Morphology with parabolic structuring elements

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Morphological erosion and dilation filters employ a structuring function, with flat structuring functions being the most common example. This article will use the term ``parabolic'', but much of the literature uses ``quadratic'' structuring functions are less well known but theoretically very important and practically very useful. This paper briefly introduces morphology using parabolic structuring functions, describes the ITK classes used to implement them and includes a number of sample applications.
plus Automatic Testing Results by Insight-Journal Dashboard on Mon Jun 9 14:58:44 2008 for revision #2
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plus Automatic Testing Results by Insight-Journal Dashboard on Mon Jun 9 15:01:17 2008 for revision #1
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minus Great contribution by Gaetan Lehmann on 2009-01-06 04:28:26 for revision #3
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The author describes the parabolic operators and the implementation he made.

Open Science:

The source code is provided as well as the input images.


I've been able to download, build, run the code with the test program, validate the results and measure the perfomance with the test suite. Just perfect!

Open source Contributions:

The code is usable without any problem, and very clearly documented both in the article and in the code. Using it is a matter of minutes.

Code Quality :

Some problems in the style, like the usage on tabs and things of that kind. You should try to run KWStyle to fix them.

Excepted those minor problems, the code is nice and should build everywhere.


As said in the article, this transform is used in microscopy to correct the non-uniform background. The exact distance transform is a very important transform.

Free comment :

I ran the performance suite and get quite different result than yours:

Parabolic  Maurer   Danielsson
12.2    12.5    27.2

The parabolic implementation and Maurer's one gives similar result in that case. Maurer and Danielsson filters can also be modified to use a more efficient contour detector. I then get an execution time of 8.06 s. It might be interesting to see how it performs for you.

On the multithreading issue. I have to disagree with you on that point: ITK way of cutting the image in regions is well adapted to the separable decomposition, when the lines are parallels to the axes. That was not the case for the flat morphology, but I beleive it is in for parabolic operators. I have used it to thread the implementation of the Maurer filter currently in ITK. For the Maurer filter, I get an execution time of 8.98 s (not the same computer than above) with one thread, and 4.58 s with two threads - not that bad :-).

A great contribution - as usual :-)

Don't be surprised if you see a patch appear in the repository to add the wrapitk support in the next days :-)


plus Great contribution! by Julien Jomier on 2008-11-29 10:44:25 for revision #2
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Categories: Filtering, Geometric transforms, Mathematical Morphology
Keywords: mathematical morphology, parabolic structuring functions, quadratic structuring functions, sharpening, distance transforms
Toolkits: ITK
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