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Digital shapes, digital boundaries and rigid transformations: A topological discussion

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Academic year: 2021

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Figure 1. (a,b) Continuous shapes S 1 and S 2 in R 2 (in cyan) and their bound- bound-aries (in blue)
Figure 2. (a) An r-regular shape (in cyan). Some inner and outer r-radius open balls are depicted in magenta, with r higher that the pixel size of the  “topology-preserving” digitization grid
Figure 3. (a) A well-composed shape X 1 of Z 2 (in black). Its boundary ∂X 1 (in green) is a 1-manifold
Figure 4. An original digital circle (left) and its rigid transformations (center and right)
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