GPUDriven MRF DeNoising

1
GPU-Driven MRF De-Noising
University of Central Florida Summer REU Program
2007
Computer Vision
Computer Graphics
James Painter Dr. Marshall Tappen Andrew
Miller
Harnessing the power of todays massively
parallel graphics processors to offload
computationally-intensive image processing tasks
from the CPU. In doing so, we establish a basis
for real-time Fields of Experts usage.
Fields of Experts
State of GPU
De-Noising
We use Roth Blacks MRF-trained filters to find
the most likely image behind applied Gaussian
noise.
With graphics processor advancement far outpacing
that of CPUs, we recognize the GPU as a medium
with potential to accelerate Fields of Experts
methods. GPU transistor counts, which are
increasing at 3.6x per 18 months, far exceed the
2x standard set by Moores Law.
We use Fields of Experts to repair an image
containing random Gaussian noise. Implementing
Formula A in Cg, with OpenCV and a GPGPU helper
library, we are able to obtain results nearly
identical to Roth Blacks MATLAB implementation
that utilizes the CPU.
By adjusting the step size, we can generate more
accurate results, possibly in fewer iterations.
We can experiment with various step sizes to make
an inference-based selection in our final model.
As shown in Figure 5, the most desirable step
size funnels toward 0.30 as we increase the
iterations. A measurement of decibels per second
helps us find the most efficient
iteration/step-size combination. The greatest
value, among our test data, is found at 100
iterations using step size 1.20, where we have a
value of 0.70dB/s.
500 iterations
Figure 1 Selection of Roth Blacks 5x5 filters
trained from a generic image database.
1000 iterations
Using Bayes theorem, we can begin deriving a
gradient descent formula. We wish to maximize
Step Size
Iterations
Original
1500 iterations
The likelihood for applied Gaussian noise of zero
mean and standard deviation s
Figure 2 GPU performance, measured in
floating-point operations per second, growing
more rapidly than GPU performance. (Christopher
E. Davis)
2000 iterations
2500 iterations
3000 iterations
General-purpose usage of the GPU (GPGPU) has been
implemented in applications ranging from image
processing, to databases, to the biomedical
field. The GPU architecture is ideally suited for
inherently parallel applications, but research
has developed techniques for transposing
sequential operations into parallel for dramatic
GPU optimization. Recent advances in pixel
shader languages give developers the ability to
write high-level code strictly for execution on
the GPU. NVIDIAs C for Graphics Cg is our
shader language of choice for its strong industry
support, maturity, and maximum compatibility with
our chosen NVIDIA hardware.
Figure 3 Fields of Experts de-noising, GPU
implementation using Cg. (Step size of 0.8)
We calculate the gradient of the log-likelihood
and the gradient of the log-prior
Timing benchmarks illustrate the GPUs remarkable
advantage over CPU. We achieve over 30x speedup
for images of size 512x512.
Figure 5 Peak signal-to-noise ratio (dB) for
image de-noised on GPU. Timings measured using an
NVIDIA GeForce 8800GTX graphics board. Blue
indicates highest PSNR per row, red per column.
Green indicates highest dB/s, normalized to our
smallest PSNR of 24.16dB.
Our work paves the way for real-time usage of
Fields of Experts de-noising. Inevitably, over
time, hardware advancements will enable such a
feat. By utilizing GPU power rather than relying
on the CPU, we draw the goal much nearer. The
successful exploitation of de-noising on the GPU
sheds light on a variety of additional GPU image
processing applications.
Combining the log-gradients and introducing a
step size ? to re-form Bayes theorem (Formula
A)
Figure 4 Fields of Experts de-noising, CPU vs.
GPU timings. The GPU clearly handles larger
images more efficiently.
Elizabethtown College
UCF Computer Vision Lab - Under Direction of
Dr. Mubarak Shah Dr. Niels Lobo - Funding
Provided by National Science Foundation