In this paper, we introduce a new set of invariant and local descriptors, which are independent under a General Affine group transformation's (GA (20): rotation, uniform scaling, translation, and stretching) of planar curves: a new Invariant in Affine Scale-Space (IASS). For their extraction, we propose a method based on multiple convolutions between the affine-parametrized curve and Gaussian kerner. The IASS representation of planar curves generalizes, in the affine case, a CSS invariant description under similarity transformation's (rotation, uniform scaling and translation).