Matching and parameter estimation of two point patterns related through an affine transform is a very important research topic in the field of computer vision. The key step is to find some invariant features. As contrast to traditional techniques employing geometric moments or cross- ratios, the unique and orthonormal coordinate system, i.e. the eigen one, whose polar radiuses are invariant to an affine transform, is considered. Then, by using SVD, it is shown that after using a whitening transformation, the two point patterns related through an affine transform are respectively mapped to the eigen point patterns related through a rotation transformation. Based on this, an algorithm exactly estimating the affine parameters and correctly determining point correspondence on the condition that the only a priori knowledge is that the two patterns are corresponding in pattern-to-pattern way is developed. By fusing it with a robust estimation technique, which utilizes randomly sampling minimum redundant subset concept, K- RANSAC-wise architecture, joint criterion of maximum matching point pair support and minimum matching error, and linear optimal refinement procedure, we develop the robust version of the algorithm. The experiments have demonstrated that the proposed algorithm is very robust, exact and efficient.