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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Andres, E.: Cercles Discrets et Rotations Discrétes. Thesis, Université Louis Pasteur Strasbourg (1992)
Andres, E.: The Quasi-Shear Rotation. In: Miguet, S., Ubéda, S., Montanvert, A. (eds.) DGCI 1996. LNCS, vol. 1176, pp. 307–314. Springer, Heidelberg (1996)
Anglin, W.S.: Using Pythagorean triangles to approximate angles. American Mathematical Monthly 95, 540–541 (1988)
Hansen, M., Anandan, P., Dana, K., van der Wal, G., Burt, P.: Real-time scene stabilization and mosaic construction. In: 2nd IEEE workshop on Applications of Computer Vision, pp. 54–64 (1994)
Nouvel, B., Rémila, E.: Incremental and transitive discretized rotations. In: Reulke, R., Eckardt, U., Flach, B., Knauer, U., Polthier, K. (eds.) IWCIA 2006. LNCS, vol. 4040, pp. 199–213. Springer, Heidelberg (2006)
Volder, J.E.: The CORDIC Trigonometric Computing Technique. IRE Transactions on Electronic Computers EC-8, 330–334 (1959)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thibault, Y., Kenmochi, Y., Sugimoto, A. (2008). Computing Admissible Rotation Angles from Rotated Digital Images. In: Brimkov, V.E., Barneva, R.P., Hauptman, H.A. (eds) Combinatorial Image Analysis. IWCIA 2008. Lecture Notes in Computer Science, vol 4958. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78275-9_9
Download citation
DOI: https://doi.org/10.1007/978-3-540-78275-9_9
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78274-2
Online ISBN: 978-3-540-78275-9
eBook Packages: Computer ScienceComputer Science (R0)