Range determination for generating point clouds from airborne small footprint LiDAR waveforms

doi:10.1364/OE.20.025935

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Range determination for generating point clouds from airborne small footprint LiDAR waveforms

Yuchu Qin, Tuong Thuy Vu, Yifang Ban, and Zheng Niu »View Author Affiliations

Optics Express, Vol. 20, Issue 23, pp. 25935-25947 (2012)
http://dx.doi.org/10.1364/OE.20.025935

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▸ Article Outline
– Abstract
1. Introduction
2. Methodology
3. Experiment and results
4. Discussion and conclusion
– References and links

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Abstract

This paper presents a range determination approach for generating point clouds from small footprint LiDAR waveforms. Waveform deformation over complex terrain area is simulated using convolution. Drift of the peak center position is analyzed to identify the first echo returned by the illuminated objects in the LiDAR footprint. An approximate start point of peak in the waveform is estimated and adopted as the indicator of range calculation; range correction method is proposed to correct pulse widening over complex terrain surface. The experiment was carried out on small footprint LiDAR waveform data acquired by RIEGL LMS-Q560. The results suggest that the proposed approach generates more points than standard commercial products; based on field measurements, a comparative analysis between the point clouds generated by the proposed approach and the commercial software GeocodeWF indicates that: 1). the proposed approach obtained more accurate tree heights; 2). smooth surface can be achieved with low standard deviation. In summary, the proposed approach provides a satisfactory solution for range determination in estimating 3D coordinate values of point clouds, especially for correcting range information of waveforms containing deformed peaks.

1. Introduction

In past decades, airborne (Light Detection And Ranging) LiDAR has been widely used in 3D data acquisition of land surfaces [1

F. Ackermann, “Airborne laser scanning—present status and future expectations,” ISPRS J. Photogramm. Remote Sens. 54(2-3), 64–67 (1999). [CrossRef]

–4

A. Chauve, C. Vega, S. Durrieu, F. Bretar, T. Allouis, M. P. Deseilligny, and W. Puech, “Advanced full-waveform lidar data echo detection: Assessing quality of derived terrain and tree height models in an alpine coniferous forest,” Int. J. Remote Sens. 30(19), 5211–5228 (2009). [CrossRef]

]. It integrates laser ranging, Inertial Measurement Unit (IMU) and Differential Global Positioning System (DGPS) to determine the distance between the LiDAR system and targets, and provides a direct way of obtaining 3D information of land surface. Conventional pulse LiDAR systems based on time-of-flight ranging technique only capture limited discrete points for one laser pulse [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

–7

Y. C. Qin, B. Li, Z. Niu, W. J. Huang, and C. Y. Wang, “Stepwise decomposition and relative radiometric normalization for small footprint LiDAR waveform,” Sci China Earth Sci. 54(4), 625–630 (2011). [CrossRef]

]. Recently, full digitizing LiDAR systems have become available for LiDAR waveform acquisition. They record full waveform by digitizing the backscatter of illuminated objects, and therefore both range and radiometric information of targets can be obtained from the waveform data [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

W. Wagner, A. Ullrich, V. Ducic, T. Melzer, and N. Studnicka, “Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner,” ISPRS J. Photogramm. Remote Sens. 60(2), 100–112 (2006). [CrossRef]

G. Sun and K. J. Ranson, “Modeling lidar returns from forest canopies,” IEEE Trans. Geosci. Rem. Sens. 38(6), 2617–2626 (2000). [CrossRef]

Full waveform LiDAR can be categorized into two types: large footprint and small footprint systems [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

,10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

,11

H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “ICESat full-waveform altimetry compared to airborne laser scanning altimetry over the netherlands,” IEEE Trans. Geosci. Rem. Sens. 47(10), 3365–3378 (2009). [CrossRef]

]. Large footprint waveform LiDAR systems are mounted either on airborne platforms such as Laser Vegetation Imaging Sensor (LVIS) [12

J. B. Blair, D. L. Rabine, and M. A. Hofton, “The laser vegetation imaging sensor: a medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography,” ISPRS J. Photogramm. Remote Sens. 54(2-3), 115–122 (1999). [CrossRef]

] or spaceborne platforms such as Geoscience Laser Altimeter System (GLAS) [2

M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies,” Bioscience 52(1), 19–30 (2002). [CrossRef]

] and [13

M. A. Lefsky, D. J. Harding, M. Keller, W. B. Cohen, C. C. Carabajal, F. D. B. Espirito-Santo, M. O. Hunter, and R. de Oliveira, “Estimates of forest canopy height and aboveground biomass using ICESat,” Geophys. Res. Lett. 32(22), 1–4 (2005). [CrossRef]

]. GLAS data has been widely used in cryosphere observation and estimation of forest height and biomass [2

M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies,” Bioscience 52(1), 19–30 (2002). [CrossRef]

], [14

V. H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “Single and two epoch analysis of ICESat full waveform data over forested areas,” Int. J. Remote Sens. 29(5), 1453–1473 (2008). [CrossRef]

–18

L. I. Duncanson, K. O. Niemann, and M. A. Wulder, “Estimating forest canopy height and terrain relief from GLAS waveform metrics,” Remote Sens. Environ. 114(1), 138–154 (2010). [CrossRef]

]. Most small footprint full waveform LiDAR systems are developed by commercial industrials such as the Optech ALTM 3100, Topeye MK II, Riegl LMS-Q560, TopoSys Harrier5600, and Falcon III [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

], [10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

], and [19

Y. C. Qin, Y. C. Wu, Z. Niu, Y. L. Zhan, and Z. P. Xiong, “Reconstruction of sparse forest canopy height using small footprint lidar data,” J. Nat Resour. 23, 507–513 (2008).

]. These are mainly used for topographical mapping and 3D modeling of land surface. On one hand, LiDAR waveform data provides more details on the illuminated targets, which can be used for advanced interpretation; on the other hand, the processing of LiDAR waveform data requires users have more knowledge and experience with LiDAR systems and signal processing. Moreover, the shortage of efficient approaches for LiDAR waveform processing makes it difficult to handle the massive data [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

], [8

], [20

W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens. 48, 3571–3579 (2010).

–23

A. Persson, U. Söderman, and S. Ahlberg, “Visualization and analysis of full-waveform airborne laser scanner data”, in the IAPRS Vol.XXXVI, Part 3/W19, Enschede, Netherlands, 103–108 (2005).

