz.

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The quantitative analysis results were summarized in Table 1, and Figs. 12(a)-12(c) show the F-measure values of different noise filtering algorithms for all data sets. The statistical results in Table 1, Figs. 12(a)-12(c) indicate that all the three noise filtering algorithms had high F-measure values for almost all the data sets with low background noise levels, and the F-measure values decreased with the increase of background noise levels. This means that lower background noise rate leads to slightly better detection of signal photons. Additionally, the results also show that all the three algorithms have better noise filtering results over the Pine Barrens than SERC regardless of background noise levels. This finding is in agreement with the study of Moussavi et al. [28]. The canopy cover over Pine Barrens is obviously lower than that of SERC, allowing more emitted pulses to penetrate through the canopy and hit the ground surface, thus the ground photons can be easily separated from the noise photons. In contrast, the vegetation over SERC is very dense, which leads to very low density of ground returns. In this case, the ground returns may be misclassified as noise photons.

Table 1. Three statistical indicators of three different noise removal algorithms.

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Fig. 12 Comparison of F-measure values of three different noise removal algorithms over simulated ICESat-2 data generated from Sigma Space LiDAR data: (a) with a noise rate of 0.5 MHz; (b) with a noise rate of 2.0 MHz; (c) with a noise rate of 5.0 MHz.

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From Table 1, Figs. 12(a)-12(c), we can see that the F-measure values of NR algorithm 1 are higher than that of NR algorithm 3 for all data sets regardless of the background noise levels. Both NR algorithm 1 and NR algorithm 2 have good noise filtering results in processing the photon-counting data with low background noise level. This is maybe because the point density of signal photons is significantly higher than that of noise photons, thus the signal photons can be easily differentiated from noise photons. However, for data sets with high background noise levels, higher F-measure values were observed using NR algorithm 1 compared with NR algorithm 2. The higher F value of our noise removal algorithm will require less manual filtering and greatly shorten the time of noise filtering process.

Overall, both the results of qualitative and quantitative assessments indicated that the NR algorithm 1 performed better than NR algorithm 2 and NR algorithm 3 in filtering out noise photons. This can be explained by the two following reasons. On one hand, the previous noise filtering algorithms didn’t consider the edge effect on the detection of signal photons. In contrast, our new noise removal algorithm effectively reduces the edge effect by conducting data filling. On the other hand, our new noise removal algorithm induced an adjusting factor to reduce the influence of inconsistent noise photon density along track.

4.2 Photon classification

In this study, we validated the retrieved ground elevations over different experiment sites using the reference ground elevations derived from airborne discrete-return LiDAR data. For both PC algorithm 1 and PC algorithm 2, the estimated ground elevations showed strong agreement with reference ground elevations as demonstrated by the high R² values, and the retrieved ground elevations had higher accuracy over the EC (Figs. 13(a)-13(d)) than those in WC forest (Figs. 14(a)-14(d)) due to the higher R² and lower RMSE values. This can be explained that the topography over WC is much more complex than EC, making it challenging to effectively differentiate signal photons from noise photons.

Fig. 13 The scatterplots of (a) the LiDAR-derived ground elevations versus retrieved ground photon elevations using our adapted photon classification algorithm; (b) the LiDAR-derived ground elevations versus estimated ground photon elevations using PC algorithm 2; (c) the LiDAR-derived DTM elevations versus estimated DTM elevations using our adapted photon classification algorithm; (d) the LiDAR-derived DTM elevations versus estimated DTM elevations using the PC algorithm 2 over EC.

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Fig. 14 The scatterplots of (a) the LiDAR-derived ground elevations versus retrieved ground photon elevations using our adapted photon classification algorithm; (b) the LiDAR-derived ground elevations versus estimated ground photon elevations using PC algorithm 2; (c) the LiDAR-derived DTM elevations versus estimated DTM elevations using our adapted photon classification algorithm; (d) the LiDAR-derived DTM elevations versus estimated DTM elevations using the PC algorithm 2 in WC forest.

