[Insight-users] Kd-tree implementation in ITK is buggy and unreliable
Luis Ibanez
luis.ibanez at kitware.com
Tue Apr 29 13:08:54 EDT 2008
What will be the right way of doing this when
the MeasurementType is "unsigned char" ?
Should we do something like checking if the
type is signed before we use -vcl_sqr() ?
Luis
---------------------
Bill Lorensen wrote:
> No, you need the sqrt.
>
> On Tue, Apr 29, 2008 at 12:27 PM, Luis Ibanez <luis.ibanez at kitware.com> wrote:
>
>>Hi Bill,
>>
>>
>>I undid part of those changes this
>>morining when fixing compiler warnings :-(
>>
>>...
>>
>>Here is the problem,
>>
>>In the effort to reduce the bounds
>>http://public.kitware.com/cgi-bin/viewcvs.cgi/Code/Numerics/Statistics/itkKdTree.txx?root=Insight&r1=1.23&r2=1.24
>>
>>the code used:
>>
>>lowerBound[d] = -vcl_sqrt(NumericTraits< MeasurementType >::max())/2.0;
>>
>>but some of the examples use MeasurementTypes that are unsinged,
>>and the negative value is misinterpreted in that context. In
>>general we cannot assume that the vector use signed components.
>>
>>The code above was replaced with
>>http://public.kitware.com/cgi-bin/viewcvs.cgi/Code/Numerics/Statistics/itkKdTree.txx?root=Insight&r1=1.23&r2=1.26
>>
>>
>>lowerBound[d] =
>> NumericTraits< MeasurementType >::NonpositiveMin() / 2.0;
>>
>>
>>It is missing the sqrt() part of your fix...
>>
>>Do you think that the 1/2.0 factor may be enough for
>>dealing with the numerical overflow ?
>>
>>
>>----
>>
>>BTW: Somewere in the MeanShift class there is a mislead
>> typedef for MeasurementType.
>>
>> I had to add the declaration:
>>typedef typename TSample::MeasurementType MeasurementType;
>>
>> in order to avoid conversion warnings with gcc.
>>
>>
>>
>>
>> Luis
>>
>>
>>
>>---------------------
>>
>>
>>Bill Lorensen wrote:
>>
>>>I committed last night. You should see the results on tomorrow's
>>
>>dashboard.
>>
>>>Bill
>>>
>>>On Tue, Apr 29, 2008 at 11:43 AM, Luis Ibanez <luis.ibanez at kitware.com>
>>
>>wrote:
>>
>>>
>>>>Hi Bill,
>>>>
>>>> Great !
>>>>
>>>>
>>>>Have you committed the fix ?
>>>>Or, could you post the patch
>>>>
>>>>
>>>>On a parallel note,
>>>>I'm tracking the problem with the time out
>>>>of about 6 test. The new version of QuickSelect
>>>>fails for cases where there are many repeated
>>>>values in the collection. I'm looking at
>>>>replacing it with the implementation of
>>>>NthElement from STL.
>>>>
>>>>
>>>>
>>>>Thanks
>>>>
>>>>
>>>>
>>>>
>>>> Luis
>>>>
>>>>
>>>>-------------------
>>>>Bill Lorensen wrote:
>>>>
>>>>
>>>>
>>>>>Luis,
>>>>>
>>>>>I fixed the floating point overflow problem in KdTree.
