Volume 3, Issue 4
Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds

Elena Franchini, Serena Morigi & Fiorella Sgallari

Numer. Math. Theor. Meth. Appl., 3 (2010), pp. 405-430.

Published online: 2010-03

Preview Full PDF 142 1780
Export citation
  • 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.

  • Keywords

Shape reconstruction, RBF interpolation, PDE diffusion model, segmentation.

  • AMS Subject Headings

65D18, 65F10, 65N08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-3-405, author = {}, title = {Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2010}, volume = {3}, number = {4}, pages = {405--430}, 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.2010.m9009}, url = {http://global-sci.org/intro/article_detail/nmtma/6006.html} }
TY - JOUR T1 - Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 405 EP - 430 PY - 2010 DA - 2010/03 SN - 3 DO - http://doi.org/10.4208/nmtma.2010.m9009 UR - https://global-sci.org/intro/article_detail/nmtma/6006.html KW - Shape reconstruction, RBF interpolation, PDE diffusion model, segmentation. AB -

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.

Elena Franchini, Serena Morigi & Fiorella Sgallari. (2020). Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds. Numerical Mathematics: Theory, Methods and Applications. 3 (4). 405-430. doi:10.4208/nmtma.2010.m9009
Copy to clipboard
The citation has been copied to your clipboard