In general, the majority of LiDAR applications use point clouds generated from small footprint LiDAR waveforms. Many studies have been conducted focusing on generating point clouds from LiDAR waveforms. Jutzi and Stilla [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

] analyzed the LiDAR waveform deformation over complex illuminated objects, e.g. vegetation canopy, sloped surface and other small objects within the footprint. The influence of the emitted waveform was removed from the original return waveform using deconvolution, followed by wiener filtering to reduce noise. The study applied the Leveberg-Marquardt method for range determination. Yao and Stilla [20

W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens. 48, 3571–3579 (2010).

] adopted the same approach for range determination in point clouds enrichment by enhancing weak laser pulses. Although these studies provide solutions for range determination, the algorithms were implemented on terrestrial laser scanning waveforms. Moreover, the wiener filters was performed for data smoothing rather than range correction with the time consuming signal deconvolution.

Wagner et al. [8

] provided a systematical analysis of full waveform LiDAR from a theoretical view. In addition, a waveform decomposition-based method was proposed to generate point clouds from airborne LiDAR waveforms acquired by a Riegl LMS-Q560 system. The study adopted two “traditional” pulse detection methods: the center of gravity and zero-crossing of the first derivative for pulse detection. The method causes negative amplitudes and peak positions exceeding the waveform length which are undesirable in waveform processing. The paper did not provide details of the range determination algorithm.

GeocodeWF is standalone software for converting raw waveform data collected by the Riegl LMS-Q560 LiDAR system into geocoded points in a projected coordinate system [24

GeoLas Consulting, www.geolas.com/Downloads/GeocodeWF, (Last access on 8 Jan, 2012).

]. As a commercial tool, it provides a practical way for the user community to handle LiDAR waveform and generates point clouds from LiDAR waveforms at industrial standards, and has been widely used in LiDAR mapping projects. It applies a centroid (weighted average of sample positions) of each LiDAR waveform pulse for calculating range from the waveform peak +/− 5 bins. In case of overlapping return pulses, the centroid is calculated from the waveform peak +/−3 bins [25

C. Hug, private communication, Dec (2011).

In practice, airborne small footprint LiDAR system acquires high-density waveforms. The peak deformation of the waveform, especially the widening peak effect over complex terrain is still a challenge in range determination. Consequently, this study aims to develop an approach to determine the 3D coordinate values of LiDAR returns from small footprint LiDAR waveforms. The main motivation is to present a practical way of range correction in generating point clouds from airborne small footprint LiDAR waveforms. An optimal algorithm is applied for waveform decomposition [10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

]. Based on the simulation of waveform deformation over complex terrain area, a correction method is proposed for range determination. 3D coordinate values of point clouds are directly calculated from the decomposition parameters of both emitted and return waveforms.

2. Methodology

Range determination is the most important step in generating point clouds from LiDAR waveforms, since it allows the estimation of the 3D coordinate values of point clouds [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

], [20

W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens. 48, 3571–3579 (2010).

]. Full waveform LiDAR systems record range offsets of each bin in the waveform, and range determination estimates the position of the first echo bin returned from illuminated objects. Ideally, the center position of each peak in waveform can be used for range calculation. However, deformation of the pulse peak over complex terrain will affect the range accuracy [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

,17

Q. Chen, “Retrieving vegetation height of forests and woodlands over mountainous areas in the Pacific Coast region using satellite laser altimetry,” Remote Sens. Environ. 114(7), 1610–1627 (2010). [CrossRef]

,26

M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens. 38(4), 1989–1996 (2000). [CrossRef]

]. For a given emitted laser pulse, the return waveform depends on the surface response in LiDAR footprint. From the mathematic view, the surface response can be described by a function of time. The length of the response function (LRF) depends on the complexity of the terrain in LiDAR footprint. Jutzi and Stilla [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

] analyzed four waveform deformation scenarios, the scenarios can be generalized as two types: 1) significantly different elevated targets in two peaks and 2) slightly different elevated targets in one peak with overlapping scatters. Figure 1 illustrates three scenarios of LiDAR waveforms which have deformed and non-deformed returns. The range determination method proposed in this paper is based on waveform decomposition. Firstly, we introduce a waveform decomposition method, and the waveform deformation over complex terrain surface is simulated based on the waveform decomposition. Based on the simulation, a method for range correction is proposed to calculate 3D coordinate values of point clouds.

Fig. 1 Waveform shapes over different land surfaces

2.1 Waveform decomposition

Gaussian decomposition has been widely used in LiDAR waveform processing [5

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]

,10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

,26

M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens. 38(4), 1989–1996 (2000). [CrossRef]

]. In theory, LiDAR waveform can be described by the sum of several components, each component is represented by a Gaussian function:

G (x_{i}) = h_{i} \exp [- \frac{{(x_{i} - α_{i})}^{2}}{w_{i}^{2}}]

(1)

G (x) = \sum_{i = 1}^{k} G (x_{i})

(2)

where

G (x i)

is a single Gaussian component,

h_{i}

α_{i}

w_{i}^{2}

are parameters of component: amplitude, position and width.

G (x)

is the sum of k components. The challenges of waveform decomposition are the identification of the number of Gaussian components and initial estimate of the parameters.

In past years, several algorithms have been developed for waveform Gaussian decomposition [7

], [23

A. Persson, U. Söderman, and S. Ahlberg, “Visualization and analysis of full-waveform airborne laser scanner data”, in the IAPRS Vol.XXXVI, Part 3/W19, Enschede, Netherlands, 103–108 (2005).

], [26

M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens. 38(4), 1989–1996 (2000). [CrossRef]

]. Most existing algorithms were developed using algebraic iteration, and r-squared (R²) values were adopted to assess accuracy. The issue is that the high R² does not denote that the decomposed waveform matches the original shape. In this study, an optimal algorithm based on the geometrical analysis of LiDAR waveforms is utilized for waveform decomposition. It estimates the initial parameters of a Gaussian model using the Ramer-Douglas-Peucker curve-fitting algorithm followed by Gaussian decomposition using the estimated initial parameters. Experiments indicated that the curve fitting-based decomposition achieves reliable results. More details of the algorithm can be found in [10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

2.2 Simulation of waveform deformation

Generally, the center position of a single peak in a waveform is adopted as an estimate of range. However, the surface response introduces peak deformation in return waveforms, especially over complex terrain. In general, the deformation is the widening effect of peaks [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

]. It is well established that return waveforms can be described by the convolution of the emitted waveform and surface response [6

B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]

], [27

J. Y. Wu, J. A. N. van Aardt, and G. P. Asner, “A comparison of signal deconvolution algorithms based on small-footprint lidar waveform simulation,” IEEE Trans. Geosci. Rem. Sens. 49(6), 2402–2414 (2011). [CrossRef]

G_{r} = G_{e} \otimes f_{o}

(3)

where G_r, G_e are the return and emitted LiDAR waveforms, respectively, and f₀ is the response function of illuminated targets in the LiDAR footprint.

