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1. Iñesta, J.M.; Buendía, M.; Sarti, M.A.
   "Local symmetries of digital contours from their chain codes"
   Pattern Recognition, vol. 29, pp. 1737-1749 (1996)
   : bibtex
   Abstract:

   In this work, symmetry is evaluated as a numeric feature for each point of the contour of a shape, using only the positions of a local vicinity of points. A measurement is defined, named as 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 previous ones both from a conceptual point of view and for its implementation, since it is reduced only to a suitable manipulation of the Freeman chain code of the studied curve. A vicinity of pi is determined, in which the amount of local symmetry of the curve is evaluated. We can state that it reflects a similarity rate between the arriving and exiting parts of the curve relative to the point, in a "radius" of k points. A smoothed version of the local symmetric deficiency can be used as input for algorithms of minima seeking, in order to detect local maxima of symmetry. Its computational cost is very low since its performance is close to a linear complexity, and it has the advantages of a parallel algorithm, since values for LSD can be computed for each point independently. This scheme can be used in a number of applications, like shape description, curve matching, labelling points of interest in shapes as landmarks, and corner detection. We combine the measurement of local symmetry with an evaluation of the curvature as angle deflection at each candidate point, in order to distinguish between symmetric corners and symmetric flat points. The results have shown the feasibility of this approach and its good performance. The algorithm is suitable for analyzing biological or medical shapes, because it is able to deal with non perfectly symmetric shapes.

@article {
 author = "Iñesta, J.M.; Buendía, M.; Sarti, M.A.",
 title  = "Local symmetries of digital contours from their chain codes",
 journal = "Pattern Recognition",
 pages = "1737-1749",
 volume = "29",
 year = "1996"
}