>>>>>
>>>>>Bill
>>>>>
>>>>>On Mon, Apr 28, 2008 at 8:21 AM, Luis Ibanez <luis.ibanez at kitware.com>
>>>>>
>>>>wrote:
>>>>
>>>>
>>>>
>>>>>
>>>>>>Hi Ali,
>>>>>>
>>>>>>
>>>>>>A quick update on the status of this problem:
>>>>>>
>>>>>>
>>>>>>Bugs were identified and fixed at the level of the
>>>>>>StatisticsAlgorithms:
>>>>>>
>>>>>>* Partition
>>>>>>* QuickSelect
>>>>>>
>>>>>>
>>>>>>
>>>>>
>>>>
>>http://www.itk.org/cgi-bin/viewcvs.cgi/Code/Numerics/Statistics/itkStatisticsAlgorithm.txx?root=Insight&r1=1.19&r2=1.21&sortby=date
>>
>>>>
>>http://www.itk.org/cgi-bin/viewcvs.cgi/Code/Numerics/Statistics/itkKdTreeGenerator.txx?root=Insight&r1=1.14&r2=1.18&sortby=date
>>
>>>>
>>>>>>Explicit tests were added for
>>>>>>
>>>>>>* QuickSelect
>>>>>>* KdTree
>>>>>>* KdTreeGenerator
>>>>>>
>>>>>>(about 12 new tests).
>>>>>>
>>>>>>These new tests are passing.
>>>>>>
>>>>>>
>>>>>>There are still side effects in the following (now failing) tests
>>>>>>
>>>>>>* BayesianClassifierInitializeTest
>>>>>>* itkSampleMeanSjhiftClusteringFilterTest
>>>>>>* RBFTest1
>>>>>>* ScalarImageKmeansClassifierTest
>>>>>>
>>>>>>They are currently timing-out, (probably due to infinite-loops)
>>>>>>We suspect that they are related to the
>>
>>WeightedCentroidKdTreeGenerator
>>
>>>>>>(but that is only early speculation).
>>>>>>
>>>>>>
>>>>>>We are now tracking those issues...
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>> Luis
>>>>>>
>>>>>>
>>>>>>
>>>>>>--------------------
>>>>>>Luis Ibanez wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>Hi Bill,
>>>>>>>
>>>>>>>Yeap, the problem was in the combination of QuickSelect and
>>
>>Partition.
>>
>>>>>>>Both of them are defined in
>>>>>>>
>>>>>>>Insight/Code/Numerics/Statistics/itkStatisticsAlgorithms.txx
>>>>>>>
>>>>>>>Sorting the list before QuickSelect would only work when the
>>>>>>>
>>>>>>
>>>>measurement
>>>>
>>>>
>>>>
>>>>>>>vector has a single dimension. Otherwise, a single sort can not
>>>>>>>
>>>>>>
>>>>possibly
>>>>
>>>>
>>>>
>>>>>>>organize the list in all dimensions. We could call sort just
>>
>>before
>>
>>>>>>>Partition, to sort the activeDimension, but this is an overkill,
>>
>>since
>>
>>>>>>>Partition is indeed intended for parforming a partial sorting.
>>>>>>>
>>>>>>>
>>>>>>>I have replaced both the QuickSelect and Partition functions with
>>>>>>>implementations based on the description of the Partition and
>>>>>>>QuickSelect algorithms in the Wikipedia:
>>>>>>>
>>>>>>> http://en.wikipedia.org/wiki/Quickselect
>>>>>>>
>>>>>>>This works fine for KdTreeTest1 and KdTreeTest2.
>>>>>>>
>>>>>>>
>>>>>>>However, the test for the StatisticsAlgorithms itself fails
>>
>>(timesout)
>>
>>>>>>>due to the fact that its list contains multiple entries with
>>>>>>>values equal to the partition value. A case that is not considered
>>>>>>>in the current algorithm. The current algorithm enters into an
>>>>>>>infinite loop in this case.
>>>>>>>
>>>>>>>I'm modifying the implementation for covering that case.
>>>>>>>
>>>>>>>--
>>>>>>>
>>>>>>>BTW, about 10 test more were added, for exercising the KdTree
>>>>>>>at different bucket sizes.
>>>>>>>
>>>>>>>
>>>>>>>To be revisited: The tests in Borland are producing floating-point
>>>>>>> overflows... not a good sign. There are possible
>>>>>>> other issues in the computation.
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>Luis
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>---------------------
>>>>>>>Bill Lorensen wrote:
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>
>>>>>>>>Luis,
>>>>>>>>
>>>>>>>>I think the main problem is that the samples need to be sorted.
