| Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds |
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| 作者姓名： | Elena |
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| 作者单位： | [1]Department of Mathematics-CIRAM, University of Bologna, Via Saragozza 8,40123 Bologna, Italy [2]Department of Mathematics, University of Bologna, Piazza Porta S. Donato 5,40126 Bologna, Italy |
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| 基金项目： | project，"Progetti Strategici EF2006" University of Bologna，University of Bologna "Funds for selected research topics" |
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| 摘 要： | <正>In this work we consider the problem of shape reconstruction from an unorganized 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 Differential 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 surface 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.
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| 关 键 词： | Partial Differential Equation surface reconstruction numerical computation Boolean operations distance function level set method data set complex geometry approach diffusion model effectiveness high quality different problems changing used in medical initial defined PDE |
Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds |
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| Elena.Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds[J].Numerical Mathematics A Journal of Chinese Universities English Series,2010,3(4). |
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| Authors: | Elena Franchini Serena Morigi Fiorella Sgallari |
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| Abstract: | In this work we consider the problem of shape reconstruction from an unorganized 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 Differential 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 surface 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. |
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| Keywords: | Shape reconstruction RBF interpolation PDE diffusion model segmentation |
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