To investigate the relationship between the surface response function and waveform deformation, a waveform simulation is conducted using Eq. (3). Figure 2 shows the standard emitted waveform adopted in the simulation, which is an emitted waveform of LMS-Q560 with a length of 58 bins. It is fitted by a Gaussian model with single component, and the amplitude, center position and peak width are 103, 15, and 2.5 respectively.

Fig. 2 The standard emitted waveform used in deformation simulation.

Two generalized scenarios of waveform deformation are considered in the simulation: 1) only one peak is captured in the illuminated footprint as the LRF varies; 2) two apparently separated peaks are acquired in the LiDAR footprint.

According to the nature of signal convolution, the amplitude of the original signal does not change the length of the resulting signal. Consequently, a constant value is adopted to describe the reflective capability of each bin in the response function. The reflective capability of each bin in the waveform is computed as:

R_{b} = R_{c} / L R F

(4)

where R_b is the reflectance value of each bin, R_c is the reflectance value of all targets in footprint. The unit of LRF is bin in this study.

First, single peak waveforms with varied LRF are simulated, and the resulting waveforms are decomposed using a Gaussian model. The range of LRF for a single object is 1-8, and the overall reflectance of targets in the footprint is 0.3. Figure 3 illustrates the varied response functions as well as the simulated waveforms. Table 1 shows the Gaussian parameters of simulated waveforms.

Fig. 3 (a). Single peak scenarios of varied LRF ground response. (b). Simulated single peak waveforms.

Table 1 Gaussian parameters of simulated single-peak waveforms with varied LRF

LRF	Int	Pos	Wid
1	30.9	15	2.5
2	29.7	15.4	2.6
3	27.9	16	2.8
4	25.80	16.5	3.1
5	23.6	17	3.3
6	21.4	17.5	3.7
7	19.5	18	4.0
8	17.7	18.5	4.5

In Table 1, Int, Wid and Pos are the amplitude, width and center position of peaks in the simulated waveforms, respectively. The simulation results suggest that the varying LRF will induce a shift of peak center and the widening pulse.

Waveforms with two apparently separated peaks are simulated to explore how the deformation of the first peak affects the subsequent peak. LRF of the first peak is varied within a range of 1-6, the reflectance of the apparently separated objects is 0.3, and the distance between the first and second peak is 6 bins. Figure 4 illustrates the response functions and the resulting waveforms. Table 2 shows the input parameters as well as the decomposed results from the simulated waveforms.

Fig. 4 (a). Double peak scenarios of varied LRF ground response. (b). Simulated double peak waveforms.

Table 2 Gaussian parameters of simulated two-peak waveforms with varied LRF

LRF_1st	Dis	LRF_T	Ref_1st	Int_1st	Pos_1st	Wid_1st	Int_2nd	Pos_2nd	Wid_2nd
1	6	8	0.3	30.9	15	2.5	30.9	22	2.5
2	6	9	0.15	29.7	15.5	2.6	30.9	23	2.5
3	6	10	0.1	27.9	16	2.8	30.9	24	2.5
4	6	11	0.075	25.8	16.5	3.0	30.9	25	2.5
5	6	12	0.06	23.5	17	3.3	30.9	26	2.5
6	6	13	0.05	21.4	17.5	3.7	31.0	27	2.5

In Table 2, LRF_1st is the LRF of the first peak in LiDAR waveforms. D_is is the distance between the first and second peaks in the response function. The LRF of the second peak is assigned to 1, and LRF_T is the length of the entire response function. Ref _1st is the reflectance value of each bin in the response function of the first peak. Int_1st, Pos_1st, Wid_1st, Int_2nd, Pos_2nd and Wid_2nd are the Gaussian parameters of the two peaks in the simulated LiDAR waveforms. The simulation of two-peak waveforms suggests that the varied LRF of the first peak will not cause the deformation of the neighboring peak, and that the center position of all peaks in the waveform changed corresponding to the LRF of the first peak.

In summary, LiDAR waveform deformation depends on the variation of surface elevation in the footprint. In practice, especially over complex terrain, it is difficult to determine accurate terrain changes in the footprint during waveform processing. Consequently, the center position of the peak is not a good indicator for range determination. Comparison between Table 1 and 2 suggests that the peak width does not change if the LRF of illuminated objects is less than or equal to 1. Consequently, an alternative indicator with a conceptual “start point” of peaks will improve the accuracy of range determination.

2.3 Range determination

In theory, the “start point” of each peak in LiDAR waveform can be identified by a threshold

value. Efforts have been made to determine the start point of the peak [13

]. However, it is difficult to implement in practice due to background noise. According to the nature of the Gaussian model, about 99.7% of values drawn from a Gaussian distribution are within three σ (standard deviation) of the mean value [28

http://en.wikipedia.org/wiki/Normal_distribution, (Last access on 8 Jan, 2012).

]. Consequently, an approximate boundary of each peak in the LiDAR waveform can be estimated using the center position and width of Gaussian parameters:

P b = P c - N * W r

(5)

where P_b is the estimated conceptual “start point”, P_c is the center position of peak, N is multiple number for peak width and W_r is the peak width of the return waveform.

According to the waveform simulation and the identification of conceptual “start point”, a “virtual” center position of peak is estimated by an approximate boundary and the peak width of the emitted waveform. Based on this approximation, the center drift is corrected and a more accurate center position of deformation-free waveform is approximated by the equation:

P c r = P b + N * W e

(6)

where P_cr is the corrected center position, W_e is the peak width of the emitted waveform.

