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Bijective rigid motions of the 2D Cartesian grid

Abstract : Rigid motions are fundamental operations in image processing. While they are bijective and isometric in R^2, they lose these properties when digitized in Z^2. To investigate these defects, we first extend a combinatorial model of the local behavior of rigid motions on Z^2, initially proposed by Nouvel and Rémila for rotations on Z^2. This allows us to study bijective rigid motions on Z^2, and to propose two algorithms for verifying whether a given rigid motion restricted to a given finite subset of Z^2 is bijective.
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Submitted on : Thursday, May 12, 2016 - 6:18:55 PM
Last modification on : Wednesday, October 27, 2021 - 12:49:46 PM
Long-term archiving on: : Wednesday, November 16, 2016 - 3:36:21 AM

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Kacper Pluta, Pascal Romon, Yukiko Kenmochi, Nicolas Passat. Bijective rigid motions of the 2D Cartesian grid. Discrete Geometry for Computer Imagery (DGCI), 2016, Nantes, France. pp.359-371, ⟨10.1007/978-3-319-32360-2_28⟩. ⟨hal-01275598v2⟩

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