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I am looking for a CNN method, or any other machine learning method, to recognize 3D natural geometries that are similar to each others, and compare these geometries with a reference 3D model. To illustrate this, consider the following crater topographic map (x,y,z) of the Moon as an example:

enter image description here

The exercise would be to recognize the craters, and compare their (3D) geometry (scale-invariant) with a reference 3D crater model (e.g. the one within the blue square). The result I am looking for is a kind of heatmap showing the similarity measure of (1) a sampled crater with the crater model, and/or (2) the geometry of some parts of the sampled crater (e.g. the inner crater steep sides) with those of the reference model. No classification.

I tend to think that a 3D-oriented CNN method (OctNet, Octree CNN... etc) is a starting point for the above-mentioned task but I would rather prefer getting opinions on this matter since I am still a newbie in machine learning and we are dealing with direct application to real-world natural objects here.

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