Image processing has very interesting applications of multipole moments as well as other kinds of moments (e.g. complex-valued moments).
Objects in images have complicated shapes. Using moments helps in automatic recognition of these shapes by representing them as combinations of simpler shapes that can be processed by algorithms.
There is a lot of knowledge about moments accumulated in that field. I enjoyed learning from them. I think, we can apply many of those things in chemistry/physics, or other applications where complicated shapes are present.
I recommend these sources:
Wilhelm Burger, Mark J. Burge. Digital Image Processing. An Algorithmic Introduction Using Java (2016)
J. Flusser, On the independence of rotation moment invariants, Pattern Recognition, V33, 9 (2000), 1405-1410
Jan Flusser, Tomáš Suk and Barbara Zitová. 2D and 3D image analysis by moments (2016)
This topic was modified 1 year, 9 months ago by vladgladkikh.