Group-theoretical methods in image understanding

By 金谷健一. 1990

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Learning the Irreducible Representations of Commutative Lie Groups (2014, neutral): “The DFT of a discrete 1D signal x = ( x 1 , . . . , x D ) T is deﬁned: where ρ = e 2 πi/D is the D -th primitive root of unity.”
Lie-algebraic averaging for globally consistent motion estimation (2004, methodology): “The structure of Lie groups forms the basis of our averaging method.”
Integral Invariants for Shape Matching (2006, background): “Differential invariants to actions of various Lie groups have been addressed thoroughly [44] , [36], [17], [58], [76], [30], [48], [64], [91], [85], [37].”
Rotation Averaging (2013, background): “For a more in-depth discussion of the use of group theory in computer vision see the book by Kanatani [37].”
Linear scale-space (1994, background): “( 1992 , 1993 ) and Kanatani ( 1990 ) have pursued this approach of deriving diierential invariants in an axiomatic manner , and considered image properties deened in terms of directional derivatives along certain preferred coordinate directions .”
FFTs for the 2-Sphere-Improvements and Variations (1996, background): “For example, potential applications are found in astronomy [39], computer vision [31, 44], medical imaging [11], biology [37], statistical analysis of directional data [25, 24] and chemistry [34].”