Development of Advanced
Algorithms for AstroMed
Applications
Ron Kneusel
ITT Visual Information Solutions
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AstroMed 2009 Sydney
Outline
• Image enhancement via the generalized
histogram
• Curve fitting via Particle Swarm Optimization
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Generalized Histogram Enhancement
• Motivation
• Locally adaptive histogram equalization often results in “unnatural”
images in which contrast is over enhanced.
• Key Concepts
• Image enhancement can be based on a histogram built using noninteger values.
• The value added to the histogram from a particular pixel is based
on the local environment of that pixel.
“Image contrast enhancement based on the generalized histogram”
B. Yoon, W. Song, Journal of Electronic Imaging, Vol 16(3), 2007
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Generalized Histogram Enhancement
y = f(x)
Mapping
function
fij(m) = S wij(k), m = 0,1,…, Q-1 ; k = 0,1,…,m
Contrast gain
function
wij(k) = hij(k) / Nij, k = 0,1,…,Q-1
Standard
histogram
hij(k) = S d(xuv,k), k = 0,1,…,Q-1 ; u,v Aij
But, we can replace hij(k) with gij(k):
Generalized
histogram
gij(k) = S (ruvd(xuv,k) + (1-ruv)/Q), k = 0,1,…,Q-1
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Generalized Histogram Enhancement
gij(k) = S (ruvd(xuv,k) + (1-ruv)/Q), k = 0,1,…,Q-1
where ruv is the fractional count for the pixel at (u,v)
ruv = a (1 – e-gsuv)
suv = | xnm – xuv | / x, x = mean intensity in 3x3 region
Effectively,
a affects brightness, a = 0,…,1
g affects contrast, g = 0,…
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Generalized Histogram Enhancement
Original
Global Contrast Enhanced
a = 1, g = 300
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Generalized Histogram Enhancement
• The generalized histogram still considers all pixels in an image
• It is reasonable to apply the generalized histogram to smaller
image regions as in locally adaptive histogram equalization
Therefore…
• Create an adaptive generalized histogram equalization by
applying GH to a region and updating the center pixel value as
in convolution.
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Generalized Histogram Equalization
Original
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Locally Adaptive (145x145 pixels)
a= 1, g = 300
unsharp mask, radius 3 (both)
Particle Swarm Optimization
• PSO is a genetic algorithm for exploring a parameter space
• Key concepts:
• The parameter space is randomly populated by a swarm of
“particles”
• Each particle evaluates the fitness function and stores its own
best position
• Each new step of the algorithm moves the particles according to
its own best position and the best overall position of the swarm
(the global best)
• Iteration continues until some convergence criterion has been met
“Particle swarm optimization”, J. Kennedy, R. Eberhart, in Proc. of the IEEE Int. Conf.
on Neural Networks, Piscataway, NJ, pp. 1942–1948, 1995.
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Particle Swarm Optimization
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Particle Swarm Optimization
• In order to do curve fitting with PSO, the fitness function becomes the
c2 between the measured points and the fit function with the current
particle parameter values.
• For the examples here, the fit function is a 2D Gaussian:
zi = p0 + p1 * exp(-0.5 * (((xi – p4)/p2)2 + ((yi-p5)/p3)2))
• The goal is to fit 11x11 images of “peaks” during 3D PALM
reconstruction. There are 2 to 6 million peaks to be fit.
• PALM = “Photo-activated Localization Microscopy”
“Interferometric fluorescent super-resolution microscopy resolves 3D cellular ultrastructure”,
G. Shtengel, et. al. PNAS March 3, 2009, vol 106, no 9, 3125-3130.
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Particle Swarm Optimization
• PSO is very computationally expensive
• On a single CPU it is about 1000x slower than gradient search
(which IDL uses)
• So, why use it in this case?
• The answer lies in the fact that there are millions of images to
be fit:
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PSO is straightforward to implement in CUDA
In this case, convergence is reached in 25 to 30 iterations
The CUDA architecture enables thousands of simultaneous fits
Added benefit: fits always converge, no failures, no initial guesses
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Particle Swarm Optimization
• CUDA programming is in low-level C code, still difficult
• IDL provides the framework
• Visualization in 3D
• Easy implementation of advanced reconstruction algorithms
• Easy interface to CUDA
• CUDA provides the computational engine for time-critical tasks
beyond what can be reasonably done with optimized code
using multiple CPUs (IDL and C)
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Fit time (s)
Particle Swarm Optimization
IDL
CUDA
Number of images
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Particle Swarm Optimization
• Initialize seeds for the PRNGs (hybrid Tausworthe, CPU)
• On the GPU:
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•
•
•
•
Each image fit by single block of threads
Each thread is one particle (256 particles/image)
Canonical algorithm iterated set number of times (25-30)
Per thread PRNG – Park & Miller MINSTD with CPU seed
Parameter uncertainties estimated from the standard deviation of
the last 5 global best positions
• Parameters, uncertainties and reduced c2 returned to IDL
• Block test for multi-stream PRNG demonstrates that the hybrid
Tausworthe seeds work well for the MINSTD generator
(Jarque-Bera 94%).
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Euclidean Distance
(swarm to CURVEFIT)
Particle Swarm Optimization
30
Number of Swarm Iterations
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Conclusion
• IDL provides researchers with a powerful array processing
language combined with superb 2D and 3D visualizations
enabling rapid and sophisticated analysis of data
• CUDA adds raw “supercomputing” power to desktop
• IDL + CUDA enable researchers to accomplish with an
inexpensive PC what in the past would have been impossible
or required a large mainframe or cluster.
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A final example… home-grown in Australia!
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