Ultra fast cnn based Hardware Computing Platform Concepts for adas visual Sensors and Evolutionary Mobile Robots - bet 20

3.3
Contribution of Ideal ADAS architecture
Our main goal is developing a relatively universal processing architecture for image
processing which should be running on hardware and work in a highly parallel manner.
Hence, we have considered two different platforms based on FPGA and GPU. Developing
highly parallel systems needs a proper platform which should be flexible and robust. In
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traditional parallel processing models many processors have access to a shared memory.
Message Passing Interface
(MPI) and directive-based interface are two important
approaches in shared memory techniques. Figure 3-1 does illustrate the essentials of this
model.
Figure
3-1:
Shared memory’s parallel processing model
The main advantage of this processing model/architecture is that one can calculate very
complex algorithms on the stream of data with a shared memory. A major drawback of this
model is however the latency and bottleneck in memory as well as the complexity of the
task scheduling. Nevertheless, by coupling a simple distributed memory as the state
variable of a single element and a simple processing unit in form of a 2-dimensional grid, to
a nonlinear operation that is coupled also to the neighbors through local connections one
can overcome too many problems of classical parallel image processing. Figure
3-2 has
shown this type of architecture.
Shared Memory
Task Scheduler
Processor array
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Figure
3-2: General idea for distributed processing
Worth a mentioning is that CNN is providing a similar model for processing data and
images. By changing templates we can define a new model for different
operations/functions. Coupling more than one layer of CNN can enable the designer to
model very complex image processing operators [65, 66]. Due to the related robustness
modeling image processing by PDE’s is getting more popular
[67, 68]. Some equations
comes from minimizing energy function and some others are designed using geometrical
arguments like mean curvature motion [69]. There are many application based on PDE
such as inpainting for recovering corrupted regions in image [70], image segmentation
[71], noise reduction edge preservation [72]. All of these examples and similar techniques
are essential for video processing in ADAS. The procedure of solving PDEs in CNN is by
transforming a PDE to set of ODEs. After transforming a continuous spatial PDE to an array
of discrete interactive systems which are ODEs, we can map it on CNN cells. Because CNN is
natural and flexible paradigm for modeling a simple locally interconnected dynamical
system which are grid base.
The CNN architecture is very close to PDE’s and even a direct mapping of PDE’s into a CNN
processor matrix is possible [73]. In the case of linear PDEs we can map each independent
variable with related partial derivative of that to a CNN layer. If we have more than one
Memory Block
Local Processor
Memory Links
Main Processor
Global Memory
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independent variable we have to couple many CNN layer together to provide the solution.
By defining the right templates one can model the behavior of PDEs through a CNN
processor system that will generate the solution. T. Roska
et al
have shown in [73] a way
of how to simulate a space invariant nonlinear PDE by CNN. They have described the
dynamics of three different systems (i.e. 2D heat equation, Burgers’ equation and Navier
-
Stokes equation) by sets of equations. Mapping a two-dimensional heat equation which is
modeled by the Laplace operator has been solved in [73]. Equation 3-1 is showing this heat
model.
(3-1)
𝜕𝑢
(
𝑥
,
𝑦
,
𝑡
)
𝜕𝑡
=
𝑐∇
2
u(x, y, t)
In this equation,
∇
2
is the Laplace operator and it is applied to the intensity which is
𝑢
(
𝑥
,
𝑦
,
𝑡
)
. After spatial discretization of this equation, the PDE is transformed into a system
of ODEs. If we discrete the equation in space by steps of
∆
𝑥
= ∆
𝑦
=
ℎ
, then we can map the
𝑢(𝑥
,
𝑦
,
𝑡)
on a CNN layer. Before that we need a numerical solution of the equation based
on Taylor-series. Equation 3-2 has shown this approximation.
(3-2)
𝜕
2
𝑢
𝜕𝑥
2
~
1
ℎ
2
[
𝑢
(
𝑥
+
ℎ
,
𝑦
) −
𝑢
(
𝑥
,
𝑦
) − (
𝑢
(
𝑥
,
𝑦
) −
𝑢
(
𝑥
−
ℎ
,
𝑦
))]
=
1
ℎ
2
[
𝑢
𝑖
+1,
𝑗
− 2
𝑢
𝑖
,
𝑗
+
𝑢
𝑖
−1,
𝑗
]
Using this approximation, it is easy to map this equation onto the CNN template.
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(3-3)
𝐴
=
⎣
⎢
⎢
⎢
⎡
0
1
2
0
1
2
−4
2
1
2
0
1
2
0
⎦
⎥
⎥
⎥
⎤
,
𝐵
= 0,
𝐼 = 0
The time evolution of the CNN processors using this template will therefore give the
solution of heat equation.
For image processing there is a discrete time version of CNN that is easy to implement on
digital platforms like CPU and FPGA. Out first trial/exercise has consisted of two simple
cells which are connected to each other for solving a 2
nd
order ODE. Each CNN cell has an
internal integrator which fits for solving 1
st
order derivative equations. For solving higher
order equation such as 2
nd
or 3
rd
and etc, we should couple them as a system of simple 1
st
order derivative equations. In chapter 6 we have shown how to solve a nonlinear Rössler
equation by this technique. Later on, it is possible to model CNN by direct coupling of cells
and integrators by local connections.
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