Ok. Since mathematical morphology is a field I’m starting to ‘get’, working within its framework is helpful, as it allows a precise mapping from anything mathematical to a hierarchical graph that can be displayed on a 2D computer screen. So, if I’m understanding it right, CAT(0) spaces are a Hadamard manifold. So, that means EVERY two points can be connected by a minimizing geodesic. (learned that just now in: Riemannian mathematical morphology, J Angulo, S Velasco-Forero – Pattern Recognition Letters, 2014) But I’m learning that success depends upon having a range. You have to chose a subset – a Infimum and supremum — IF I’m understanding the formula right… and knowing a bit about restrictions inherent to displaying images. This will probably give a better clue but I haven’t read it yet. https://arxiv.org/abs/1401.5053

Ok. Since mathematical morphology is a field I’m starting to ‘get’, working within its framework is helpful, as it allows a precise mapping from anything mathematical to a hierarchical graph that can be displayed on a 2D computer screen.
 
So, if I’m understanding it right, CAT(0) spaces are a Hadamard manifold.
 
So, that means EVERY two points can be connected by a minimizing geodesic. (learned that just now in: Riemannian mathematical morphology, J Angulo, S Velasco-Forero – Pattern Recognition Letters, 2014)
 
But I’m learning that success depends upon having a range. You have to chose a subset – a Infimum and supremum — IF I’m understanding the formula right… and knowing a bit about restrictions inherent to displaying images.
 
This will probably give a better clue but I haven’t read it yet.
 
https://arxiv.org/abs/1401.5053
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hadamard space mathematical morphology
is what I used for my scholar search and had a bunch of hits.
 
Summarizing: Yes, it’s possible and practical to visualize such spaces, particularly as they are useful in doing things like simplifying 3D or hypergraphs to a 2D plane (a computer screen) while performing functions such as erosion and dilation.
 
As a mental exercise it can be useful to imagine it all by itself but as a pragmatic matter, it’s useful in transforming images between dimensions while minimizing loss of accuracy and precision.
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