This Article 
 Bibliographic References 
 Add to: 
Toward a Symbolic Representation of Intensity Changes in Images
September 1988 (vol. 10 no. 5)
pp. 610-625

The symbolic representation of gray-value variations is studied, with emphasis on the gradient of the image function. The goal is to relate the results of this analysis to the structure of the picture, which is determined by the physics of the image generation process. Candidates for contour points are the maximal magnitudes of the gray-value gradient for different scales in the direction of the gradient. Based on the output of such a bank of gradient filters, a procedure is proposed to select automatically a suitable scale, and with that, the size of the right convolution kernel. The application of poorly adapted filters, which make the exact localization of gray-value corners or T-, X-, and Y-junctions more difficult, is thus avoided. Possible gaps at such junctions are discussed for images of real scenes, and possibilities for the closure of some of these gaps are demonstrated when the extrema of the magnitudes of the gray-value gradients are used.

[1] T. Kanade, "Region segmentation: Signal versus semantics," inProc. Int. Joint Conf. Pattern Recognition, Kyoto, Japan, Nov. 7-10, 1978, pp. 95-105; see also,Comput. Graphics Image Processing, vol. 13, pp. 279-297, 1980.
[2] H.-H. Nagel, "Principles of (low-level) computer vision," inFundamentals in Computer Understanding: Speech, Vision, and Natural Language, J. P. Haton, Ed. Cambridge, UK: Cambridge Univ. Press, to be published.
[3] D. Marr,Vision. San Francisco, CA: W. H. Freeman, 1982.
[4] A. Rosenfeld, Ed.,Multiresolution Image Processing and Analysis. New York: Springer-Verlag, 1984.
[5] J. L. Crowley and A. C. Sanderson, "Multiple resolution representation and probabilistic matching of 2-D gray scale shape," inProc. Workshop Comput. Vision: Representation Contr., Annapolis, MD, Apr. 30-May 2, 1984, pp. 95-105.
[6] Y. Leclerc and S. W. Zucker, "The local structure of image discontinuities on one dimension," inProc. 7th Int. Conf. Pattern Recognition, Montreal, P.Q., Canada, July 30-Aug. 2, 1984, pp. 46-48.
[7] R. M. Haralick, "Digital step edges from zero crossings of second directional derivatives,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-6, pp. 58-68, 1984.
[8] D. Marr and E. Hildreth, "Theory of edge detection,"Proc. Roy. Soc. London B, vol. 207, pp. 187-217, 1980.
[9] R. Hartley, "A Gaussian-weighted multiresolution edge detector,"Comput. Vision, Graphics, Image Processing, vol. 30, pp. 70-83, 1985.
[10] J. J. Koenderink, "The structure of images,"Biol. Cybernet., vol. 50, pp. 363-370, 1984.
[11] E. Hildreth, "The detection of intensity changes by computer and biological vision systems,"Comput. Vision, Graphics, Image Processing, vol. 22, pp. 1-27, 1983.
[12] A. P. Witkin, "Scale-space filtering," inProc. Int. Joint Conf. Artif. Intell., Karlsruhe, FRG, Aug. 8-12, 1983, pp. 1019-1022.
[13] V. Berzins, "Accuracy of Laplacian edge detectors,"Comput. Vision, Graphics, Image Processing, vol. 27, pp. 195-210, 1984.
[14] R. M. Haralick, "Author's reply to Grimson and Hildreth,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI-7, pp. 127-129, 1985.
[15] H.-H. Nagel, "Displacement vectors derived from second order intensity variations in image sequences,"Comput. Vision, Graphics, Image Processing, vol. 21, pp. 85-117, 1983.
[16] J. F. Canny, "Finding lines and edges in images," Artificial Intell. Lab., Massachusetts Inst. Technol., Tech. Rep. TM-720, 1983.
[17] A. Korn, "Combination of different spatial frequency filters for modeling edges and surfaces in gray-value pictures," inProc. Comput. Vision Robots, Cannes, France, Dec. 2-6, 1985, SPIE vol. 595, pp. 22-30.
[18] J. P. Frisby,Seeing, Illusion, Brain and Mind. Oxford, UK: Oxford Univ. Press, 1979.
[19] D. H. Ballard and C. M. Brown,Computer Vision. Englewood Cliffs, NJ: Prentice-Hall, 1982.
[20] T. Poggio and V. Torre, "Ill-posed problems and regularization analysis in early vision," Memo 773, MIT AI Lab., Apr. 1984.
[21] R. Machuca and K. Phillips, "Applications of vector fields to image processing,"IEEE Trans. Pattern Anal. Mach. Intell., vol. PAMI- 5, pp. 316-329, 1983.
[22] A. Korn, "Das visuelle System als Merkmalfilter," inAspekte der Informationsverarbeitung, H. Bodmann Ed.,Fachberichte Messen, Steuern, Regeln, Bd. 13. Berlin, Heidelberg, FRG: Springer-Verlag, 1985, pp. 112-165.
[23] P. H. Winston,Artificial Intelligence. Reading, MA: Addison-Wesley, 1977, p. 45ff.
[24] R. M. Haralick, L. T. Watson, and T. J. Laffey, "The topographic primal sketch,"Int. J. Robotics Res., vol. 2, pp. 50-72, 1983.
[25] J. J. Koenderink and A. van Doom, "The shape of smooth objects and the way contours end,"Perception, vol. 11, pp. 129-137, 1982.
[26] V. Torre and T. A. Poggio, "On edge detection,"IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 147-163, Mar. 1986.
[27] M. A. Gennert, "Detecting half-edges and vertices in images," inProc. Comput. Vision Pattern Recognition, Miami Beach, FL, June 22-26, 1986, pp. 552-557.

Index Terms:
picture processing; symbolic representation; gray-value variations; image function; image generation; contour points; gradient filters; convolution kernel; picture processing
A.F. Korn, "Toward a Symbolic Representation of Intensity Changes in Images," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 610-625, Sept. 1988, doi:10.1109/34.6770
Usage of this product signifies your acceptance of the Terms of Use.