Essay About Novel Kernel And Global Uncertainty Function

Clustering for Surface Reconstruction
Essay Preview: Clustering for Surface Reconstruction
Report this essay
Clustering for Surface Reconstruction
Francesco Isgro
DISI – Universita di Genova
[email protected]
www.disi.unige.it/person/IsgroF
Francesca Odone
DISI – Universita di Genova
[email protected]
www.disi.unige.it/person/OdoneF
Waqar Saleem
Max-Planck-Institut fЁur Informatik
[email protected]
www.mpi-sb.mpg.de/?wsaleem
Oliver Schall
Max-Planck-Institut fЁur Informatik
[email protected]
www.mpi-sb.mpg.de/?schall
Abstract
We consider applications of clustering techniques,
Mean Shift and Self-Organizing
Maps, to surface reconstruction (meshing)
from scattered point data and review
a novel kernel-based clustering method.
Keywords: clustering, meshing, scattered
data
Introduction
Clustering of a set of objects consists of partitioning
the set into groups (clusters) of similar
objects. Clustering is one of the core data mining
techniques. This paper describes an ongoing
joint research between DISI and MPII teams
with AIM@SHAPE project framework 1 on using
clustering techniques for surface reconstruction
from scattered data. The paper consists of
two parts (clusters). In the rst part, we consider
applications of clustering to surface reconstruction
from scattered point data. In the second
part, we briey review an alternative clustering
method which we plan to employ for surface re-
1AIM@SHAPE is a Network of Excellence project
within EUs Sixth Framework Programme. The project
involves research groups from 14 institutions and is
aimed at basic and applied studies of digital shape
modeling.
construction in combination or as an alternative
to the two presented algorithms.
1 Clustering Techniques for
Meshing Scattered Data
While clustering has found successful use in
mesh decimation [20, 18], the predominant surface
applications where clustering is employed
are surface reconstruction [12, 19] and multiresolution
modeling [13, 14, 4]. In this section,
we present two applications of clustering techniques
for surface reconstruction. The rst [22]
is based on kernel density estimation and makes
use of the Mean Shift technique [6, 7, 11] while
the other [15, 21], inspired by Growing Cell
Structures (GCSs) [10], utilizes Self-Organizing
Maps (SOMs) [16] to identify sharp features in
a point cloud.
1.1 Clustering for sparse meshing
Schall et al. [22] propose a clustering method for
sparse surface reconstruction from dense, noisy
surface scattered data. Their approach is inspired
by the kernel density estimation method
(Parzen-window estimation method). The approach
computes for every input point 􀀀 of a
noisy point cloud 􀀀
􀀀 a local
uncertainty function measuring the contribution
of 􀀀 to the smooth surface which was sampled
by . After the local functions are combined
to a global uncertainty function, their local
minima are determined using a procedure
similar to the Mean Shift technique [6, 7, 11].
Therefore, a subset of is chosen as start points
for the gradient-descent like algorithm proposed
in [22]. After a small number of iterations,
the start points converge to local minima of the
global uncertainty function which are aligned on
a smooth surface.
This method can be considered as a clustering
approach as several start points converge to
the same local minimum of the dened global
uncertainty function. As it is not necessary that
several points represent one minimum, one approximation
center is calculated for them using
standard Mean Shift. The clustering starts by
centering