Extract 3D shape information

I have a binary 3 dimensional matrix that represent shapes in space. For ease of understanding, imagine a box shaped element in space. I am looking for a description of its main features like breath, width, length, MajorAxisLength, MinorAxisLength, orientation and angle. The image processing toolbox is very powerful in 2D, however in 3D usinjg bwlabeln I only get area, centroid, bounding box and pixellist. I have checked on the work of David Legland (<http://www.mathworks.com/matlabcentral/fileexchange/33690-geometric-measures-in-2d-3d-images)>, which is great. But here, for example using imMeanBreadth, a mean over the three directions will be given. Therefore I am looking for an even more comprehensive description of shapes and would be happy about hints.

Answer 1

[Image Analyst]

You could look at image moments. I'm attaching a demo that could easily be adapted to 3D.

You could look at Morphometrics for shape descriptors: https://en.wikipedia.org/wiki/Morphometrics

Perhaps Hu's moments: http://www.youtube.com/watch?v=Nc06tlZAv_Q

You can check out my attached demo that finds the two points farthest from each other, again adaptable to 3D.

Let's say that you had a set of numbers that described very well your 3D shape. What would you do with that information? Knowing what you want to do may suggest which attributes should be measured.

[Ahmet Cecen]

If your shapes are simple enough the above should work.

I will add that if your shapes are reasonably complex, much more robust and helpful descriptors than average non-descript measures like mean length this, maxlenght that, can be obtain by using Chord Length Distributions or Spatial Correlations. These are especially useful for comparative purposes, even more so in real datasets from XCT and such, versus randomly generated digital data.

They are not straightforward concepts to write here though, so hit me up (my contact info is easy to find) if the above suggestions from ImageAnalyst doesn't work.

[Julia]

Dear Image Analyst, thank you for your excellent hints. The adaption of these concepts to 3D is what I am struggeling with. Could you please explain how you do it? In terms of application, I want to describe different fracture networks (with their respective apertures, connectivities, length etc) and correlate the shape parameters to their ability to let fluids pass.