The paper provides a useful geometric pattern matching method, invariant under affine transformation, that allows for some random perturbations of the patterns. A pattern consists of a finite set of points characterized using spatial coordinates and labels denoting their properties. The pattern matching method is based on Delaunay triangulation, thus providing the invariance under affine transformation of the matching process and saving computation costs. The method introduced in the paper is valuable in registration problems, identification of objects in an image, and classification. The author presents an experiment related to the matching of constellations.