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Image Surface Approximation with Irregular Samples
February 1989 (vol. 11 no. 2)
pp. 206-212

A method to approximate image surfaces using irregular samples is proposed. Experimental results show that a high compression ratio can be achieved for simple or complicated images. A method accounting for the three-dimensional effects is proposed as a way of selecting the irregular samples from the image. Approximation spline knots are chosen along the contours, and the knot replacement is sensitive to the curvature along contours and the density of contours in the near neighborhood. In general, the proposed method was shown to reduce the reconstruction error both qualitatively and quantitatively, and can be used to model the image surface for the purpose of data compression and representation. This approach retains key features in images and throws away redundant data.

[1] D. G. McCaughey and H. C. Andrews, "Image approximation by variable knot bicubic splines,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-3, no. 3, pp. 299-310, May 1981.
[2] G. Ram, "On the encoding and representing of images,"Comput. Vision, Graphics, Image Processing, vol. 26, pp. 224-232, 1984.
[3] U. Shani and D. H. Ballard, "Splines as embeddings for generalized cylinders,"Comput. Vision, Graphics, Image Processing, vol. 27, pp. 129-156, 1984.
[4] D. N. Graham, "Image transmission by two-dimensional contour coding,"Proc. IEEE, vol. 55, no. 3, pp. 336-345, Mar. 1967.
[5] R. E. Barnhill and R. F. Riesenfeld, Eds.,Computer Aided Geometric Design. New York: Academic, 1974.
[6] B. A. Barsky and D. P. Greenberg, "Determining a set of B-spline control vertices to generate an interpolating surface,"Comput. Graphics Image Processing, vol. 14, pp. 203-265, 1980.
[7] P. Block and J. K. Udupa, "Display of three dimensional data: A survey of methodologies and applications,"Proc. IEEE, vol. 71, pp. 351-355, Mar. 1983.
[8] E. Keppel, "Approximating complex surfaces by triangulation of contour-lines,"IBM J. Res. Develop., vol. 19, pp. 2-11, Jan. 1975.
[9] H. Fuchs. Z. M. Kedem, and S. P. Uselton, "Optimal surface reconstruction from planar contours,"Commun. ACM, vol. 20, Oct. 1977.
[10] J. R. Jancaitus and J. L. Junkins, "Modeling inndimensions using a weighting function approach,"J. Geophys. Res., vol. 79, no. 23, pp. 3361-3366, Aug. 1979.
[11] T. K. Peucker, R. J. Fowler, J. L. Little, and D. M. Mark, "Digital representation of three dimensional surfaces by triangulation irregular network (TIN)," Office Naval Res., Tech. Rep. 10, Contract N00014- 75-C-0886 (NR 389-71), 1976.
[12] K. R. Sloan, Jr. and L. M. Hrechanyk, "Surface reconstruction from sparse data," inProc. Pattern Recognition and Image Processing, Dallas, TX, Aug. 1981, pp. 45-48.
[13] C. de Boor, A Practical Guide to Splines. New York: Springer-Verlag, 1978.
[14] P. Dierckx, "Algorithms for smoothing data with periodic and parametric splines,"Comput. Graphics Image Processing, vol. 20, pp. 171-184, 1982.
[15] P. Dierckx, "An algorithm for smoothing differentiation and integration of experimental data using spline functions,"J. Comput. Appl. Math., vol. 1, pp. 165-184, 1975.
[16] L. L. Schumaker, "Fitting surface to scattered data," inApproximation Theory II, G. G. Lorentz, C. K. Chui, and L. L. Schumaker, Eds. New York: Academic, 1976, pp. 203-268.
[17] R. Franke, "Smooth interpolation of scattered data by local thin plate splines,"Comput. Math. Applicat., vol. 8, no. 4, pp. 273-281, 1982.
[18] C. L. Lawson, "Software forC1Surface interpolation,"Math. Software III, pp. 161-194, 1977.
[19] J. Duchon, "Fonctions-spline du type plaque mince en dimension 2," Univ. Grenoble, Rep. 231, 1975.
[20] J. Meinquet, "Multivariate interpolation at arbitrary points made simple,"ZAMP, vol. 30, pp. 292-304, 1979.
[21] W. E. L. Grimson, "An implementation of a computational theory of visual surface interpolation,"Comput. Vision, Graphics, Image Processing, vol. 22, pp. 39-69, 1983.
[22] D. Terzopoulos, "Multilevel computational processes for visual surface reconstruction,"Comput. Vision, Graphics, Image Processing, vol. 24, pp. 52-96, 1983.
[23] G. T. Toussaint, Ed.,Practical Use of Bucketing Techniques in Computational Geometry. Amsterdam, The Netherlands: North-Holland.
[24] W. K. Pratt,Digital Image Processing. New York: Wiley, 1978.

Index Terms:
image surface approximation; computerised picture processing; irregular samples; compression ratio; spline knots; reconstruction error; data compression; computerised picture processing; data compression; splines (mathematics)
Citation:
C.H. Lee, "Image Surface Approximation with Irregular Samples," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 2, pp. 206-212, Feb. 1989, doi:10.1109/34.16716
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