LiDAR systems emit laser pulses and record backscatter as well as the 3D range between the carrying platform and each bin in the waveforms. Figure 5 shows the LiDAR waveform data structure. The real time coordinate values of LiDAR system during data acquisition are accurately estimated using the data acquired by DGPS and the Inertial Navigation System (INS). 3D coordinate values of illuminated objects can be calculated from range and accurate coordinates of LiDAR systems as:

X = E_{0} + D_{E} * (D_{o} + P_{c r})

(7)

Y = N_{0} + D_{N} * (D_{o} + P_{c r})

(8)

Z = H_{0} + D_{H} * (D_{o} + P_{c r})

(9)

where X, Y, Z are the 3D coordinate values of point clouds. E₀, N₀, H₀ are the real time 3D coordinate values of the LiDAR system. D_E, D_N, D_H are the length of a single bin in different directions. D_o is the first sample of surface return waveform in bins, and P_cr is the corrected center position estimated by Eq. (6).

Fig. 5 Data structure of LiDAR waveforms.

3. Experiment and results

3.1 Study area and data set

The Watershed Allied Telemetry Experimental Research (WATER) was carried out in 2008 over the Heihe River Basin, a typical inland river basin in northwest China. It was a simultaneous airborne, satellite-borne, and ground-based remote sensing experiment. Twenty five airborne flight missions were flown in the experiment. The airborne sensors included microwave radiometers, imaging spectrometer CCD, and full waveform LiDAR [7

]. The main experimental area of WATER consisted of farmland and grassland. Zhangye, the largest city within the experimental area, is an oasis city surrounded by a large desert. The city downtown was selected as the area of interest, which includes buildings, roads, lakes, grass, bare land and trees. The Rigel LMS-Q560 was deployed for LiDAR waveform data acquisition in the WATER. The flight mission was carried out in Jun 2008. Flight height of the airplane was about 700m above ground.

3.2 Data processing

GeocodeWF is a standalone software for converting raw waveform data collected by RIEGL LMS-Q560 laser scanner-based LiDAR systems into geocoded points in a projected coordinate system [24

GeoLas Consulting, www.geolas.com/Downloads/GeocodeWF, (Last access on 8 Jan, 2012).

]. This study used this software to import raw waveforms from the data recorder of the LiDAR system. The average density of waveforms was about 1.7 echoes per m². Point clouds of all flights in the WATER experiment were generated with GeocodeWF, and points falling within the study area were selected from the large volume of point clouds for further study.

Thirteen LiDAR flight strips covering the downtown of Zhangye city were acquired during the experiment, with overlap between adjacent strips. The total size of the thirteen strips is more than thirteen gigabytes in binary format. The ground swath of flight missions depends on the flight height of the airplane and the scan angle of the LiDAR system. In the WATER experiment, the LiDAR waveform data was acquired with a scan angle of ± 22.5°. The maximum distance between footprint and LiDAR nadir point was 289.95m on a XY plane. Consequently, the coverage of our study area was extended more than 289.5m in all directions. The central area (500m*300m) of downtown with an extended border is identified, waveforms falling into the extended core were selected from the original waveform files, and waveform decomposition is implemented using the approach proposed in [10

Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]

]. The maximum number of peaks in a LiDAR waveform is 3, and the threshold of R² was 0.9.

As mentioned in the previous section (Eq. (6)), the range of the multiple number N was a value between 1 and 3. In this study, the LiDAR waveforms are decomposed using the Eq. (2). That means the model is not a standard Gaussian function. Consequently, the decomposed width of waveforms is normalized to standard Gaussian function by dividing

\sqrt{2}

. The optimum values of N needed to be identified to determinate the accurate range. Consequently, the range of N was assigned from 1 to 3, three types point clouds data are generated corresponding to the different N values.

3.3 Results and validation

The point density of the products generated by GeocodeWF and the proposed approach were 2.06 and 2.14 points/m², respectively. It means that the proposed approach generated about 4% more points than GeocodeWF.

Quality evaluation of the point clouds product includes assessments of precision and accuracy. Accuracy is the absolute distance between measurements and the true values, whereas precision refers to the variation of measurements around the true values. Currently, DGPS can be used to collect accurate 3D points, but it is time consuming. Moreover, the variability of the LiDAR footprint also makes it difficult to identify point locations before data acquisition, especially for tree canopies. Thus, the difference of two absolute elevation values, such as buildings with a flat roof and trees, was adopted instead of absolute accuracy in validation. The field survey was conducted using a high-resolution mobile laser rangefinder to validate the accuracy of point clouds. Based on the field measurements and visual inspections of the point clouds product, measured buildings and trees were identified on the point clouds, and the heights of treetops and building roofs were estimated from the point clouds generated by GeocodeWF and the proposed approaches.

Figure 6 illustrates the comparison between the estimated and field-measured heights. The 1st, 2nd and 3rd in the following sections refer to N values of 1, 2 and 3 in Eq. (6), respectively. The figure shows that all approaches achieved highly accurate results in estimating building heights. In terms of treetop estimation, GeocodeWF underestimated the heights and the approach with N = 3 overestimated the heights of treetop. The most accurate results are achieved while N is 2 (R² = 0.8081).

Fig. 6 Comparison of estimated height and field measurement for building roof (a) and treetop (b).

Table 3 shows the detailed statistics of regression models between the field measurements and the estimated values. It suggests that the 2nd approach achieved the most satisfactory result over building roofs, the maximum absolute difference (MAD) between field measurement and estimated height was obtained by the 3rd approach. GeocodeWF, 1st and 2nd achieved more acceptable results over building roofs. GeocodeWF, 1st and 2nd approaches underestimated the treetop heights, while the 3rd approach overestimated the treetop heights. GeocodeWF obtained results with maximum estimation error. The MAD and R² are 2.5292m and 0.7227, respectively. The 2nd approach achieved the most reliable results among all approaches.

Table 3 Statistic of regression parameters between field measurement and estimation

Type	Parameters	GeocodeWF	1st	2nd	3rd
Building	Slope	1.0012	1.0005	0.9994	0.9985
	R²	0.9999	1.0000	1.0000	0.9998
	MAD (m)	0.0611	0.0332	0.0444	0.0967
Treetop	Slope	0.8287	0.8891	0.9498	1.0157
	R²	0.7211	0.8055	0.8081	0.7978
	MAD (m)	2.5292	1.8531	1.2046	0.697

Two trees in the downtown area were selected to visualize the 3D points generated by GeocodeWF and the 2nd approach. Figure 7 illustrates the subset aerial photography of the plot, and the image that was acquired on the same date as LiDAR waveforms. Sample tree A and B labeled by red circles were selected for visualization. Figure 8 shows the 3D model of the two trees, the results suggest that the two approaches obtained very similar points at the ground surfaces, but the 2nd approach achieved higher treetop estimation than GeocodeWF.

