Computing Admissible Rotation Angles from Rotated Digital Images

Abstract

Rotations in the discrete plane are important for many applications such as image matching or construction of mosaic images. In this paper, we propose a method for estimating a rotation angle such that the rotation transforms a digital image A into another digital image B. In the discrete plane, there are many angles that can give the rotation from A to B, called admissible angles for the rotation from A to B. For such a set of admissible angles, there exist two angles α ₁,α ₂ that are its upper and lower bounds. To find those upper and lower bounds, we use hinge angles as used in Nouvel and Rémila [5]. Hinge angles are particular angles determined by a digital image, such that any angle between two consecutive hinge angles gives the identical digital image after the rotation with the angle. Our proposed method obtains the upper and lower bounds of hinge angles from a given Euclidean angle and from a pair of digital images.