>>
>>I
>>
>>>>added:
>>>>
>>>>
>>>>
>>>>>>>>HeapSort<SubsampleType>(m_Subsample, partitionDimension,
>>
>>beginIndex,
>>
>>>>>>>>endIndex);
>>>>>>>>just before the QuickSelect call and itkKdTreeTest1 passes
>>>>>>>>consistently.
>>>>>>>>
>>>>>>>>However, this is not a good fix. I think the QuickSelect code
>>
>>should
>>
>>>>>>>>work. Probably the error is in Partition. It should group a list
>>>>>>>>
>>>>>>>
>>>>into
>>>>
>>>>
>>>>
>>>>>>>>two parts, one less than the partition value and another greater
>>>>>>>>
>>>>>>>
>>>>than
>>>>
>>>>
>>>>
>>>>>>>>or equal the value. Currently it looks like Partition assumes
>>
>>the
>>
>>>>list
>>>>
>>>>
>>>>
>>>>>>>>is sorted.
>>>>>>>>
>>>>>>>>BTW, itkKdTreeTest2 produces a tree different from the one in
>>>>>>>>
>>>>>>>
>>>>wikipedia.
>>>>
>>>>
>>>>
>>>>>>>>HTH,
>>>>>>>>Bill
>>>>>>>>
>>>>>>>>On Fri, Apr 25, 2008 at 12:59 PM, Luis Ibanez
>>>>>>>>
>>>>>>>
>>>><luis.ibanez at kitware.com>
>>>>
>>>>
>>>>>>wrote:
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>
>>>>>>>>>Hi Ali,
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>An update on the KdTree segmentation fault
>>>>>>>>>(that may or may not be related to the problem that you
>>
>>observe).
>>
>>>>>>>>>
>>>>>>>>>This test is running the example tree provided in the
>>
>>Wikipedia
>>
>>>>>>>>>http://en.wikipedia.org/wiki/Kdtree
>>>>>>>>>http://en.wikipedia.org/wiki/Kdtree#Constructing_a_kd-tree
>>>>>>>>>
>>>>>>>>>We are feeding the set of points:
>>>>>>>>>
>>>>>>>>> (2,3), (5,4), (9,6), (4,7), (8,1), (7,2)
>>>>>>>>>
>>>>>>>>>and expecting to get the tree:
>>>>>>>>>http://upload.wikimedia.org/wikipedia/en/f/f1/Kd_tree.png
>>>>>>>>>
>>>>>>>>> (7,2)
>>>>>>>>> /\
>>>>>>>>> / \
>>>>>>>>> / \
>>>>>>>>> (5,4) (9,6)
>>>>>>>>> /\ \
>>>>>>>>> / \ \
>>>>>>>>> / \ \
>>>>>>>>> (2,3) (4,7) (8,1)
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Here is what we currently observe as output for different
>>>>>>>>>bucket sizes:
>>>>>>>>>
>>>>>>>>>-----
>>>>>>>>>
>>>>>>>>>Case BucketSize == 1:
>>>>>>>>>
>>>>>>>>>The segmentation fault of itkKdTreeTest2 with BucketSize==1
>>>>>>>>>happens because the recursive function:
>>>>>>>>>
>>>>>>>>>KdTreeGenerator::GenerateTreeLoop() (line 179)
>>>>>>>>>
>>>>>>>>>ends up calling itself indifinitely, until it overflows the
>>
>>stack.
>>
>>>>>>>>>It enter in an infinite (recursive) loop calling:
>>>>>>>>>
>>>>>>>>>GenerateTreeLoop( 0, 0, level++)
>>>>>>>>>GenerateTreeLoop( 0, 2, level++)
>>>>>>>>>GenerateTreeLoop( 0, 0, level++)
>>>>>>>>>GenerateTreeLoop( 0, 2, level++)
>>>>>>>>>GenerateTreeLoop( 0, 0, level++)
>>>>>>>>>GenerateTreeLoop( 0, 2, level++)
>>>>>>>>>....
