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- W2315671944 abstract "In this work we consider the problem of shape reconstruction from an unor- ganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differen- tial Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the sur- face reconstruction allows us to handle complex geometry and even changing topology, without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets. AMS subject classifications: 65D18, 65F10, 65N08" @default.
- W2315671944 created "2016-06-24" @default.
- W2315671944 creator A5020812203 @default.
- W2315671944 date "2010-06-01" @default.
- W2315671944 modified "2023-09-25" @default.
- W2315671944 title "Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds" @default.
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- W2315671944 doi "https://doi.org/10.4208/nmtma.2010.m9009" @default.
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