TY - JOUR
T1 - Implicit Shape Reconstruction of Unorganized Points Using PDE-Based Deformable 3D Manifolds
AU - Elena Franchini, Serena Morigi & Fiorella Sgallari
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 - <p style="text-align: justify;">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.</p>