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Compared with the PC algorithm 2 proposed by the study of Moussavi et al. [28], higher R² and lower RMSE were observed regardless of ground photon elevations or DTM interpreted from ground returns using PC algorithm 1. This means our adapted photon classification performed better than the PC algorithm 2 in separating ground returns from canopy returns. This is maybe because the PC algorithm 2 represents the true ground surface using a moving curve, which cannot reflect small changes in topography. In contrast, our adapted photon classification algorithm can better obtain the details of complex terrain by detecting more ground returns.

4.3 Vegetation canopy height estimation

Comparisons between estimated canopy heights and reference canopy heights derived from airborne discrete-return LiDAR data indicates that our approach were able to obtain vegetation canopy heights with moderate accuracy (Fig. 15(a) and Fig. 16(a)), which demonstrated the capability of photon-counting LiDAR data in estimating forest canopy height. For both HE method 1 and HE method 2, the retrieved canopy heights over EC had lower estimate bias, lower RMSE and higher R² than those in WC forest. Thus, the canopy heights estimated over EC had higher accuracy. As demonstrated above, higher accuracy of ground elevations was obtained over EC, which resulted in more reliable estimation of vegetation canopy height.

Fig. 15 The scatterplots of (a) the LiDAR-derived canopy heights versus estimated canopy heights using HE method 1; (b) the LiDAR-derived canopy heights versus estimated canopy heights using HE method 2 over EC site.

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Fig. 16 The scatterplots of (a) the LiDAR-derived canopy heights versus estimated canopy heights using HE method 1; (b) the LiDAR-derived canopy heights versus estimated canopy heights using HE method 2 in WC forest.

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Compared with HE method 2, lower estimate bias, lower RMSE, and higher R² (see Figs. 15(a) and 15(b) and Figs. 16(a) and 16(b)) of retrieved canopy heights were observed using our new vegetation height estimation approach. This indicates that our method performed much better than the HE method 2 in estimating vegetation height from photon-counting LiDAR data. This can be explained that our vegetation height estimation approach adopted more effective noise removal algorithm and photon classification.

Different from the previous study of Gwenzi et al. [26] that estimated the forest canopy height using MATLAS data, and obtain RMSE of canopy height estimates ranging from 3.6 m to 4.6 m, slightly higher RMSE of canopy height estimates was reported in our study. This is maybe due to the two following reasons. On one hand, the canopy cover in our experiment sites is extremely high of larger than 90%, which greatly affected the effective detection of ground photons, and thereafter limited the estimation accuracy of vegetation canopy height. On the other hand, more complex topography in our study area may be also a reason that resulted in higher RMSE of canopy height estimates. Both the performances of noise removal algorithm and photon classification algorithm are limited in environments with complex terrain. Thus the canopy height estimation is generally affected.

5. Conclusion

In this paper, an automatic approach was developed to accurately retrieve vegetation canopy height from photon-counting LiDAR data. This automatic approach includes a new noise removal algorithm and an adapted photon classification algorithm. The new noise removal algorithm was applied to the simulated ICESat-2 data produced from Sigma Space LiDAR data, and the adapted photon classification algorithm was test to MATLAS data. The accuracy of retrieved vegetation canopy heights was assessed by the CHM derived from airborne discrete-return LiDAR data. Based on the results, we finally came to following conclusions. 1) Compared with the previous noise filtering algorithms, our new algorithm can effectively reduce the edge effect and the influence of inconsistent noise photon density, and thereafter better remove the noise photons. 2) The adapted photon classification algorithm performed better than the previous algorithm in separating canopy photons from ground photons. 3) The vegetation canopy height can be effectively estimated with satisfied accuracy using photon-counting LiDAR data.

To summarize, these conclusions provide valuable information for estimating vegetation canopy height using photon-counting LiDAR data. However, two issues remain unsolved and need to be addressed in the future. First, the emitted pulses might not penetrate through the vegetation canopy in areas with extremely high canopy cover. In this case, only several signal photons can be returned from the ground surface, which makes noise removal and photon classification challenging, and subsequently limits the estimation accuracy of vegetation canopy height. Second, only limited return signals can be obtained from vegetation canopy when the vegetation is sparse, which also affects the effective estimation of vegetation canopy height. Therefore, our next plan should focus on the development of more effective noise removal algorithm and photon classification algorithm which can be applicable even in areas with dense vegetation. Additionally, effective measures should be also taken to better obtain canopy-top under the environments with extremely sparse vegetation.