Fig. 7 Subset aerial photography of the downtown: The circles and rectangles label the selected tree samples; the hexagon with arrow indicates the tower in the downtown.

Fig. 8 Visualization of 3D points for sample trees: (a) is the tree A in Fig. 7, (b) is the tree B in Fig. 0.7.

The bell tower of the city was selected as a validation sample. The tower in the center of downtown is a legend of Zhangye city. It was illustrated in Fig. 7 by the hexagon with arrow. According to an official report, the tower height is about 30m, and field measurements were carried out in the WATER experiment as well. Table 4 suggests that the proposed approach obtained a better result than GeocodeWF.

Table 4 Comparison of tower height estimations (Unit: m)

Field measurement	GeocodeWF	1st	2nd	3rd
30.67	24.05	26.61	27.28	27.95

Generally, standard deviation is adopted as an indicator of how much the variation or “dispersion” is from the “average” (mean, or expected value). It was selected for precision assessment of LiDAR point clouds. There were three main land-cover types in the study area: buildings, trees and roads. The nature of the tree canopy elevation is complicated, so it is difficult to implement precision assessment of point clouds located on the canopy. For most cases, the elevation changes in building roofs and roads are smooth, and the surfaces tend to be flat especially over small areas. Consequently, standard deviation of a moving window on building roofs and roads is selected for a precision assessment. The size of moving windows is 2m, 4m and 6m. 12 plots over building roofs and 14 plots over roads were identified for statistical analysis.

Table 5 shows standard deviations within the moving windows. All approaches obtained similar results over building roofs. GeocodeWF approach produced the least standard deviations at different window sizes over roads inferring that GeocodeWF obtained the smoothest elevation values. There were several plots with large standard deviations over roads due to the presence of cars and pedestrians during data acquisition. Visual inspection of the point clouds suggests that GeocodeWF obtains relatively low standard deviations and elevation values over these areas.

Table 5 Standard deviation of elevation within moving windows

		Window size (2m)				Window size (4m)				Window size (6m)
Type	SD	WF	1st	2nd	3rd	WF	1st	2nd	3rd	WF	1st	2nd	3rd
Road	Max	0.82	0.84	0.91	1.02	0.76	0.78	0.80	0.85	0.56	0.57	0.62	0.73
	Min	0.02	0.03	0.03	0.03	0.04	0.04	0.06	0.07	0.05	0.05	0.06	0.07
	Median	0.05	0.07	0.07	0.09	0.06	0.06	0.07	0.09	0.08	0.12	0.16	0.19
	Mean	0.13	0.15	0.17	0.19	0.13	0.16	0.18	0.22	0.16	0.21	0.26	0.29
Building	Max	0.07	0.09	0.10	0.11	0.11	0.09	0.10	0.14	0.07	0.09	0.10	0.12
	Min	0.01	0.01	0.01	0.01	0.03	0.02	0.03	0.04	0.03	0.03	0.03	0.04
	Median	0.04	0.04	0.04	0.05	0.05	0.04	0.07	0.08	0.05	0.07	0.08	0.09
	Mean	0.04	0.04	0.04	0.05	0.05	0.05	0.06	0.08	0.05	0.06	0.06	0.09

* WF is GeocodeWF and SD is standard deviation.

4. Discussion and conclusion

This paper presented an effective approach for generating point clouds from airborne small footprint LiDAR waveforms. Peak deformation scenarios over different elevation surfaces were simulated to investigate the waveform deformation regime. The simulation results indicated that the variety of the elevations in the footprint affect the shape of return waveforms, especially when complex elevation surfaces cause widening effect of peaks. A range determination approach was proposed based on Gaussian mixture models of waveform and deformation simulation, where parameters of emitted and return waveforms are mutually adopted to correct the widening peaks.

Experiments were carried out on small footprint LiDAR waveform data acquired by LMS-Q560. Comparison of the results suggests that the proposed approach generated more points than commercial software-GeocodeWF. In terms of the accuracy of point clouds, the 2nd approach achieved the most accurate results over trees, whereas GeocodeWF underestimated the treetop. All approaches achieved acceptable accuracy over building roofs.

Among the approaches, GeocodeWF obtained the smoothest point clouds over building roofs with high precision. In practice, it is necessary to smooth point clouds due to the noise in the original data. However, for applications such as vehicle extractions, the elevation smoothing in point clouds generation will eliminate the feature points of such targets [29

W. Yao and U. Stilla, “Comparison of two methods for vehicle extraction from airborne lidar data toward motion analysis,” IEEE Geosci. Remote Sens. Lett. 8(4), 607–611 (2011). [CrossRef]

]. There were many vehicles and people on the street in the downtown of Zhangye city in the data acquisition. LiDAR point clouds products should contain accurate elevation information of such targets. The proposed approach generates point clouds without smoothing, so it provides more options to different applications.

Generally, LiDAR point clouds contain both 3D coordinate values and radiometric information. The approach proposed in this paper is based on waveform decomposition. Consequently, the return energy of each peak can be estimated from the Gaussian model. Future studies are planned to investigate intensity calculations and radiometric corrections using the decomposition parameters. In terms of validation, this study focused on the vertical accuracy and precision, further validation should be carried out to assess the horizontal accuracy.

LiDAR systems provide a unique opportunity to acquire 3D information of land surfaces. They have been efficiently used in elevation mapping, forest structure detection, as well as 3D city modeling, etc. Moreover, the launch of spaceborne LiDAR systems makes it possible to obtain 3D vegetation parameters at a global scale [30

B. E. Schutz, H. J. Zwally, C. A. Shuman, D. Hancock, and J. P. DiMarzio, “Overview of the ICESat mssion,” Geophys. Res. Lett. 32(21), 1–4 (2005). [CrossRef]

]. The most important goal of our study is to provide open source tools for LiDAR waveform processing. It is expected to further contribute to the expansion of LiDAR waveform applications.

Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant No. 41101342). The authors would like to thank the Watershed Allied Telemetry Experimental Research for providing LiDAR data.

