Affine alignment of compound objects: A direct approach

A direct approach for parametric estimation of 2D affine deformations between compound shapes is proposed. It provides the result as a least-square solution of a linear system of equations. The basic idea is to fit Gaussian densities over the objects yielding covariant functions, which preserves the effect of the unknown transformation. Based on these functions, linear equations are constructed by integrating nonlinear functions over appropriate domains. The main advantages are: linear complexity, easy implementation, works without any time consuming optimization or established correspondences. Comparative tests show that it outperforms state-of-the-art methods both in terms of precision, robustness and complexity.