A local approach to recovering global skewed symmetry

Abstract

A local approach is adopted to allow recovery of global skewed symmetry in the presence of occlusion. Local skewed symmetries are established by extending the definition of local symmetries to affine geometries through the use of local derivatives. Symmetricity, a quantitative gauge of local symmetry based on Mahalanobis distances from the tangent-curvature states of local structures to the local skewed symmetry state-subspace, is also introduced to cope with noise. The symmetricity values and local symmetry axes for each pair of points are then spatially related in the local skewed symmetry field. The global symmetry detection algorithm implemented involves obtaining fast, initial estimates of the symmetry axis from a separate Hough transform technique, followed by maximising a global symmetry measure via a straight active contour model which is driven by effective symmetricity values. This produces useful estimates for the axis of symmetry and the angle of skew in the presence of contour fragmentation, artifacts and occlusion.