References and links

1.	F. Ackermann, “Airborne laser scanning—present status and future expectations,” ISPRS J. Photogramm. Remote Sens. 54(2-3), 64–67 (1999). [CrossRef]
2.	M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies,” Bioscience 52(1), 19–30 (2002). [CrossRef]
3.	C. Wang, M. Menenti, M. Stoll, A. Feola, E. Belluco, and M. Marani, “Separation of ground and low vegetation signatures in LiDAR measurements of salt-marsh environments,” IEEE Trans. Geosci. Rem. Sens. 47(7), 2014–2023 (2009). [CrossRef]
4.	A. Chauve, C. Vega, S. Durrieu, F. Bretar, T. Allouis, M. P. Deseilligny, and W. Puech, “Advanced full-waveform lidar data echo detection: Assessing quality of derived terrain and tree height models in an alpine coniferous forest,” Int. J. Remote Sens. 30(19), 5211–5228 (2009). [CrossRef]
5.	C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens. 64(1), 1–16 (2009). [CrossRef]
6.	B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens. 61(2), 95–107 (2006). [CrossRef]
7.	Y. C. Qin, B. Li, Z. Niu, W. J. Huang, and C. Y. Wang, “Stepwise decomposition and relative radiometric normalization for small footprint LiDAR waveform,” Sci China Earth Sci. 54(4), 625–630 (2011). [CrossRef]
8.	W. Wagner, A. Ullrich, V. Ducic, T. Melzer, and N. Studnicka, “Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner,” ISPRS J. Photogramm. Remote Sens. 60(2), 100–112 (2006). [CrossRef]
9.	G. Sun and K. J. Ranson, “Modeling lidar returns from forest canopies,” IEEE Trans. Geosci. Rem. Sens. 38(6), 2617–2626 (2000). [CrossRef]
10.	Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett. , doi:. [CrossRef]
11.	H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “ICESat full-waveform altimetry compared to airborne laser scanning altimetry over the netherlands,” IEEE Trans. Geosci. Rem. Sens. 47(10), 3365–3378 (2009). [CrossRef]
12.	J. B. Blair, D. L. Rabine, and M. A. Hofton, “The laser vegetation imaging sensor: a medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography,” ISPRS J. Photogramm. Remote Sens. 54(2-3), 115–122 (1999). [CrossRef]
13.	M. A. Lefsky, D. J. Harding, M. Keller, W. B. Cohen, C. C. Carabajal, F. D. B. Espirito-Santo, M. O. Hunter, and R. de Oliveira, “Estimates of forest canopy height and aboveground biomass using ICESat,” Geophys. Res. Lett. 32(22), 1–4 (2005). [CrossRef]
14.	V. H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “Single and two epoch analysis of ICESat full waveform data over forested areas,” Int. J. Remote Sens. 29(5), 1453–1473 (2008). [CrossRef]
15.	L. A. Magruder, C. E. Webb, T. J. Urban, E. C. Silverberg, and B. E. Schutz, “ICESat altimetry data product verification at white sands space harbor,” IEEE Trans. Geosci. Rem. Sens. 45(1), 147–155 (2007). [CrossRef]
16.	G. Sun, K. J. Ransonb, D. S. Kimesb, J. B. Blairb, and K. Kovacs, “Forest vertical structure from GLAS: an evaluation using LVIS and SRTM data,” Remote Sens. Environ. 112(1), 107–117 (2008). [CrossRef]
17.	Q. Chen, “Retrieving vegetation height of forests and woodlands over mountainous areas in the Pacific Coast region using satellite laser altimetry,” Remote Sens. Environ. 114(7), 1610–1627 (2010). [CrossRef]
18.	L. I. Duncanson, K. O. Niemann, and M. A. Wulder, “Estimating forest canopy height and terrain relief from GLAS waveform metrics,” Remote Sens. Environ. 114(1), 138–154 (2010). [CrossRef]
19.	Y. C. Qin, Y. C. Wu, Z. Niu, Y. L. Zhan, and Z. P. Xiong, “Reconstruction of sparse forest canopy height using small footprint lidar data,” J. Nat Resour. 23, 507–513 (2008).
20.	W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens. 48, 3571–3579 (2010).
21.	W. Wagner, M. Hollaus, C. Briese, and V. Ducic, “3D vegetation mapping using small‐footprint full waveform airborne laser scanners,” Int. J. Remote Sens. 29, 1433–1452 (2008) (</jrn>).
22.	M. Kirchhof, B. Jutzi, and U. Stilla, “Iterative processing of laser scanning data by full waveform analysis,” ISPRS J. Photogramm. Remote Sens. 63(1), 99–114 (2008). [CrossRef]
23.	A. Persson, U. Söderman, and S. Ahlberg, “Visualization and analysis of full-waveform airborne laser scanner data”, in the IAPRS Vol.XXXVI, Part 3/W19, Enschede, Netherlands, 103–108 (2005).
24.	GeoLas Consulting, www.geolas.com/Downloads/GeocodeWF, (Last access on 8 Jan, 2012).
25.	C. Hug, private communication, Dec (2011).
26.	M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens. 38(4), 1989–1996 (2000). [CrossRef]
27.	J. Y. Wu, J. A. N. van Aardt, and G. P. Asner, “A comparison of signal deconvolution algorithms based on small-footprint lidar waveform simulation,” IEEE Trans. Geosci. Rem. Sens. 49(6), 2402–2414 (2011). [CrossRef]
28.	http://en.wikipedia.org/wiki/Normal_distribution, (Last access on 8 Jan, 2012).
29.	W. Yao and U. Stilla, “Comparison of two methods for vehicle extraction from airborne lidar data toward motion analysis,” IEEE Geosci. Remote Sens. Lett. 8(4), 607–611 (2011). [CrossRef]
30.	B. E. Schutz, H. J. Zwally, C. A. Shuman, D. Hancock, and J. P. DiMarzio, “Overview of the ICESat mssion,” Geophys. Res. Lett. 32(21), 1–4 (2005). [CrossRef]

OCIS Codes
(100.6890) Image processing : Three-dimensional image processing
(280.3640) Remote sensing and sensors : Lidar

ToC Category:
Remote Sensing

History
Original Manuscript: June 1, 2012
Revised Manuscript: July 27, 2012
Manuscript Accepted: August 19, 2012
Published: November 1, 2012

Citation
Yuchu Qin, Tuong Thuy Vu, Yifang Ban, and Zheng Niu, "Range determination for generating point clouds from airborne small footprint LiDAR waveforms," Opt. Express 20, 25935-25947 (2012)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-20-23-25935

