Relative geodesics and pattern matching

Abstract: Given a Lie group G acting smoothly on a Riemannian manifold X, let c0 ,c1 : D  → X be smooth functions, where D is also a smooth manifold (possibly with boundary). A geodesic relative to (c0 , c1) is a curve g : D → G with the property that gc0(s) = c1(s) for all sD, which minimises an energy integral over all such curves.

The talk will focus on G=SE(2), X=E2, D=[0,1] and applications to curve-matching. Another case, applicable to matching grayscale images, will also be mentioned if time permits.