Bijective Rigid Motions of the 2D Cartesian Grid

Published in DGCI, 2016

Recommended citation: Pluta K., Romon P., Kenmochi Y., Passat N. (2016) Bijective Rigid Motions of the 2D Cartesian Grid. In: Normand N., Guédon J., Autrusseau F. (eds) Discrete Geometry for Computer Imagery. DGCI 2016. Lecture Notes in Computer Science, vol 9647. Springer, pp 359-371, doi:10.1007/978-3-319-32360-2_28

Author(s): K. Pluta, P. Romon, Y. Kenmochi, N. Passat

Abstract: Rigid motions are fundamental operations in image processing. While they are bijective and isometric in , they lose these properties when digitized in . To investigate these defects, we first extend a combinatorial model of the local behavior of rigid motions on , initially proposed by Nouvel and Rémila for rotations on . This allows us to study bijective rigid motions on , and to propose two algorithms for verifying whether a given rigid motion restricted to a given finite subset of is bijective.

File(s): Pre-print (PDF), BibTeX

Errata is not provided but several typos and mistakes were corrected in the journal version of this paper (see Bijective Digitized Rigid Motions on Subsets of the Plane)