SMOOTH SIGNED DISTANCE SURFACE RECONSTRUCTION AND APPLICATIONS


			 Prof. Gabriel Taubin
		       Division of Engineering
			   Brown University
			 Providence, RI, USA


				RESUMO

In this talk I will  describe a new and simple variational formulation
for the problem of  reconstructing the surface geometry, topology, and
color map of a 3D scene  from a finite set of colored oriented points.
These data sets  are nowadays obtained using a  variety of techniques,
including  3D  shape capture  systems  based  on structured  lighting,
pasive multi-view  stereo algorithms, and 3D laser  scanning.  In this
formulation  the   implicit  function  is   forced  to  be   a  smooth
approximation  of the  signed distance  function to  the  surface. The
formulation   allows    for   a   number    of   different   efficient
discretizations, reduces to a finite dimensional least squares problem
for  all linearly parameterized  families of  functions, and  does not
require  the  specification  of  boundary  conditions.  The  resulting
algorithms  are significantly  simpler  and easier  to implement  than
alternative methods. This method is particularly good at extrapolating
missing and/or  irregularly sampled data.  An efficient implementation
based  on  a primal-graph  octree-based  hybrid finite  element-finite
difference  discretization,  and the  Dual  Marching Cubes  isosurface
extraction  algorithm, is  shown  to produce  high quality  crack-free
adaptive  manifold polygon  meshes.  After  the geometry  and topology
have  been reconstructed,  the method  then smoothly  extrapolates the
color  information  from  the  points  to  the  surface.  Experimental
evidence is presented to show  that the resulting method produces high
quality  polygon  meshes  with  smooth color  maps,  which  accurately
approximate  the  source  colored  oriented points.   An  open  source
implementation  of this  method  is available  for  download.  I  will
conclude  describing  applications   to  digital  archaeology  and  3D
forensics.


				  Organizador: Prof. Siome Goldenstein
				 IC -- Unicamp   Fone: (019) 3521-5888