Affine point pattern matching

Abstract

This paper presents a general solution for the problem of affine point pattern matching (APPM). Formally, given two sets of two-dimensional points (x,y) which are related by a general affine transformation(up to small deviations of the point coordinates and maybe some additional outliers). Then we can determine the six parameters aik of the transformation using new Hu point-invariants which are invariant with respect to affine transformations. With these invariants we compute a weighted point reference list. The affine parameters can be calculated using the method of the least absolute differences (LAD method) and using linear programming. In comparison to the least squares method, our approach is very robust against noise and outliers. The algorithm works in O(n) average time and can be used for translation and/or rotations, isotropic and non-isotropic scalings, shear transformations and reflections.