[Insight-users] random number generator

[Blezek, Daniel J (Research)]

Stefan,  I started a thread on this a while ago relating to non-deterministic behavior across platforms.  If the ITK design committee approves the move, it would be great to standardize the random number generator to be sufficiently random, fast and generate the same sequences (from a given seed) across platforms.  The discussion culminated with Brad's post: http://www.itk.org/mailman/private/insight-developers/2005-January/006220.html  I'm not sure any action happened on the suggestions.
 
As you point out, many registration algorithms depend on random sampling, exactly where I came across the problem.
 
Cheers,
-dan

-----Original Message-----
From: insight-users-bounces at itk.org [mailto:insight-users-bounces at itk.org]On Behalf Of Stefan Klein
Sent: Wednesday, March 16, 2005 9:16 AM
To: Insight-users at itk.org
Subject: [Insight-users] random number generator



Dear itk-users,

I did some tests with the underlying random generator of the itkImageRandomIteratorWithIndex and it seems that, in Windows, it is 'not very random'. 

The itkImageRandomIterator uses the following random-generator:
<ITKSOURCE>\Utilities\vxl\core\vnl\vnl_sample.<h/cxx>

In Linux the drand48 random-generator is used, which is a good choice.
In Windows however a "simple congruential random number generator" is implemented, since drand48 is not available in Windows. This gives inferior results, in my experience.

To get a feel for the result look at the image1.<mhd/raw>, which is in the file: randomtestresults.zip, which you can download from: http://www.isi.uu.nl/People/Stefan/
The gray-values in this image show how many times a pixel was sampled. The sampling
process works was defined as follows:
   "An ImageRegionIterator walks N=200 times through the image and tests
   at each voxel whether to sample it or not. The test is performed by 
   drawing a number between 0 and 1 using the random generator defined in
   vnl_sample.h; a value >=0.5 means that the voxel is sampled"
As you can see in the image the pixels are not really selected at random...

If we use the itkImageRandomIteratorWithIndex to sample the image, the result (image3.<mhd,raw>) may look better at first sight, but the histogram looks terrible.

On the internet I found the following link:
http://paine.wiau.man.ac.uk/pub/doc_vxl/core/vnl/html/classvnl__random.html
It describes the files vnl_random.<h,cxx>; those files are not included in the vxl-version that comes with ITK. I tried to use these as a random generator. The results are now much better. Image2, which is generated in the same was as image1, but with the random generator defined in vnl_random, does not show any structure anymore. Image4, which is generated using an ImageRandomIterator that uses the vnl_random as its underlying random number generator, has the histogram that you would expect.

For more details please look at the source of the test program, which you can also download from http://www.isi.uu.nl/People/Stefan/ : itkrandomtestsource.zip. You may reproduce the results with this program. Note that only in Windows bad results will be obtained. In Linux there is no problem.

Algorithms that rely on a good random generator may fail if you use the itkRandomImageIteratorWithIndex under Windows. For example, in my research on nonrigid registration I tried to use a stochastic gradient descent optimisation method for minimising the MattesMutualInformation in combination with a B-spline transform (it may speed up your registration algorithms; if you are interested: 
http://www.isi.uu.nl/Research/Publications/publicationview.php?id=1011 ). When I used the itkImageRandomConstIteratorWithIndex for selecting spatial samples the registration results got significantly worse than when I used the itkImageMoreRandomConstIteratorWithIndex (which uses the vnl_random as underlying random number generator).

Any comments on this would be appreciated!

Stefan








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