Sort: Author | Year | Journal | Reset

References

F. Ackermann, “Airborne laser scanning—present status and future expectations,” ISPRS J. Photogramm. Remote Sens.54(2-3), 64–67 (1999). [CrossRef]
M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies,” Bioscience52(1), 19–30 (2002). [CrossRef]
C. Wang, M. Menenti, M. Stoll, A. Feola, E. Belluco, and M. Marani, “Separation of ground and low vegetation signatures in LiDAR measurements of salt-marsh environments,” IEEE Trans. Geosci. Rem. Sens.47(7), 2014–2023 (2009). [CrossRef]
A. Chauve, C. Vega, S. Durrieu, F. Bretar, T. Allouis, M. P. Deseilligny, and W. Puech, “Advanced full-waveform lidar data echo detection: Assessing quality of derived terrain and tree height models in an alpine coniferous forest,” Int. J. Remote Sens.30(19), 5211–5228 (2009). [CrossRef]
C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens.64(1), 1–16 (2009). [CrossRef]
B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens.61(2), 95–107 (2006). [CrossRef]
Y. C. Qin, B. Li, Z. Niu, W. J. Huang, and C. Y. Wang, “Stepwise decomposition and relative radiometric normalization for small footprint LiDAR waveform,” Sci China Earth Sci.54(4), 625–630 (2011). [CrossRef]
W. Wagner, A. Ullrich, V. Ducic, T. Melzer, and N. Studnicka, “Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner,” ISPRS J. Photogramm. Remote Sens.60(2), 100–112 (2006). [CrossRef]
G. Sun and K. J. Ranson, “Modeling lidar returns from forest canopies,” IEEE Trans. Geosci. Rem. Sens.38(6), 2617–2626 (2000). [CrossRef]
Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett., doi:. [CrossRef]
H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “ICESat full-waveform altimetry compared to airborne laser scanning altimetry over the netherlands,” IEEE Trans. Geosci. Rem. Sens.47(10), 3365–3378 (2009). [CrossRef]
J. B. Blair, D. L. Rabine, and M. A. Hofton, “The laser vegetation imaging sensor: a medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography,” ISPRS J. Photogramm. Remote Sens.54(2-3), 115–122 (1999). [CrossRef]
M. A. Lefsky, D. J. Harding, M. Keller, W. B. Cohen, C. C. Carabajal, F. D. B. Espirito-Santo, M. O. Hunter, and R. de Oliveira, “Estimates of forest canopy height and aboveground biomass using ICESat,” Geophys. Res. Lett.32(22), 1–4 (2005). [CrossRef]
V. H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “Single and two epoch analysis of ICESat full waveform data over forested areas,” Int. J. Remote Sens.29(5), 1453–1473 (2008). [CrossRef]
L. A. Magruder, C. E. Webb, T. J. Urban, E. C. Silverberg, and B. E. Schutz, “ICESat altimetry data product verification at white sands space harbor,” IEEE Trans. Geosci. Rem. Sens.45(1), 147–155 (2007). [CrossRef]
G. Sun, K. J. Ransonb, D. S. Kimesb, J. B. Blairb, and K. Kovacs, “Forest vertical structure from GLAS: an evaluation using LVIS and SRTM data,” Remote Sens. Environ.112(1), 107–117 (2008). [CrossRef]
Q. Chen, “Retrieving vegetation height of forests and woodlands over mountainous areas in the Pacific Coast region using satellite laser altimetry,” Remote Sens. Environ.114(7), 1610–1627 (2010). [CrossRef]
L. I. Duncanson, K. O. Niemann, and M. A. Wulder, “Estimating forest canopy height and terrain relief from GLAS waveform metrics,” Remote Sens. Environ.114(1), 138–154 (2010). [CrossRef]
Y. C. Qin, Y. C. Wu, Z. Niu, Y. L. Zhan, and Z. P. Xiong, “Reconstruction of sparse forest canopy height using small footprint lidar data,” J. Nat Resour.23, 507–513 (2008).
W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens.48, 3571–3579 (2010).
W. Wagner, M. Hollaus, C. Briese, and V. Ducic, “3D vegetation mapping using small‐footprint full waveform airborne laser scanners,” Int. J. Remote Sens.29, 1433–1452 (2008) (</jrn>).
M. Kirchhof, B. Jutzi, and U. Stilla, “Iterative processing of laser scanning data by full waveform analysis,” ISPRS J. Photogramm. Remote Sens.63(1), 99–114 (2008). [CrossRef]
A. Persson, U. Söderman, and S. Ahlberg, “Visualization and analysis of full-waveform airborne laser scanner data”, in the IAPRS Vol.XXXVI, Part 3/W19, Enschede, Netherlands, 103–108 (2005).
GeoLas Consulting, www.geolas.com/Downloads/GeocodeWF , (Last access on 8 Jan, 2012).
C. Hug, private communication, Dec (2011).
M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens.38(4), 1989–1996 (2000). [CrossRef]
J. Y. Wu, J. A. N. van Aardt, and G. P. Asner, “A comparison of signal deconvolution algorithms based on small-footprint lidar waveform simulation,” IEEE Trans. Geosci. Rem. Sens.49(6), 2402–2414 (2011). [CrossRef]
http://en.wikipedia.org/wiki/Normal_distribution , (Last access on 8 Jan, 2012).
W. Yao and U. Stilla, “Comparison of two methods for vehicle extraction from airborne lidar data toward motion analysis,” IEEE Geosci. Remote Sens. Lett.8(4), 607–611 (2011). [CrossRef]
B. E. Schutz, H. J. Zwally, C. A. Shuman, D. Hancock, and J. P. DiMarzio, “Overview of the ICESat mssion,” Geophys. Res. Lett.32(21), 1–4 (2005). [CrossRef]