>>>>>>>>>
>>>>>>>>>where "0" and "2" here are the indexes of the points in the
>>>>>>>>>
>>>>>>>>
>>>>sample.
>>>>
>>>>
>>>>
>>>>>>>>>-----
>>>>>>>>>
>>>>>>>>>Case BucketSize == 2:
>>>>>>>>>
>>>>>>>>>The segmentation fault of itkKdTreeTest2 with BucketSize==2
>>>>>>>>>happens also because the recursive function:
>>>>>>>>>
>>>>>>>>>KdTreeGenerator::GenerateTreeLoop() (line 179)
>>>>>>>>>
>>>>>>>>>ends up calling itself indifinitely, until it overflows the
>>
>>stack.
>>
>>>>>>>>>It enter in an infinite (recursive) loop calling:
>>>>>>>>>
>>>>>>>>>GenerateTreeLoop( 3, 3, level++)
>>>>>>>>>GenerateTreeLoop( 3, 6, level++)
>>>>>>>>>GenerateTreeLoop( 3, 3, level++)
>>>>>>>>>GenerateTreeLoop( 3, 6, level++)
>>>>>>>>>GenerateTreeLoop( 3, 3, level++)
>>>>>>>>>GenerateTreeLoop( 3, 6, level++)
>>>>>>>>>....
>>>>>>>>>
>>>>>>>>>where "3" and "6" here are the indexes of the points in the
>>>>>>>>>
>>>>>>>>
>>>>sample.
>>>>
>>>>
>>>>
>>>>>>>>>-----
>>>>>>>>>
>>>>>>>>>Case BucketSize == 3:
>>>>>>>>>
>>>>>>>>>When using a bucket size of 3, the function GenerateTreeLoop()
>>>>>>>>>is being called only once, but it generates the following tree
>>>>>>>>>
>>>>>>>>> NTN
>>>>>>>>> /\
>>>>>>>>> / \
>>>>>>>>> / \
>>>>>>>>>[(2,3),(4,7)] NTN
>>>>>>>>> /\
>>>>>>>>> / \
>>>>>>>>> / \
>>>>>>>>> [(8,1)] [ (7,2) (5,4) (9,6)]
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Where "NTN" stands for "non-terminal node".
>>>>>>>>>and the groups with parenthesis "[ ]" represent buckets.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>That is a first plane dividing the space at X=4.5
>>>>>>>>>One bucket on the left for points with X values < 4.5
>>>>>>>>>and on the right, a second plane dividing the space
>>>>>>>>>at Y = 1.5, to create on bucket on the left with (8,1)
>>>>>>>>>and on the right another bucket with points with Y values
>>>>>>>>>larger than 1.5, namely: [ (7,2) (5,4) (9,6)]
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>-----
>>>>>>>>>
>>>>>>>>>Case BucketSize == 4:
>>>>>>>>>
>>>>>>>>>When using a bucket size of 4 , the function
>>
>>GenerateTreeLoop()
>>
>>>>>>>>>is being called three times, and it generates the following
>>
>>tree
>>
>>>>>>>>>
>>>>>>>>> NTN
>>>>>>>>> /\
>>>>>>>>> / \
>>>>>>>>> / \
>>>>>>>>>[(2,3),(4,7)] [(8,1) (7,2) (5,4) (9,6)]
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>That is a single plane dividing the space at X=4.5
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>----------
>>>>>>>>>
>>>>>>>>>In either case,
>>>>>>>>>the partition is not what we could expect from a KdTree...
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Just to clarify, the real problem seems to be in the
>>>>>>>>>implementation of the algorithm in the KdTreeGenerator,
>>>>>>>>>not in the KdTree class itself...
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Luis
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>-------------------
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>Luis Ibanez wrote:
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>Hi Ali,
>>>>>>>>>>
>>>>>>>>>>Thanks for the additinonal information.
