# Application of topology in image processing

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?

• 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. – lightxbulb Jan 15 at 10:47