Ackermann, F.
Allouis, T.
Asner, G. P.
Ban, Y.
Belluco, E.
Blair, J. B.
Blairb, J. B.
Bretar, F.
Briese, C.
Carabajal, C. C.
Chauve, A.
Chen, Q.
Cohen, W. B.
de Oliveira, R.
Deseilligny, M. P.
DiMarzio, J. P.
Ducic, V.
Duncanson, L. I.
Duong, H.
Duong, V. H.
Durrieu, S.
Espirito-Santo, F. D. B.
Feola, A.
Hancock, D.
Harding, D. J.
Hofton, M. A.
Hollaus, M.
Huang, W. J.
Hunter, M. O.
Jutzi, B.
Keller, M.
Kimesb, D. S.
Kirchhof, M.
Kovacs, K.
Lefsky, M. A.
Li, B.
Lindenbergh, R.
Magruder, L. A.
Mallet, C.
Marani, M.
Melzer, T.
Menenti, M.
Minster, J. B.
Niemann, K. O.
Niu, Z.
Parker, G. G.
Pfeifer, N.
Puech, W.
Qin, Y. C.
Rabine, D. L.
Ranson, K. J.
Ransonb, K. J.
Schutz, B. E.
Shuman, C. A.
Silverberg, E. C.
Stilla, U.
Stoll, M.
Studnicka, N.
Sun, G.
Ullrich, A.
Urban, T. J.
van Aardt, J. A. N.
Vega, C.
Vosselman, G.
Vu, T. T.
Wagner, W.
Wang, C.
Wang, C. Y.
Webb, C. E.
Wu, J. Y.
Wu, Y. C.
Wulder, M. A.
Xiong, Z. P.
Yao, W.
Zhan, Y. L.
Zwally, H. J.

Bioscience

M. A. Lefsky, W. B. Cohen, G. G. Parker, and D. J. Harding, “Lidar remote sensing for ecosystem studies,” Bioscience52(1), 19–30 (2002). [CrossRef]

Geophys. Res. Lett.

M. A. Lefsky, D. J. Harding, M. Keller, W. B. Cohen, C. C. Carabajal, F. D. B. Espirito-Santo, M. O. Hunter, and R. de Oliveira, “Estimates of forest canopy height and aboveground biomass using ICESat,” Geophys. Res. Lett.32(22), 1–4 (2005). [CrossRef]
B. E. Schutz, H. J. Zwally, C. A. Shuman, D. Hancock, and J. P. DiMarzio, “Overview of the ICESat mssion,” Geophys. Res. Lett.32(21), 1–4 (2005). [CrossRef]

IEEE Geosci. Remote Sens. Lett.

W. Yao and U. Stilla, “Comparison of two methods for vehicle extraction from airborne lidar data toward motion analysis,” IEEE Geosci. Remote Sens. Lett.8(4), 607–611 (2011). [CrossRef]
Y. C. Qin, T. T. Vu, and Y. Ban, “Towards an optimal algorithm for lidar waveform decomposition,” IEEE Geosci. Remote Sens. Lett., doi:. [CrossRef]

IEEE Trans. Geosci. Rem. Sens.

H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “ICESat full-waveform altimetry compared to airborne laser scanning altimetry over the netherlands,” IEEE Trans. Geosci. Rem. Sens.47(10), 3365–3378 (2009). [CrossRef]
C. Wang, M. Menenti, M. Stoll, A. Feola, E. Belluco, and M. Marani, “Separation of ground and low vegetation signatures in LiDAR measurements of salt-marsh environments,” IEEE Trans. Geosci. Rem. Sens.47(7), 2014–2023 (2009). [CrossRef]
G. Sun and K. J. Ranson, “Modeling lidar returns from forest canopies,” IEEE Trans. Geosci. Rem. Sens.38(6), 2617–2626 (2000). [CrossRef]
L. A. Magruder, C. E. Webb, T. J. Urban, E. C. Silverberg, and B. E. Schutz, “ICESat altimetry data product verification at white sands space harbor,” IEEE Trans. Geosci. Rem. Sens.45(1), 147–155 (2007). [CrossRef]
M. A. Hofton, J. B. Minster, and J. B. Blair, “Decomposition of laser altimeter waveforms,” IEEE Trans. Geosci. Rem. Sens.38(4), 1989–1996 (2000). [CrossRef]
J. Y. Wu, J. A. N. van Aardt, and G. P. Asner, “A comparison of signal deconvolution algorithms based on small-footprint lidar waveform simulation,” IEEE Trans. Geosci. Rem. Sens.49(6), 2402–2414 (2011). [CrossRef]
W. Yao and U. Stilla, “Mutual enhancement of weak laser pulses for point cloud enrichment based on full-waveform analysis,” IEEE Trans. Geosci. Rem. Sens.48, 3571–3579 (2010).

Int. J. Remote Sens.

W. Wagner, M. Hollaus, C. Briese, and V. Ducic, “3D vegetation mapping using small‐footprint full waveform airborne laser scanners,” Int. J. Remote Sens.29, 1433–1452 (2008) (</jrn>).
V. H. Duong, R. Lindenbergh, N. Pfeifer, and G. Vosselman, “Single and two epoch analysis of ICESat full waveform data over forested areas,” Int. J. Remote Sens.29(5), 1453–1473 (2008). [CrossRef]
A. Chauve, C. Vega, S. Durrieu, F. Bretar, T. Allouis, M. P. Deseilligny, and W. Puech, “Advanced full-waveform lidar data echo detection: Assessing quality of derived terrain and tree height models in an alpine coniferous forest,” Int. J. Remote Sens.30(19), 5211–5228 (2009). [CrossRef]

ISPRS J. Photogramm. Remote Sens.

C. Mallet and F. Bretar, “Full-waveform topographic lidar: State-of-the-art,” ISPRS J. Photogramm. Remote Sens.64(1), 1–16 (2009). [CrossRef]
B. Jutzi and U. Stilla, “Range determination with waveform recording laser systems using a Wiener Filter,” ISPRS J. Photogramm. Remote Sens.61(2), 95–107 (2006). [CrossRef]
J. B. Blair, D. L. Rabine, and M. A. Hofton, “The laser vegetation imaging sensor: a medium-altitude, digitisation-only, airborne laser altimeter for mapping vegetation and topography,” ISPRS J. Photogramm. Remote Sens.54(2-3), 115–122 (1999). [CrossRef]
F. Ackermann, “Airborne laser scanning—present status and future expectations,” ISPRS J. Photogramm. Remote Sens.54(2-3), 64–67 (1999). [CrossRef]
W. Wagner, A. Ullrich, V. Ducic, T. Melzer, and N. Studnicka, “Gaussian decomposition and calibration of a novel small-footprint full-waveform digitising airborne laser scanner,” ISPRS J. Photogramm. Remote Sens.60(2), 100–112 (2006). [CrossRef]
M. Kirchhof, B. Jutzi, and U. Stilla, “Iterative processing of laser scanning data by full waveform analysis,” ISPRS J. Photogramm. Remote Sens.63(1), 99–114 (2008). [CrossRef]

J. Nat Resour.

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