1. A computer-accessible memory medium that stores program instructions for detecting symmetries of configurations of discrete curves, wherein the program instructions are executable by a processor to perform: receiving configuration characterization information for a configuration of discrete curves, wherein the configuration comprises a plurality of discrete curves, and wherein the configuration characterization information comprises rotational symmetry groups for each of the plurality of discrete curves; determining a greatest common divisor of the rotational symmetry groups of the discrete curves, wherein the greatest common divisor is a maximum possible object-based mutual rotational symmetry group for the configuration; and storing the maximum possible object-based mutual rotational symmetry group, wherein the maximum possible object-based mutual rotational symmetry group is usable to perform pattern matching between configurations.