You could build models of the surface features based on a syntax, and then detect and compare their dimensions. For example -

Use of shape-from-shading to estimate three-dimensional architecture in the small intestinal lumen of celiac and control patients.

Ciaccio EJ, Tennyson CA, Bhagat G, Lewis SK, Green PH.

Comput Methods Programs Biomed. 2013;111:676-684.

These are 2 different questions.

For the 2nd one I would look into the countless packages available with imageJ. Worse case scenario you can reuse existing codes from various plugins to solve your problem.

You can try out meshlab. It incorporates many functions to compute different distances between surfaces. You can also use ICP algorithm to calculate an rms for matching the two surfaces.

without seeing your surfaces (are they closed surfaces?) is hard to tell. We've done a couple of works where surface distances are a key metric in the evaluation: http://link.springer.com/article/10.1007%2Fs00138-013-0490-4

look for Symmetric Surface Distance. It's implementation it's straighforward in matlab for instance.

Regards

Did you try the package CloudCompare?

http://www.danielgm.net/cc/

I think it could be useful, although you should convert the 3D surfaces into point-clouds.

Regards

Thanks for your useful answers. In particular, my problem is to compare 3D cardiac scar tissue surfaces generated using different reconstruction/interpolation methods to a ground truth surface. I would like not to use point-wise distance based metrics because scar tissues surface can comprise of many isolated sub-regions and surfaces, thus correspondence using automated techniques will lead to large distance errors.

It looks like Meshlab has answer to some of my requirements. For example, I would like to colormap the Gaussian curvature into the surface.

Not sure if these will help, but I have previously published an ImageJ/Fiji plugin Shape3D (formerly 3D Convex Hull) to calculate morphologic measures of 3D image data. Thomas Boudier incorporated some of this into his more advanced plugin, 3D ImageJ Suite.

Your problem seems to me very similar to 3D mesh comparison for biometric purposes (e.g. face recognition algorithms). You could easily find a big corpus of knowledge in this field where there is a need for accurate metrics to match irregular surfaces coming from 3D scan of actual subjects or 3D reconstruction from multiple photos. Methods range from Iterative Closest Point to Isogeodesical Paths, just to name a few. My suggestion: try searching for "3D face recognition"

I think that is you are just trying to compare two surfaces you can use a very well recognized library proposed by Paolo Cignone. You can get it from the web site:

http://vcg.isti.cnr.it/activities/surfacegrevis/simplification/metro.html

It allows you to measure distances between set of points in two surfaces or generate sampling points over the faces and edges of the mesh in order to improve the error estimation. It can also generate ply files containing a color map of the distance or error (Hausdorff, RMS, etc) between the meshes.

@Eranga I'm trying to do the exact thing: compare a mesh with a ground truth and use a metric to compute their difference! What method did you use in the end? I couldn't find anything in MeshLab...

Also, do the meshes have to be aligned or is there an algorithm to align them?

Thanks in advance.

I am sorry that my researchgate account was associated with an discontinued email, so I didn't receive any notifications on new updates. 

@Mehran I ended up using distance metrics such as mean absolute distance (you need to setup a kd tree) and Euler characteristic. The following is the resulting publication. 

Ukwatta, Eranga, et al. "Image-based reconstruction of three-dimensional myocardial infarct geometry for patient-specific modeling of cardiac electrophysiology." Medical physics 42.8 (2015): 4579-4590.

@Mehran "Also, do the meshes have to be aligned or is there an algorithm to align them?" did you get any further information on this?

@Eranga: Oh my apologies now. It's been almost a year since you replied, and the notification to must've got lost. We happened to move to a different problem so it was put on hold. Now we are back in the same spot for comparing mesh similarity and I remembered that I had asked a question here!! Thanks for linking to you paper, I will read over it and bug you in case I have any questions! : )

@Naveen: Yes, there are methods for aligning two meshes. Off the top of my head, one method I can think of is to sample points, uniformly on both meshes, then performing a RANSAC-based alignment (to get a rough alignment of the two meshes), then performing ICP to refine the alignment further. The drawback of this approach is (obviously) speed, and also the fact that the alignment will only account for rigid transformations (so no scaling can happen).

PCL already provides a lot of these stuff for you. Take a look here: http://pointclouds.org/documentation/tutorials/template_alignment.php

Hope this helps!

You can use our software Checkpoint (below) to collect 3D landmark points on surface and perform some 3D shape analysis. For example, you could collect a large set of points covering the surfaces and compare (and/or average) them across specimen.

https://www.stratovan.com/products/checkpoint

If you model 3D surface from probability distribution view, then optimal transport may be a good choice.

Some references:

https://arxiv.org/pdf/1809.07083.pdf

https://math.unice.fr/~rifford/Papiers_en_ligne/IRMA_LR.pdf

Article Optimal Mass Transport for Shape Matching and Comparison

https://www3.cs.stonybrook.edu/~gu/software/omt/IPAM_OMT.pdf

http://archive.ymsc.tsinghua.edu.cn/pacm_download/232/8889-O7-_Geometric_Data_Analysis_based_on_Optimal_Mass_Transportation.pdf