doi:10.1016/j.gmod.2003.08.001 
Copyright © 2003 Published by Elsevier Science (USA).
Interpolating scattered data using 2D self-organizing feature maps
George K. Knopf
, 
and Archana Sangole
Department of Mechanical and Materials Engineering, Faculty of Engineering, The University of Western Ontario, London, Ont., Canada N6A 5B9
Received 12 December 2001;
accepted 26 August 2003. ;
Available online 30 October 2003.
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Abstract
Many computer-aided design, computer graphics, and data visualization applications require freeform surfaces to be created from irregularly spaced and unorganized digitized data. Most surface interpolation and approximation techniques require information about the connectivity between these measured points. In contrast, the scattered data interpolation method described in this paper exploits the topological structure and unsupervised learning algorithm of a 2D self-organizing feature map (SOFM) to iteratively create a polygonal surface mesh that takes the general shape of the underlying object. The mesh representation, with quadrilateral elements, can be used to produce a facetted surface model for direct visualization or provide the means to “parametrize” the scattered data prior to generating a smooth continuous surface. Several illustrative examples using scattered range data are provided to demonstrate the data interpolation and surface reconstruction capability of the proposed 2D SOFM.
Author Keywords: Scattered data interpolation; Clustering; Self-organizing feature map; Surface reconstruction; Computer-aided design; Geometric modeling; Reverse engineering; Visualization
Fig. 1. Schematic representation of the data fitting procedure using a 1D self-organizing feature map (SOFM). Weight vectors connecting just one sample vector to the SOFM nodes have been shown.
Fig. 2. The basic structure of a 2D self-organizing feature map (SOFM).
Fig. 3. The SOFM polygon mesh with quadrilateral elements.
Fig. 4. The hand-carved wooden mask of unknown free-form shape and two views of the scattered coordinate data. Each point is given by vector
Xp, where
p=1,…,1406.
Fig. 5. The polygon mesh using of the weights of the 38 × 38 SOFM using an initial neighbourhood radius of (a)
NEi,j=5 (11×11 units) and (b)
NEi,j=15 (31×31 units).
Fig. 6. Spread of nodes in regions of incomplete data (a)
NEi,j=5 (11×11 units) and (b)
NEi,j=15 (31×31 units).
Fig. 7. Spread of nodes in the area of noisy data (a)
NEi,j=5(11×11 units) and (b)
NEi,j=15(31×31 units).
Fig. 8. Grey level image, range image and the scattered coordinate data of the man’s face. Each point is given by vector
Xp, where
p=1,…,3416.
Fig. 9. The polygon mesh using of the weights of the 45 × 45 SOFM using an initial neighbourhood radius of (a)
NEi,j=5 (11×11 units) and (b)
NEi,j=15 (31×31 units).
Fig. 10. Grey level image, range image and the scattered coordinate data of the man’s nose. Each point is given by vector
Xp, where
p=1,…,7636.
Fig. 11. The polygon mesh using of the weights of the 45 × 45 SOFM using an initial neighbourhood radius of (a)
NEi,j=5 (11×11 units) and (b)
NEi,j=15 (31×31 units).
Fig. 12. Coordinate data of half a torus. Each point is given by vector
Xp, where
p=1,…,10440.
Fig. 13. The polygon mesh using of the weights of the 45 × 45 SOFM using an initial neighbourhood radius of (a)
NEi,j=5 (11×11 units) and (b)
NEi,j=15 (31×31 units).
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