Computing Admissible Rotation Angles from Rotated Digital Images

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 α1, α2 that are its upper and lower bounds. To find those upper and lower bounds, we use hinge angles as used in Nouvel and Remila [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.

[1]  W. S. Anglin Using Pythagorean triangles to approximate angles , 1988 .

[2]  Eric Andres Cercles discrets et rotations discrètes , 1992 .

[3]  Jack E. Volder The CORDIC Trigonometric Computing Technique , 1959, IRE Trans. Electron. Comput..

[4]  Eric Rémila,et al.  Incremental and Transitive Discrete Rotations , 2006, IWCIA.

[5]  Eric Andres,et al.  The Quasi-Shear Rotation , 1996, DGCI.

[6]  Kristin J. Dana,et al.  Real-time scene stabilization and mosaic construction , 1994, Proceedings of 1994 IEEE Workshop on Applications of Computer Vision.