Shape Invariants Of Reflectional Symmetry From Elliptic Fourier Descriptors Under Parallel Projection

Abstract

The determination of reflectional symmetric planar shapes is important for pattern recognition, shape analysis and quantitative shape recovery. In this paper, forms of shape invariants for reflectional symmetry using elli]?tic Fourier descriptors are derived. They are found Ito be independent of shape rotation, translation and orl:hographic parallel projection. By theoretical analysis, these invariants provide sufficient information for (i) detection of reflectional symmetry and skewed symmetry, (ii) the axes of symmetry and skewed-symmetry, and the skewed-transverse axis, (iii) the root locus of the gradient vector (p,q) that can interpret the vkewed symmetry as a real symmetry.