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On properties of discretized convex curves
February 1989 (vol. 11 no. 2)
pp. 217,218,219,220,221,222,223
The connection between a continuous convex curve and its discrete image is investigated using an appropriate definition of discrete convexity. It is shown that the discrete image of continuous convex curve may not be convex; however, its deviation from convexity (in the discrete definition) is bounded by a small constant. The actual pixel patterns that are obtained by discretizing convex curves are studied. Certain constraints on the context of discrete images of continuous convex curves were discovered.<>

[1] J. E. Bresenham, "Algorithm for computer control of digital plotter,"IBM Syst. J., vol. 4, pp. 25-30, 1965.
[2] H. Freeman, "Computer processing of line-drawing images,"Computer Surveys, vol. 6, no. 1, Mar. 1974.
[3] C. E. Kim, "Digital convexity, straightness, and convex polygons,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, pp. 618- 626, Nov. 1982.
[4] C. E. Kim and A. Rosenfeld, "Digital straight lines and convexity of digital regions,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-4, pp. 149-153, Nov. 1982.
[5] Z. Kulpa, "On the properties of discrete circles, rings and disks,"Comput. Graphics Image Processing, vol. 10, pp. 348-365, Aug. 1979.
[6] F. P. Preparata and M. I. Shamos,Computational Geometry, an Introduction. New York: Springer-Verlag, 1985.
[7] G. B. Regiori, "Digital computer transformation for irregular line drawings," New York Univ., New York, NY, Tech. Rep. 403-22, pp. 46-61, 1972.
[8] A. W. Roberts and D. E. Varberg,Convex Functions. New York: Academic, 1973, ch. 1.
[9] C. Ronse, "A bibliography on digital and computational convexity (1961-1986)," Philips Res. Lab., Brussels, Belgium, 1987.
[10] A. Rosenfeld, "Digital topology,"Amer. Math. Monthly, vol. 89, pp. 230-235, Apr. 1982.
[11] A. Rosenfeld and C. E. Kim, "How can a computer tell whether a line is straight?"Amer. Math. Monthly. vol. 86, pp. 621-630. Oct. 1979.
[12] L. A. Santalo,Integral Geometry and Geometric Probability. Reading, MA: Addison-Wesley, 1976, ch. 1, p. 1.
[13] J. Sklansky, "Recognition of convex blobs,"Pattern Recognition. vol. 2, pp. 3-10, 1970.
[14] X. Wu and J. Rokne, "Double-Step Incremental Generation of Lines and Circles, "Computer Vision, Graphics, and Image Processing, Vol. 37, No. 3, Mar. 1987, pp. 331-344.

Index Terms:
picture processing,computational geometry,convex curves,picture processing,discrete image,discrete convexity,pixel patterns,Lattices,Graphics,Image processing,Pattern recognition,Image coding,Psychology,Digital images,Inspection,Image analysis,Feature extraction
"On properties of discretized convex curves," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 2, pp. 217,218,219,220,221,222,223, Feb. 1989, doi:10.1109/34.16719
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