Kacper Pluta

Bijective Digitized Rigid Motions on Subsets of the Plane

Rigid motions in

Honeycomb geometry: Rigid motions on the hexagonal grid

\mathbb {R}^2

Bijectivity Certification of 3D Digitized Rotations

R2 are fundamental operations in 2D image processing. They satisfy many properties: in particular, they are isometric and therefore bijective. Digitized rigid motions, however, lose these two properties. To investigate the lack of injectivity or surjectivity and more generally their local behavior, we extend the framework initially proposed by Nouvel and Rémila to the case of digitized rigid motions. Yet, for practical applications, the relevant information is not global bijectivity, which is seldom achieved, but bijectivity of the motion restricted to a given finite subset of

New Algorithm for Modeling of Bronchial Trees

\mathbb {Z}^2

Rigid motions in the cubic grid: A discussion on topological issues

Z2. We propose two algorithms testing that condition. Finally, because rotation angles are rarely given with infinite precision, we propose a third algorithm providing optimal angle intervals that preserve this restricted bijectivity.

Rigid Motions on Discrete Spaces

Rigid motions are fundamental operations in image processing. While they are bijective and isometric in