The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
when the previous pulse recording is effective. Full waveform 
LiDAR systems record the entire signal of the backscattered 
laser pulse (Figure 1). 
Time (ns) 
Figure 1: Transmitted and received waveform and the 
corresponding range in a complex wooded area with a small 
footprint LiDAR system. 
The first operational system Laser Vegetation Imaging Sensor 
(LVIS), developed by the NASA, appeared in 1999 and 
demonstrated the value of recording the entire waveform for 
vegetation analysis (Blair et al., 1999). The first commercial 
full-waveform LiDAR system was introduced in 2004 (Hug et 
al., 2004). Today, most of LiDAR-involved companies (e.g. 
Riegl, Optech, Leica, Toposys) propose such an extension to 
their multiple pulse devices. 
Full waveform systems sample the received waveform of the 
backscattered pulse at a maximum frequency of 1 GHz, which is 
equivalent to 1 GSamples/s. Such systems differ in sampling 
rate, in scan pattern and in footprint size. Most commercial 
systems are small-footprint, typically 0.3 - 1 m diameter at 1km 
altitude, depending on altitude and beam divergence. 
To record full waveform LiDAR data, the main commercial 
manufacturers have added digitization terminals to their systems 
and increased the storage media capacity. Whatever the LiDAR 
system method, the constant digitization sampling period varies 
between 1 to 10 ns. The waveform is not integrally recorded but 
only for a predefined maximum number of samples. Indeed, it is 
necessary to avoid recording too many useless samples because 
they result into massive storage problems. For example, 
TopoSys ALTM systems can store up to 440 samples for each 
pulse. This is equivalent to a continuous vertical section of 66 
meters (440 x 0.15 m per sample). The TopEye Markll system 
saves 128 samples according to a predefined mode which is 
either ’’first pulse and later ” (127 samples after the first) or ’’last 
pulse and earlier ” (127 samples before the last detected). This 
means that full-waveform systems will not record both the 
echoes from the canopy and from the ground within a given 
waveform if the trees are taller than the ’’recording length” of 
the system. 
3. PROCESSING THE WAVEFORMS 
the received signal. From the local maxima of the fitted function 
the range value is calculated and 3D points can be determined. 
Pulse properties (width and amplitude) can be calculated at the 
same time. Here, waveform processing consists in decomposing 
the signal f(x) into a sum of components f(x) so as to 
characterise the different objects along the path of the laser 
beam: 
V = /O) = ^ fj (s) 
7=1 
Considered as a sum of Gaussian functions initially in (Hofton 
et al., 2000) and (Wagner et al., 2006), various formulations of 
fj(x) have been tested in Chauve et al. (2007a): the Gaussian 
function (G), the Log normal function (LG) and the Generalized 
Gaussian function (GG). 
The authors show that the waveform modelling is better using a 
GG function. More over, it introduces another pulse feature (a) 
that can be integrated in a segmentation process (Section 4.2). 
/oj(*) = 
= cij exp 
h.j(x) = 
= ajexp 
fGGj(x) = 
= Oj exp 
An other approach consists in applying signal processing 
methods based on the transmitted and the received waveform. 
The matched filter is computed by the normalized cross- 
Mr) 
r oo 
I 5 
(/) •/•(/+ x)dt 
J f s 2 (t)dt ■ f r(t)dt 
correlation function R sr between the transmitted waveform s(t) 
of the emitted pulse and the received waveform r(t) of the 
backscattered pulse. 
Here, echoes are local maxima of the correlation functions 
(Hofton & Blair, 2002; Kirchhof et al., 2008) . 
This approach considers strong echoes for further processing, 
but weak echoes have to be detected, revised and processed 
again. In order to overcome this problem and retrieve partially 
occluded objects, waveforms can no longer be processed 
independently: local neighbourhoods have to be introduced. 
(Stilla et al., 2007) propose a waveform stacking strategy of 
several weak echoes within a local environment to increase the 
signal-to-noise ratio. 
The processing of waveform data starts in maximizing the 
number of relevant detected peaks within each signal. 
A first approach consists in deriving a parametric formulation of 
Alternatively, the knowledge of the local geometry can be used 
to improve the cross-correlation techniques. Considering the 
waveform as a convolution between the transmitted waveform