The author describes the parabolic operators and the implementation he made.

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!

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.

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.

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 :-)

This papers describes concept and implementation of mathematical morphology using parabolic structuring elements.

The author provides source code and examples illustrating the algorithm.

CMAKE_MINIMUM_REQUIRED(VERSION 2.4) is missing at the beginning of the CMakeLists.txt, this is causing some warnings when using CMake 2.6 and higher.

The code compiles well using MSVC 2008 express edition. The only issue was in testspacing.cxx I had to cast the sqrt otherwise the compiler throw an error:

 (54) newspacing[0] = 1/sqrt((float)1);
 (55) newspacing[1] = 1/sqrt((float)0.5);

The author provides source code using ITK and proposes new classes to be added to ITK.

The code is usable in its form. The code is following ITK standard.

The code is very well written, well documented.

1) Small typo in the paper: "amd" -> "and"

2) In 4.1 Sharpening: Is there any relation between the the scale of the element and the scale of the object to be sharpened?

3) In 4.2 Distance Transforms: What are the units of the comparison numbers between Parabolic and Danielsson, also what kind of machine was used?

4) Along the same lines, is there any advantages using the parabolic distance transform v.s. other type of distance transforms. Is there any applications?

Great paper!