Ordering and parameterizing scattered 3D data for B-spline surfaceapproximation
Cohen, F.S.
Ibrahim, W.
Pintavirooj, C.
Dept. of Electr. & Comput. Eng., Drexel Univ., Philadelphia, PA;
This paper appears in: Pattern Analysis and Machine Intelligence, IEEE Transactions on
Publication Date: Jun 2000
Volume: 22,
Issue: 6
On page(s): 642-648
ISSN: 0162-8828
References Cited: 16
CODEN: ITPIDJ
INSPEC Accession Number: 6693747
Digital Object Identifier: 10.1109/34.862203
Current Version Published: 2002-08-06
Abstract
Surface representation is intrinsic to many applications in
medical imaging, computer vision, and computer graphics. We present a
method that is based on surface modeling by B-spline. The B-spline
constructs a smooth surface that best fits a set of scattered unordered
3D range data points obtained from either a structured light system (a
range finder), or from point coordinates on the external contours of a
set of surface sections, as for example in histological coronal brain
sections. B-spline stands as of one the most efficient surface
representations. It possesses many properties such as boundedness,
continuity, local shape controllability, and invariance to affine
transformations that makes it very suitable and attractive for surface
representation. Despite its attractive properties, however, B-spline has
not been widely applied for representing a 3D scattered nonordered data
set. This may be due to the problem in finding an ordering and a choice
for the topological parameters of the B-spline that lead to a physically
meaningful surface parameterization based on the scattered data set. The
parameters needed for the B-spline surface construction, as well as
finding the ordering of the data points, are calculated based on the
geodesics of the surface extended Gaussian map. The set of control
points is analytically calculated by solving a minimum mean square error
problem for best surface fitting. For a noise immune modeling, we elect
to use an approximating rather than an interpolating B-spline. We also
examine ways of making the B-spline fitting technique robust to local
deformation and noise
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