CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation
158
2. SIMULATION CONCEPT
The simulation approach presented in this paper is based on ray
tracing algorithms provided by POV Ray (Persistence of Vision
Ray Tracer), a free-ware ray tracing software. Main advantages
of POV Ray are free access to its source code, optimized
processing time, separability of multiple reflections and existing
interfaces to common 3D model formats. In order to provide
necessary output data for two-dimensional analysis of reflection
phenomena, additional parts have been included to POV Ray’s
source code. The simulation concept consists of four major
parts:
• Modeling of scene objects (Section 2.1)
• Sampling of the 3D model scene in POV Ray
(Section 2.2)
• Creation of reflectivity maps (Section 2.3)
• 3D analysis of reflection effects by means of output
data provided by POV Ray (Section 2.4)
In the following subsections, the processing chain will be
explained in more detail.
Cylindrical light
Elevation
Figure 1: Approximation of SAR system by a cylindrical light
source and an orthographic camera; 3D sampling due
to coordinates in azimuth, slant-range, and elevation
2.1 Modeling of scene objects
First, the 3D scene to be illuminated by the virtual SAR sensor
has to be described in the modeling step. 3D models can be
designed in POV Ray or can be imported into the POV Ray
environment. Then, parameters are adapted for describing the
reflection behavior at object surfaces. To this end, POV Ray
offers parametric models for specular reflection and diffuse
reflection. A reflectivity factor for each surface defines the loss
of intensity affecting rays specularly reflected at object
surfaces.
In the case of a modeled SAR system both the light source and
the camera are located at the same position in space. The
concept for approximating the imaging geometry of the SAR
system is shown in Figure 1. Focusing effects due to SAR
processing in azimuth and range are considered by using a
cylindrical light source and an orthographic camera whose
image plane is hit perpendicularly by incoming signals.
2.2 Sampling of the 3D model scene
For analyzing backscattered signals within the modeled 3D
scene, rays are followed in reverse direction starting at the
center of an image pixel and ending at the ray’s origin at the
light source (Whitted, 1980). This concept is commonly
referred to as Backwards Ray Tracing (Glassner, 2002). Since
ray tracing is performed for each pixel of the image plane,
output data for creating reflectivity maps is derived by discrete
sampling of the three-dimensional object scene (Auer et al.,
2008).
Coordinates in azimuth and range are derived by using depth
information in slant-range provided during the sampling step.
For instance, according to Figure 1, focused azimuth
coordinates a, and slant-range coordinates r f of double
bounce contributions are calculated by:
a r , + a
0 p
(1)
r x +r^+ r 3
(2)
where d Q , a p = azimuth coordinates of the ray’s origin and
the ray’s destination at the image plane
7j , r 2 , 7*3 = depth values derived while tracing the
ray through the 3D model scene
So far, only two axes of the three-dimensional imaging system -
azimuth and range - have been used for reflection analysis
(Auer et al., 2008). However, the third dimension, elevation,
may provide potential to enhance the simulators capacities to
3D analysis of reflection effects. To this end, extraction of
elevation data has been added to the sampling step. According
to the imaging concept shown in Figure 1, the elevation
coordinate for a double bounce contribution is derived by
means of the following equation:
*/ =
e n +e
0 p
(3)
where e 0 , e p = elevation coordinates of the ray’s origin and
the ray’s destination at the image plane
At this point, elevation data derived during the sampling step
shall be discussed in more detail. Due to Eq. (3) and the discrete
sampling of the scene, all backscattering objects are assumed to
behave as point scatterers. Resolution in elevation is not
affected by limits occurring due to the size of sampling
intervals along the elevation direction or the length of the
elevation aperture (Nannini et al., 2008). From a physical point
of view, deriving discrete points directly in elevation direction
may be a disadvantage since comparison of the processed
reflectivity function with a simulated one could be a desirable
task. For instance, in the case of single bounce, the discrete
concept will not be able to represent a planar surface
continuously but only by discrete points.
For layover caused by multiple reflections along the elevation
direction the discrete simulation concept is nonetheless
reasonable since approaches for tomographic analysis also seek
for scatterers whose backscattered intensity is concentrated in
individual points along the elevation direction. Concentration
on scene and SAR geometry and thereby neglecting the
physical characteristics provides some advantages, though, to
overcome well known limitations of tomographic analysis (Zhu
et al., 2008). For instance, it leads to a better understanding of
the SAR geometry in the elevation direction by means of
simulating the reflectivity slice which is helpful for 3D
reconstruction. Additionally, it has the potential to provide the
number of scatterers in a cell as a priori for parametric
tomographic estimators if the scene geometry is available at a
very detailed level, e.g. based on airborne LIDAR surface
models.
