Local Shape Modelling Using Warplets

A statistical shape model for the analysis of local shape variation is developed. Overlapping contour segments are parametrically modelled using an orthogonal basis set, Legendre Polynomials, and used to estimate similarity transformations to a reference segment. The alignment regresses the model to the data by least squares fitting and is followed by a PCA of the coregistered set of contour segments. The local shape space is defined jointly by the segmentto-segment ‘warps’ and the mean plus eigen vectors of the shape space, hence Warplets. The parametric modelling makes the alignment correspondence-free so that arbitrary sized segments can be aligned and the local warps can be inverted to reconstruct model approximations of the data. The approach shows potential in capturing fine details of shape variation and is applicable to complex shapes and those with repetitive structure, when only a few training examples are available.