I think in your case (for good figure images) the AFM technique is better for you than the SEM technique this for seeing  the clear porosity micrographs. 

Hi Hamida,

That's not a bad idea: I can try that and see what sorts of images I can get. And strangely enough, I have better access to an AFM than an SEM, at least to a good one.

I know that good image analysis is really dependent on a good image, which is dependent on good sample preparation. And a good instrument to MAKE the images.

And then maybe I won't need something like Minkowski Functionals to process my images!

But i'd still like to know how to use them. I see some papers discussing their use, but not that much that seems to explain it very simply.

If use AFM tech. look for the 3D images it will be clear for the porosity state. For processing Minkowski Functionals Please look for this Article may help you.

(Efficient processing of Minkowski functionals on a 3D binary image using binary decision diagrams

I. BLASQUEZ

LICN–IUT, Universite ́ de LIMOGES Alle ́e Andre ́ Maurois

87065 LIMOGES CEDEX, FRANCE [email protected]

J.-F. POIRAUDEAU LICN–IUT, Universite ́ de LIMOGES Alle ́e Andre ́ Maurois

87065 LIMOGES CEDEX, FRANCE [email protected]

At this website {http://www.unilim.fr/pages_perso/isabelle.blasquez/Blasquez_WSCG03_3ADD.ps}

hope is very good for you 

One of the most useful and functional software is Gwyddion. It has a capability of determining three Minkowski functions as depended on the z-scale level. Minkowski 1 functional would be equivalent to the bearing ratio curve used for characterising roughness. M2 serves to characterize boundaries length while M3 is for connectivity measure.

Using SEM images is not trivial since you have to provide the same brightness for a series of images you want to compare. Because height in SEm images depends not only on the height.

AFM graph usually contain height data and in this case determining Minkowski functional would be easier.

http://gwyddion.net/documentation/user-guide-en/statistical-analysis.html

Sergei,

Thanks very much: I've looked at Gwyddion and I see that it does compute three Minkowski functionals. I've also tried using some MATLAB routines from a paper by Toccafondi:

Toccafondi C, Stępniowski WJ, Leoncini M, Salerno M. Advanced morphological analysis of patterns of thin anodic porous alumina. Materials Characterization. 2014 Aug;94:26–36.

They provide some MATLAB routines that calculate:

• coverage
• boundary length
• Euler characteristics

My problem is that even with really good/consistent images I wasn't really sure how to use the Minkowski functionals.

I think that the median of coverage gives me an "average" grey level that I could then use to select a processed image, and then process with something like ImageJ (make into a binary then determine black and white statistics).

But I suspect I'm not getting the most that I can from the Minkowski functionals. But I don't see any good papers or textbook that explains how to use them for the non-image processing specialist.

Here are few examples of using M-functionals for real structure analysis.

Thanks. I shall go thru these.

The Rodriguez-Valverde one is GREAT! It really helps to explain things.

I had Legland's paper, as well as his MATLAB routines: it's also good, but a little bit too advanced for my current state of understanding now.

I shall experiment with Gwyddion some more and see if I can understand what it's doing. I made some test images of regular geometries to try to help.

still working on that? I don't know if ImageJ has plugin for Minkowski functionals. For sure Gwyddion has that. So I would suggest moving on to this other - also freeware - IP&A software.

bye