Planar Affine Rectification from Local Change of Scale and Orientation

We propose a method for affine rectification of an image plane by leveraging changes in local scales and orientations under projective distortion. Specifically, we derive a novel linear constraint that directly relates pairs of points with orientations to the parameters of a projective transformation. This constraint is combined with an existing linear constraint on local scales, leading to highly robust rectification. The method reduces to solving a system of linear equations, enabling an efficient algebraic least-squares solution. It requires only two local scales and two local orientations, which can be extracted from, e.g., SIFT features. Unlike prior approaches, our method does not impose restrictions on individual features, does not require class segmentation, and makes no assumptions about feature interrelations. It is compatible with any feature detector that provides local scale or orientation. Furthermore, combining scaled and oriented points with line segments yields a highly robust algorithm that outperforms baselines. Extensive experiments show the effectiveness of our approach on real-world images, including repetitive patterns, building facades, and text-based content.