# 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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