Skewed Symmetry Detection Through Local Skewed Symmetries

We explore how global symmetry can be detected prior to segmentation and under noise and occlusion. The definition of local symmetries is extended to affine geometries by considering the tangents and curvatures of local structures, and a quantitative measure of local symmetry known as symmetricity is introduced, which is based on Mahalanobis distances from the tangent-curvature states of local structures to the local skewed symmetry state-subspace. These symmetricity values, together with the associated local axes of symmetry, are spatially related in the local skewed symmetry field (LSSF). In the implementation, a fast, local symmetry detection algorithm allows initial hypotheses for the symmetry axis to be generated through the use of a modified Hough transform. This is then improved upon by maximising a global symmetry measure based on accumulated local support in the LSSF — a straight active contour model is used for this purpose. This produces useful estimates for the axis of symmetry and the angle of skew in the presence of contour fragmentation, artifacts and occlusion.