Funding

National Key R&D Program of China (No. 2017YFA0603002) and National Natural Science Foundation of China (No. 41671434).

Acknowledgments

We thank the editor and anonymous reviewers for reviewing our paper.

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Data sets	Noise levels	NR algorithm 1			NR algorithm 2			NR algorithm 3
Data sets	Noise levels	R	P	F	R	P	F	R	P	F
Cedar2	0.5 MHz	0.977	0.986	0.977	0.973	0.996	0.984	0.982	0.794	0.878
	2 MHz	0.915	0.985	0.948	0.911	0.981	0.945	0.932	0.821	0.874
	5 MHz	0.812	0.943	0.873	0.785	0.848	0.815	0.724	0.872	0.791
Cedar4	0.5 MHz	0.979	0.991	0.985	0.975	0.998	0.986	0.908	1.000	0.952
	2 MHz	0.920	0.986	0.952	0.919	0.985	0.951	0.661	1.000	0.796
	5 MHz	0.818	0.949	0.879	0.803	0.883	0.841	0.362	1.000	0.532
SERC1	0.5 MHz	0.946	0.993	0.969	0.944	0.987	0.965	0.974	0.539	0.694
	2 MHz	0.824	0.913	0.866	0.838	0.844	0.841	0.879	0.556	0.681
	5 MHz	0.711	0.795	0.751	0.625	0.623	0.624	0.625	0.671	0.647
SERC3	0.5 MHz	0.943	0.994	0.968	0.952	0.992	0.972	0.980	0.699	0.816
	2 MHz	0.867	0.910	0.888	0.856	0.906	0.880	0.911	0.726	0.808
	5 MHz	0.722	0.767	0.744	0.746	0.613	0.673	0.606	0.874	0.716
SERC5	0.5 MHz	0.946	0.981	0.963	0.947	0.981	0.964	0.947	0.971	0.959
	2 MHz	0.860	0.931	0.894	0.850	0.935	0.890	0.777	0.988	0.870
	5 MHz	0.714	0.872	0.785	0.678	0.795	0.732	0.360	0.999	0.529
0.5 MHz	Maximum	0.979	0.994	0.985	0.975	0.998	0.986	0.982	1.000	0.959
	Minimum	0.943	0.981	0.963	0.944	0.981	0.964	0.908	0.539	0.694
	Average	0.958	0.989	0.972	0.958	0.991	0.974	0.958	0.801	0.860
2 MHz	Maximum	0.920	0.986	0.952	0.919	0.985	0.951	0.932	1.000	0.874
	Minimum	0.824	0.910	0.866	0.838	0.844	0.841	0.661	0.556	0.681
	Average	0.877	0.945	0.910	0.875	0.930	0.901	0.832	0.818	0.806
5 MHz	Maximum	0.818	0.949	0.879	0.803	0.883	0.841	0.724	1.000	0.791
	Minimum	0.711	0.767	0.744	0.625	0.613	0.624	0.360	0.671	0.529
	Average	0.755	0.865	0.806	0.727	0.752	0.737	0.535	0.883	0.643
All	Maximum	0.979	0.994	0.985	0.975	0.998	0.986	0.982	1.000	0.959
	Minimum	0.711	0.767	0.744	0.625	0.613	0.624	0.360	0.539	0.529
	Average	0.864	0.933	0.896	0.853	0.891	0.871	0.775	0.834	0.770

Estimating the vegetation canopy height using micro-pulse photon-counting LiDAR data

Abstract

1. Introduction

2. Materials

2.1 Sigma Space LiDAR data

2.2 MATLAS data

2.3 Airborne LiDAR data

3. Methodologies

3.1 Noise photon removal

3.2 Separation of ground photons and canopy photons

3.3 Canopy height retrieval

3.4 Performance evaluation and accuracy validation

4. Results and discussion

4.1 Noise removal

4.2 Photon classification

4.3 Vegetation canopy height estimation

5. Conclusion

Funding

Acknowledgments

References and links

Cited By

Figures (16)

Tables (1)

Equations (7)

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