Planar Affine Rectification from Change of Scale

A method for affine rectification of a plane exploiting knowledge of relative scale changes is presented. The rectifying transformation is fully specified by the relative scale change at three non-collinear points or by two pairs of points where the relative scale change is known; the relative scale change between the pairs is not required. The method also allows homography estimation between two views of a planar scene from three point-with-scale correspondences. The proposed method is simple to implement and without parameters; linear and thus supporting (algebraic) least squares solutions; and general, without restrictions on either the shape of the corresponding features or their mutual position. The wide applicability of the method is demonstrated on text rectification, detection of repetitive patterns, texture normalization and estimation of homography from three point-with-scale correspondences.