Wavelet approximation-based affine invariant 2-D shape matching and classification

In this paper, an algorithm for matching and classifying 2-D shapes that undergo affine transformation is developed. The algorithm uses the 1-D dyadic wavelet transform (DWT) to decompose a shape´s boundary into multiscale levels. The curve moment invariants of the approximation coefficients are used as the shape features. Two different dissimilarities are calculated from the Euclidean distances between the decomposed scale levels of the shapes. These dissimilarities are used in shape matching and clustering by using hierarchical clustering algorithm with Ward´s linkage rules. The presented algorithm is invariant to the affine transformation and to the boundary starting point variation. The algorithm is also capable of finding and clustering similar shapes even if there are small deformations between their boundaries.