TY - GEN
T1 - Geometric tomography with topological guarantees
AU - Amini, Omid
AU - Boissonnat, Jean Daniel
AU - Memari, Pooran
PY - 2010/7/30
Y1 - 2010/7/30
N2 - We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in ℝ3 from its cross-sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. in [LBD+08] preserves the homotopy type of the original object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that shape reconstruction from cross-sections comes with such theoretical guarantees.
AB - We consider the problem of reconstructing a compact 3-manifold (with boundary) embedded in ℝ3 from its cross-sections with a given set of cutting planes having arbitrary orientations. Under appropriate sampling conditions that are satisfied when the set of cutting planes is dense enough, we prove that the algorithm presented by Liu et al. in [LBD+08] preserves the homotopy type of the original object. Using the homotopy equivalence, we also show that the reconstructed object is homeomorphic (and isotopic) to the original object. This is the first time that shape reconstruction from cross-sections comes with such theoretical guarantees.
UR - https://www.scopus.com/pages/publications/77954938535
U2 - 10.1145/1810959.1811007
DO - 10.1145/1810959.1811007
M3 - Conference contribution
AN - SCOPUS:77954938535
SN - 9781450300162
T3 - Proceedings of the Annual Symposium on Computational Geometry
SP - 287
EP - 296
BT - Proceedings of the 26th Annual Symposium on Computational Geometry, SCG'10
T2 - 26th Annual Symposium on Computational Geometry, SoCG 2010
Y2 - 13 June 2010 through 16 June 2010
ER -