Geometric Saliency of Curve Correspondances and Grouping of Symmetric Comntours

Abstract

Dependence on landmark points or high-order derivatives when establishing correspondences between geometrical image curves under various subclasses of projective transformation remains a shortcoming of present methods. In the proposed framework, geometric transformations are treated as smooth functions involving the parameters of the curves on which the transformation basis points lie. By allowing the basis points to vary along the curves, hypothesised correspondences are freed from the restriction to fixed point sets. An optimisation approach to localising neighbourhood-validated transformation bases is described which uses the deviation between projected and actual curve neighbourhood to iteratively improve correspondence estimates along the curves. However as transformation bases are inherently localisable to different degrees, the concept of geometric saliency is proposed in order to quantise this localisability. This measures the sensitivity of the deviation between projected and actual curve neighbourhood to perturbation of the basis points along the curves. Statistical analysis is applied to cope with image noise, and leads to the formulation of a normalised basis likelihood . Geometrically salient, neighbourhood-validated transformation bases represent hypotheses for the transformations relating image curves, and are further refined through curve support recovery and geometrically-coupled active contours. In the thorough application of this theory to the problem of detecting and grouping affine symmetric contours, good preliminary results are obtained which demonstrate the independence of this approach to landmark points.