A simple algorithm to evaluate the local symmetry at each point of a closed contour

In this work, contour symmetry is evaluated as a numeric feature for each point of the shape outline, using only the positions of a local vicinity of points. A measure is defined, named Local Symmetric Deficiency (LSD), so that the lower this quantity is, the higher the symmetry will be in the local region considered. This approach is simpler than related previous ones both from a conceptual point of view and for its implementation, since it is reduced just to a suitable manipulation of the Freeman chain code of the curve studied. Its computational cost is very low and it has the advantages of a parallel algorithm, since values for LSD can be computed for each point independently.