Local shape modelling using warplets

We develop a statistical shape model for the analysis of local shape variation. In particular, we consider models of shapes that exhibit self-similarity along their contours such as fractal and space filling curves. Overlapping contour segments are parametrically modelled using an orthogonal basis set, Legendre Polynomials, and used to estimate similarity transformations to a reference segment, which may or may not be from the contour being analysed. The alignment is affine and 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 segment-to-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