Computing upper and lower bounds of rotation angles from digital images

Authors:
Yohan Thibault;Yukiko Kenmochi;Akihiro Sugimoto
Affiliations:
National Institute of Informatics, Japan and Université Paris-Est, Laboratoire d'Informatique de l'Institut Gapard-Monge, UMR CNRS 8049, ESIEE Paris, France;Université Paris-Est, Laboratoire d'Informatique de l'Institut Gapard-Monge, UMR CNRS 8049, ESIEE Paris, France;National Institute of Informatics, Japan and Université Paris-Est, Laboratoire d'Informatique de l'Institut Gapard-Monge, UMR CNRS 8049, ESIEE Paris, France
Venue:
Pattern Recognition
Year:
2009

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Abstract

Rotations in the discrete plane are important for many applications such as image matching or construction of mosaic images. We suppose that a digital image A is transformed to another digital image B by a rotation. In the discrete plane, there are many angles giving the rotation from A to B, which we call admissible rotation angles from A to B. For such a set of admissible rotation angles, there exist two angles that achieve the lower and the upper bounds. To find those lower and upper bounds, we use hinge angles as used in Nouvel and Remila [Incremental and transitive discrete rotations, in: R. Reulke, U. Eckardt, B. Flash, U. Knauer, K. Polthier (Eds.), Combinatorial Image Analysis, Lecture Notes in Computer Science, vol. 4040, Springer, Berlin, 2006, pp. 199-213]. A sequence of hinge angles is a set of particular angles determined by a digital image in the sense that any angle between two consecutive hinge angles gives the identical rotation of the digital image. We propose a method for obtaining the lower and the upper bounds of admissible rotation angles using hinge angles from a given Euclidean angle or from a pair of corresponding digital images.