Abstract
The image registration problem on a group G asks, given two functions f , g : G → R that are related by a translation f ( x ) = g ( s − 1 ⋅ x ) by an element s ∈ G , to find s . For abelian groups, the Fourier transform provides an elegant and fast solution to this problem. For nonabelian groups, the problem is much more involved. This paper shows how this applied problem can shed light on the constructions of noncommutative harmonic analysis, in particular the theory of Gelfand pairs. The abstract theory then suggests a novel two-step approach to solving such problems. The Gelfand pair ( SO ( 3 ) , SO ( 2 ) ) then provides us with an intuitive solution of the registration problem for images on S 2 .
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