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I've been reading through "topological vector spaces" lately. I've realized some of the notation usually used resemble the definition of some morphological operators usually defined in image analysis.

Apart from stuff related to graph theory is there any application where actual concept of topology are used in image analysis?

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Mean-curvature motion may modify the topology in 3D but not in 2D. enter image description here

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  • $\begingroup$ What topology concepts are used here? How is the algorithm formulated? Also, please point out the references. $\endgroup$ – user8469759 Jan 15 at 10:16
  • $\begingroup$ It's not really that concepts are used, it's more about the topological properties of the method (topologically connected objects remain such under MCM in 2D, not so in 3D). As far as the algorithm goes, you basically solve $\partial_t u = |\nabla u|div(\frac{\nabla u}{|\nabla u|})$, for more details search mean curvature motion in image processing and refer to some of the papers. There's similarly continuous-scale morphology once again described by PDEs which obviously has some connection to topology. $\endgroup$ – lightxbulb Jan 15 at 10:47
  • $\begingroup$ That's not exactly what I had in mind. But I've just learned something new, thx. $\endgroup$ – user8469759 Jan 15 at 10:53

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