In this paper we obtain, for the first time, explicit formulae for integral invariants for curves in 3D with respect
to the special and the full affine groups. Using an inductive approach we first compute Euclidean integral
invariants and use them to build the affine invariants. The motivation comes from problems in computer vision.
Since integration diminishes the effects of noise, integral invariants have advantage in such applications. We use
integral invariants to construct signatures that characterize curves up to the special affine transformations.
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