>>>>>>>>>>
>>>>>>>>>>Yeap, the algorithm should work regardless
>>>>>>>>>>of the bucket size. That one was a false alarm.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>I'm tracking now the cases where itkKdTreeTest2 segfaults
>>>>>>>>>>with a bucket size == 2. Hopefully this will illuminate
>>>>>>>>>>at least part of the problem.
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>Thanks
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>Luis
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>---------------
>>>>>>>>>>Ali - wrote:
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>>Luis,
>>>>>>>>>>>
>>>>>>>>>>>I used a bucket size of 16 with about 100 particles. Like
>>
>>you
>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>mentioned,
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>the algorithm must work fine independent of these parameters.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>-Ali
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>>Hi Ali,
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>Could you please report
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>1) How many points (measurement vectors) are you
>>>>>>>>>>>>currently feeding into the KdTreeGenerator ?
>>>>>>>>>>>>
>>>>>>>>>>>>and
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>2) What value of "BucketSize" did you use ?
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>The problem reported in the bug
>>>>>>>>>>>>http://public.kitware.com/Bug/view.php?id=5082
>>>>>>>>>>>>
>>>>>>>>>>>>Seems to be simply the result of a poor choice
>>>>>>>>>>>>on the value of the bucket size parameter.
>>>>>>>>>>>>For the test case reported in that bug, increasing
>>>>>>>>>>>>the value from 16 to 30 solves the problem.
>>>>>>>>>>>>
>>>>>>>>>>>>We are wondering if the problem that you are
>>>>>>>>>>>>experiencing is also the result of poor parameter
>>>>>>>>>>>>setting.
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>Please let us know,
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>Thanks
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>> Luis
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>------------
>>>>>>>>>>>>Ali - wrote:
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>>Hi,
>>>>>>>>>>>>>
>>>>>>>>>>>>>A quick search in the mailing list shows that, during
>>
>>the
>>
>>>>past
>>>>
>>>>
>>>>
>>>>>>half
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>a decade, it has been reported many times that the kd-tree
>>
>>classes
>>
>>>>in
>>>>
>>>>
>>>>
>>>>>>ITK
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>are buggy. Writing some library based on ITK, it took me a few
>>>>>>>>>
>>>>>>>>
>>>>days to
>>>>
>>>>
>>>>
>>>>>>find
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>out that the bug in my library is actually introduced by the
>>>>>>>>>
>>>>>>>>
>>>>kd-tree
>>>>
>>>>
>>>>
>>>>>>>>>implementation in ITK which FINDS THE WRONG NEAREST NEIGHBOUR.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>>>I have no idea, against many warnings from the users,
>>
>>why
>>
>>>>the
>>>>
>>>>
>>>>
>>>>>>bug
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>has not been resolved yet. In the case it is difficult to
>>
>>address
>>
>>>>the
>>>>
>>>>
>>>>
>>>>>>bug,
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>one option is to wrap many other existing implementations,
>>>>>>>>>
>>>>>>>>
>>>>personally
>>>>
>>>>
>>>>
>>>>>>I
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>switched to libkdtree++.
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>_________________________________________________________________
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>
>>>>>>>>>>>>>100's of prizes to be won at BigSnapSearch.com
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>http://www.bigsnapsearch.com
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>>>>_______________________________________________
>>>>>>>>>>>>>Insight-users mailing list
>>>>>>>>>>>>>Insight-users at itk.org
>>>>>>>>>>>>>http://www.itk.org/mailman/listinfo/insight-users
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>>>>>>>>>
>>>>_________________________________________________________________
>>>>
>>>>
>>>>
>>>>>>>>>>>100's of prizes to be won at BigSnapSearch.com
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>http://www.bigsnapsearch.com
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>>
>>>>>>>>>_______________________________________________
>>>>>>>>>Insight-users mailing list
>>>>>>>>>Insight-users at itk.org
>>>>>>>>>http://www.itk.org/mailman/listinfo/insight-users
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>>
>>>>>>>
>>>>>
>>>
>
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