Abstract
Polyhedral approximation of range data has the advantage of being simple to obtain from raw data and of being capable of approximating any sampled surface to the desired precision. Among different possible polyhedral approximation schemes, surface triangulation is a popular one due to its efficiency in computing and storage. Surface triangulation has been used to solve many problems, such as definition of the object shape [BOIS-84], digital terrain modeling [FOWL-79], control of the automatic machining of surfaces [JERA-89], smooth interpolation between 3-D points [LAWS- 77], approximation of the digitized object surfaces [FAUG-84,DELI-91], and computer graphics.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P.J.Besl and R.C.Jain, “Segmentation through variable-order surface fitting”, IEEE Trans. on Pattern Anal. Machine Intell., vol. 10, no. 2, pp. 167–192, 1988.
J.D.Boissonnat, “Geometric structures for three-dimensional shape representation”, ACM Trans. on Graphics, vol. 3, no. 4, pp. 266–286, 1984.
X.Chen, “Vision-based geometric modeling”, Ph.D dissertation, École Nationale Supérieure des Télécommunications, PARIS-FRANCE, 1992.
L.De Floriani, B.Falcidieno, and C.Pienovi, “Delaunay-based representation of surfaces defined over arbitrarily shaped domains”, Comput. Vision, Graphics, and Image Processing, vol. 32, 127–140, 1985.
L.De Floriani and E.Puppo, “Constrained Delaunay triangulation for multiresolution surface description”, in Proc. of 9th Int. Conf. on Pattern Recognition, 1988, pp. 566–569.
H.Delingette, M.Hebert, and K.Ikeuchi, “Shape representation and image segmentation using deformable surfaces”, in Proc. of IEEE Conf. on Computer Vision and Pattern Recognition, Hawaii, June 1991, pp. 467–472.
R.Duda and P.Hart, “Pattern classification and scene analysis”, Wiley-Interscience, New York, 1973.
N.Dyn, D.Levin, and S.Rippa, “Data dependent triangulations for piecewise linear interpolation”, IMA Journal of Numerical Analysis, vol. 10, pp. 137–154, 1990.
T.J.Fan, G.Medioni, and R.Nevatia, “Segmented descriptions of 3-D surfaces”, IEEE J. Robotics and Automation, pp. 527–538, Dec., 1987.
T.J.Fan, “Describing and recognizing 3-D objects using surface properties”, SpringerVerlag, 1990.
O.D.Faugeras, M.Hebert, P.Mussi, J.D.Boissonnat, “Polyhedral approximation of 3-D objects without holes”, Comput. Vision, Graphics, and Image Processing, vol. 25, 169–183, 1984.
R.F.Fowler and J.J.Little, “Automatic extraction of irregular digital terrain models”, Computer Graphics, vol. 13, pp. 199–207, 1979.
G.D.Godin and M.D.Levine, “Structured edge map of curved objects in a range image”, in Proc. Conf. Computer Vision and Pattern Recognition, 1989, pp. 276–281.
P.Horain, “Extraction des aretes dans des images de distance”, in Proc. 7e congrès de Reconnaissance des Formes et Intelligence Artificielle, Paris, 1989, pp. 63–72.
R.B.Jerard, R.L.Drysdale, K.Hauch, B.Schaudt, and J.Magewick, “Methods for detecting errors in numerically controlled machining of sculptured surfaces”, IEEE Trans. on Computer Graphics & Applications, vol. 9, pp. 26–39, January 1989.
C.L.Lawson, “Software for Cl surface interpolation”, In Mathematical Software III (J.R.Rice, eds.) Academic Press, pp. 161–164, 1977.
Y.G.Leclerc and S.W.Zucker, “The local structure of image discontinuities in one dimension”, IEEE Trans. on Pattern Anal. Machine Intell., vol. 9, no. 3, pp. 341–355, 1987.
D.T.Lee and A.K.Lin, “Generalized Delaunay Triangulation for Planar Graphs”, Discrete Comput. Geom., vol. 1, pp. 201–217, 1986.
D.Lee, T.Nishida, and Y.Kobayashi, “Object representation for 3-D visual communications”, in Proc. of 1989 ITEJ National Convention, pp. 437–438, 1989.
D.G.Lowe, “Perceptual organization and visual recognition”, Hingham, MA: Kulwer Academic, 1985.
J. Malik, “Interpreting line drawings of curved objects”, International Journal of Computer Vision, vol. 1, pp. 73–103, 1987.
R.Mohan and R.Nevatia, “Perceptual organization for scene segmentation and description”, IEEE Trans. on Pattern Anal. Machine Intell., vol. 14, no. 6, pp. 616–634, 1992.
J.Ponce and M.Brady, “Toward a surface primal sketch”, in Three-Dimensional Machine Vision (T.Kanade, eds.), New York: Kluwer Academic, 1987, pp. 195–240.
M.Rioux and L.Cournoyer, “The NRCC three-dimensional image data files”, Technique report CNRC 29077, 1988.
F.Schmitt and X.Chen, “Fast segmentation of range images into planar regions”, in Proc. of IEEE Conf. on Computer Vision and Pattern Recognition, Hawaii, USA, June 1991, pp.710–711.
F.Schmitt, X.Chen, and W.H.Du, “Geometric Modelling from range image data”, in Proc. of Eurographics’91, Vienna, Austria, Sept. 1991, pp. 317–328.
N.M.Thalmann, H.T.Minh, M. de Angelis, and D.Thalmann, “Human prototyping”, in Proc. of CG International’88, pp. 74–82,1988.
G.T.Toussaint and D.Avis, “On a convex hull algorithm for polygons and its application to triangulation problems, Pattern Recognition, vol. 15, no. 1, pp. 23–29, 1982.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Chen, X., Schmitt, F. (1993). Adaptive Range Data Approximation by Constrained Surface Triangulation. In: Falcidieno, B., Kunii, T.L. (eds) Modeling in Computer Graphics. IFIP Series on Computer Graphics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-78114-8_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-78114-8_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-78116-2
Online ISBN: 978-3-642-78114-8
eBook Packages: Springer Book Archive