Bidirectional reflectance distribution function based
surface modeling of non-Lambertian using intensity
data of light detection and ranging
Xiaolu Li, Yu Liang, and Lijun Xu*
School of Instrument Science and Opto-Electronic Engineering, Beihang University, Beijing 100191, China
*Corresponding author: lijunxu@buaa.edu.cn
Received June 5, 2014; revised July 30, 2014; accepted August 2, 2014;
posted August 5, 2014 (Doc. ID 213399); published August 26, 2014
To provide a credible model for light detection and ranging (LiDAR) target classification, the focus of this study is
on the relationship between intensity data of LiDAR and the bidirectional reflectance distribution function
(BRDF). An integration method based on the built-in-lab coaxial laser detection system was advanced. A kind
of intermediary BRDF model advanced by Schlick was introduced into the integration method, considering diffuse
and specular backscattering characteristics of the surface. A group of measurement campaigns were carried out to
investigate the influence of the incident angle and detection range on the measured intensity data. Two extracted
parameters r and S
λ
are influenced by different surface features, which illustrate the surface features of the
distribution and magnitude of reflected energy, respectively. The combination of two parameters can be used
to describe the surface characteristics for target classification in a more plausible way. © 2014 Optical Society
of America
OCIS codes: (290.1483) BSDF, BRDF, and BTDF; (290.5880) Scattering, rough surfaces.
http://dx.doi.org/10.1364/JOSAA.31.002055
1. INTRODUCTION
Airborne light detection and ranging (LiDAR) is one of the
most effective and reliable means of terrain data collection
[
1]. LiDAR sensors not only record the time difference be-
tween transmitting and receiving signals, but they also record
the intensity data [
2]. In the terminology of LiDAR, intensity is
used for the amplitude or energy, where the energy of each
pulse is the integral over its waveform [
3]. The intensity data
have been proved to be of great potential for a variety of ap-
plications, such as object classification and modeling of the
scattering properties [
4]. To fully utilize these potentials, a
lot of research efforts have been put into the correction of
intensity data and calibration of the scattering model concern-
ing the radar equation [
3,5–7]. However, the radar equation is
deduced based on the laser radar cross section (RCS), which
is not involved with target surface approximation of micro-
structure characteristics. Thus in order to expand the further
interest of LiDAR target classification, the focus of this study
is on the relationship between the intensity data of LiDAR and
the bidirectional reflectance distribution function (BRDF),
which is determined by surface structure, including shadow-
casting, mutual view shadowing, and the spatial distribution of
elements [
8].
Theoretically, the radar equation was used to solve speckle
phenomena resulting from coherence of a laser pulse [9];
however, the practical advantages of using the radar equation
are not as high as expected [
7]. This is because scattering
modeling of coherent light is very demanding and always re-
quires some simplifying assumptions. If the speckle effects
may be ignored in real applications, the BRDF will have ob-
viously comparative advantages in characterizing the surface
features. The main advantage of the BRDF is that it is
independent of the distribution of incident radiance; thus
the evaluation of the BRDF only depends on the characteris-
tics of the material around the laser point [
10]. To date, a lot of
BRDF models have been proposed in the field of realistic ren-
dering. According to their physical foundation, the existing
BRDF models can be classified into three categories (empiri-
cal type, theoretical type, and experimental type). The empiri-
cal type of model aims to provide a simple formulation
specifically designed to mimic a kind of reflection that can be
computed fast but without much physics behind it [
11,12].
Meanwhile theoretical types of models try to accurately
simulate light scattering by using physics laws that lead to
complex expression and high computational effort [
13,14].
According to the desirable properties of different types
of BRDF models, researchers have proposed hybrid BRDF
models that integrate advantages based on practical
demands [
15]. Besides, BRDF models based on geometrical
optics, some researchers also try to develop improved BRDF
models including diffraction and coherence theory [
16]. How-
ever, in this paper for computational simplicity, the light
propagation and reflection are typically described within
the framework only concerned with geometrical optics and
incoherent light.
Theoretically, the BRDF is an idealized entity that cannot
be directly measured [
7], and the existing measurement meth-
ods for the BRDF are experimentally complex to capture all
geometries with adequate accuracy. There is a need to asso-
ciate the BRDF with intensity data obtained from the model-
ing for the LiDAR system. Thus we derived an integration
method to describe the relationship between the intensity
data of LiDAR and BRDF, and introduced a kind of interme-
diary BRDF model between empirical and theoretical models
Li et al. Vol. 31, No. 9 / September 2014 / J. Opt. Soc. Am. A 2055
1084-7529/14/092055-09$15.00/0 © 2014 Optical Society of America