Abstract
Spline representations are widely used in CAGD as well as in computer graphics. Splines are also useful in many computer vision tasks. In particular, in the manufacturing domain it is easier to share data and provide machine perception based services because similar representations are commonly used in both shape design and engineering tools.
In this paper, we study different spline representations and their applications in computer vision. The advantages and disadvantages of splines in various vision tasks are assessed. Different design options are described in detail and some guidelines for making appropriate choices are given. Examples on spline techniques using data from a 3-D imaging sensor are shown.
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References
Abdelmalek, N., “Algebraic error analysis for surface curvatures and segmentation of 3-D range images”, Pattern Recognition, Vol. 23, No. 8, pp. 807–817, 1990.
Besl, P. “Surfaces in range image understanding”, Springer-Verlag, 339 p., 1988.
Besl, P., McKay, N., “A Method for Registration of 3-D Shapes”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 2, pp. 239–256, 1992.
Bolle, R., Vemuri, B. “On three-dimensional surface reconstruction methods”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 1, pp. 1–13, 1991.
Cohen, E., Lyche, T., Riesenfeld, R., “Discrete B-Splines and Subdivision Techniques in Computer Aided Geometric Design and Computer Graphics”, Computer Graphics And Image Processing, 14, pp. 87–111, 1980.
De Boor, C. “A practical guide to splines”, Springer-Verlag, 392 p., 1978.
De Floriani, L., Puppo, E., “An On-Line Algorithm for Constrained Delaunay Triangulation”, CVGIP: Graphical Models and Image Processing, Vol. 54, No. 3, pp. 290–300, 1992.
Farin, G., “Curves and Surfaces for Computer Aided Geometric Design” Academic Press, 1990.
Field, D., “A Generic Delaunay Triangulation Algorithm for Finite Element Meshes”, Adv. Eng. Software, 1991, Vol. 13, No. 5/6 combined, pp. 263–272, 1991.
Gregory, J., “Geometric Continuity”, Mathematical Methods in CAGD, eds. Lyche & Schumaker, Academic Press, pp. 353–371, 1989.
Hettmansperger, T., Sheather, S. “A cautionary note on the method of least median squares”, The American Statistician, Vol. 46, No. 2, pp. 79–83, 1992.
Initial Graphics Exchange Standard, Version 5.1., IGES/PDES Organization, 1991.
Koivunen V., “A Robust Nonlinear Filter for Image Restoration”, Technical Report, December 1992, To appear in IEEE Transactions on Image Processing, May, 1995.
Koivunen, V., Vezien, J-M., “Multiple representation approach to geometric model construction from range data”, IEEE Cad-Based Vision Workshop '94, Seven Springs, PA, 1994.
Koivunen V., Vezien, J-M., “Machine Vision Tools for CAGD”, Technical Report, September 1994, Submitted for Publication.
Koivunen, V. “A robust approach to enhancement of multivariate images”, 1st IEEE ICIP, Nov., Austin, TX, USA, 1994.
Lipschutz M., “Differential Geometry”, McGraw-Hill, 1969.
Lounsbery, M., Mann, S., DeRose, T., “Parametric Surface Interpolation”, IEEE Computer Graphics and Applications, Vol. 12, No. 5, pp. 45–52, 1992.
Marr, D. “Vision”, Freeman, New York, 397 p., 1982.
Metaxas, D., Terzopoulos, D. “Shape and nonrigid motion estimation through physics-based synthesis”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 15, No. 6, pp. 580–591, 1993.
Mortenson, M. “Geometric modeling”, John Wiley & Sons, 763 p., 1985.
Naik, S., Jain, R., “Spline-based surface fitting on range images for CAD applications”, IEEE Conference on Computer Vision and Pattern Recognition, pp. 249–253, 1988.
Nalwa, V. “Representing oriented piecewise C 2 surfaces”, International Journal of Computer Vision, 3, pp. 131–153, 1989.
Piegl, L., “Modifying the shape of rational B-splines. Part 2: Surfaces”, Computer Aided Design, Vol. 21, No. 9, pp. 538–546, 1989.
Piegl, L., “On NURBS: a survey”, IEEE Computer Graphics and Applications, Vol. 11, No. 1, pp. 55–71, 1991.
Pratt, V., “Direct Least-Squares Fitting of Algebraic Surfaces” Computer Graphics 21, No. 4, pp. 145–152, 1987.
Rioux, M., Cornoyer, L. “The NRCC Three Dimensional Image Data Files”, CNRC 29077, National Research Council of Canada, 1988.
Rogers, D., Fog, N., “Constrained B-spline curve and surface fitting”, Computer Aided Design, Vol. 21, No. 10, pp. 641–648, 1989.
Schumaker, L. “Triangulations in CAGD”, IEEE Computer Graphics and Applications, Vol. 13, No. 1, pp. 47–52, 1993.
Sinha, S., Schunck, B. “A two-stage algorithm for discontinuity preserving surface reconstruction”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 14, No. 1, pp. 36–55, 1992.
Taubin, G. “Estimation of planar curves, surfaces, and nonplanar space curves defined by implicit equations with applications to edge and range image segmentation”, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 13, No. 11, pp. 1115–1138, 1991.
Terzopoulos, D., Qin, H., “Dynamic NURBS with Geometric Constraints for Interactive Sculpting”, ACM Transactions on Graphics, Vol. 13, No. 2, pp. 103–136, 1994.
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Koivunen, V., Bajcsy, R. (1995). Spline representations in 3-D vision. In: Hebert, M., Ponce, J., Boult, T., Gross, A. (eds) Object Representation in Computer Vision. ORCV 1994. Lecture Notes in Computer Science, vol 994. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60477-4_13
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DOI: https://doi.org/10.1007/3-540-60477-4_13
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