18
CPU GPU
Figure 2. A GPU uses more transistors as arithmetic logical
units (NVIDIA, 2007)
In rasterization, each geometry primitive is calculated separately
from the others, which allows for a highly parallel design. The
visualization is controlled by the so-called graphics pipeline
(see Figure 3). After the transformation from world to screen
space, calculated by the so-called vertex shader, the data is ras
terized by the hardware rasterizer of the graphics card. Each re
sulting pixel is piped through the pixel shader, another specia
lized and programmable part of today’s graphics hardware. The
pixel shader is used to compute the color of each displayed pix
el. This is done according to the lighting and material or texture
information of each pixel. Due to the flexible and programm
able shaders used in modem graphics cards, different methods
for calculating the reflections can be implemented. Finally, the
so called z-buffering is done before the image is displayed on
the screen or saved in the texture memory of the graphics hard
ware.
vertex shader
texture pixel shader
Figure 3. Programmable graphics pipeline of modem graphics
cards
SAR simulations are visualization applications. GPUs are there
fore well suited for SAR simulations. But radar images differ in
many ways from images acquired by passive sensor systems.
Using the flexible programmable GPUs, the different imaging
geometry and radiometry of radar images can be implemented,
as described in the following section.
3. REAL-TIME SAR SIMULATION USING SARVIZ 1.0
The real-time SAR simulation tool SARViz (Balz, 2006), has
been constantly improved since it has been presented for the
first time in 2006. The newest version is supporting squint an
gles, real multi-look, the visualization of moving objects as well
as simple bi-static configurations. SARViz is using methods de
veloped by computer graphics to simulate SAR images. The
GPU is processing triangles using local illumination. Each trian
gle is visualized independently from the other triangles. Each
triangle point is processed by the vertex shader, which treats the
geometry. After the rasterization, the radiometry of each pixel is
calculated by the pixel or fragment shader.
3.1 SAR geometry
The vertex shader is transforming each point from the model co
ordinate system to world coordinates and then subsequently to
image coordinates. The so-called camera transformation matrix
(Microsoft, 2005) has to be adapted to achieve the desired paral
lel projection.
The range position of each object in a SAR image depends on
the distance between the object and the sensor, thus higher
points, i.e. points with larger z-values, are closer to the sensor
and are therefore mapped closer to near-range. The resulting
shift in range direction Ax, depends on the height above the
ground level z and the off-nadir angle V
Ax = z-tan(0 o# )
3.2 SAR radiometry
The pixel shader is processing every pixel to compute the cor
responding radiometry. For each pixel the corresponding face
normal is determined using a 3D model. Taking material prop
erties, like the dielectric constant, and sensor properties into ac
count, the reflection strength can be calculated. SARViz offers
three different methods of backscattering computation. The sta
tistical method based on measurements of Ulaby & Dobson
(1989), a direct calculation based on the roughness and dielec
tric constant of the material developed by Zribi (2006) and an
adaptation of computer graphics methods. Most commonly used
is the adaptation of the computer graphics methods, due to its
computing time efficiency.
According to the Phong reflection model (Phong, 1975), three
illumination elements (diffuse, specular and ambient) are com
bined. In computer graphics, the diffuse element is calculated
using the material properties and the light strength as well as the
light position and face normal n (Gray, 2003). In the SAR case,
the reflection strength is determined by the reflections strength r
and the sensor position vector s\
a d = r(n, s)
The specular part of the overall reflection value can be derived
from the visualization of optical specular reflections based on
Blinn’s (1977) work, with p~32. Because in the mono-static
SAR case the “light” and “camera” position are identical, the
calculation can be simplified:
<x s = r(n, s) p
Comparing the calculated results with the statistical analysis of
Ulaby & Dobson, it is possible to retrieve realistic values for the
reflection and the roughness values, which are needed to calcu
late the overall reflection strength.
The reflection is calculated locally. Therefore, multi-reflections
as well as shadows are not supported. In the rasterization ap
proach, the paths of the rays are not traced and every vertex and
pixel is processed separately, therefore occlusions are not mod
eled. By using shadow maps (Williams, 1978) both shadows
and occluded areas can be modeled. A shadow map is generated
in two steps. First, the scene is rendered from the position of the
light source, which is in the mono-static case equivalent to the
SAR sensor position. Instead of reflection values, the distance
of every rendered pixel to the sensor is written to the so-called
shadow map, as it is depicted in Figure 4.
In the second step the scene is rendered from the position of the
virtual camera. SARViz directly simulates ground-range images
to avoid the computational intense transformation from slant-
range to ground-range. Because of this, the scene is rendered
looking from
distance of ea
the transform
object. If the <
stored in the s
rendered.
sensor view
I
Shadow map]
implemented
this method,
shadow area
camera and 1
static SAR si
and the virtu,
precision and
maps.
3.3 Soft sha
The edges of
sharp, becau:
of a shadow
visualizing s<
shadows, esj
images, then
ambient lighi
Due to the si
dow still ref
ized by gene
image centre
edges of the
maps are de’
pends on th
maps, the sh
In our appn
shadow area
two or more
areas are no
pixels inside
limited amo
in Figure 5,
lobe and is \
Figure 5. Vi
1
3.4 Spotlq
The spatial
the spotligh
radar anteni
the exposur
