This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Quantization Error in Hexagonal Sensory Configurations
June 1992 (vol. 14 no. 6)
pp. 665-671

The authors develop mathematical tools for estimating quantization error in hexagonal sensory configurations. These include analytic expressions for the average error and the error distribution of a function of an arbitrary number of independently quantized variables. These two quantities are essential for assessing the reliability of a given algorithm. They can also be used to compare the relative sensitivity of a particular algorithm to quantization error for hexagonal and other spatial samplings, e.g., square, and can have an impact on sensor design. Furthermore, it is shown that the ratio of hexagonal error to square error is bounded between 0.90 and 1.05.

[1] N. Ahuja, "On approaches to polygonal decomposition for hierarchical image representation,"Comput. Vision Graphics Image Processing, vol. 24, p. 200, 1983.
[2] S. B. M. Bell, B. M. Diaz, F. Holroydt, and M. J. Jackson, "Spatially referenced methods of processing raster and vector data,"Image Vision Comput., vol. 1, p. 211, 1983.
[3] F. R. Bevington,Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, 1969.
[4] J. A. Bucklew, "Multidimensional digitization of data followed by a mapping,"IEEE Trans. Inform. Theory, vol. IT-30, p. 107, 1984.
[5] P. J. Burt, "Tree and pyramid structures for coding hexagonally sampled binary images,"Comput. Vision Graphics Image Processing, vol. 14, p. 271, 1980.
[6] L. S. Davis, "Understanding shape: angles and sides,"IEEE Trans. Comput., vol. C-26, p. 236, 1977.
[7] A. Gersho, "Asymptotically optimal block quantization,"IEEE Trans. Inform. Theory, vol. IT-25, p. 373, 1979.
[8] N. P. Hartman and S. L. Tanimoto, "A hexagonal pyramid data structure for image processing,"IEEE Trans. Syst. Man Cybern., vol. SMC-14, p. 247, 1984.
[9] B. Kamgar-Parsi and B. Kamgar-Parsi, "Evaluation of quantization error in computer vision,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-11, p. 929, 1989.
[10] B. Kamgar-Parsi, B. Kamgar-Parsi, and W. A. Sander III, "Quantization error in spatial sampling: Comparison between square and hexagonal pixels," inProc. IEEE Comput. Soc. Conf. Comput. Vision Patt. Recogn. (San Diego, CA), 1989, p. 604.
[11] R. M. Mersereau, "The processing of hexagonally sampled two-dimensional signals,"Proc. IEEE, vol. 67, p. 930, 1979.
[12] E. M. Reingold, J. Nievergelt, and N. Deo,Combinatorial Algorithms: Theory and Practice. Englewood Cliffs, NJ: Prentice Hall, 1977, Algorithm 5.5.
[13] K. D. Rines and N. C. Gallagher, "The design of two-dimensional quantizers using prequantization,"IEEE Trans. Inform. Theory, vol. IT-28, p. 232, 1982.
[14] J. Serra and B. Lay, "Square to hexagonal lattice conversion,"Signal Processing, vol. 9, p. 1, 1985.
[15] R. L. Stevenson and G. R. Arce, "Binary display of hexagonally sampled continuous-tone images."J. Opt. Soc. Amer., vol. A2, p. 1009, 1985.
[16] R. A. Ulichney, "Dithering with blue noise,"Proc. IEEE, vol. 76, p. 56, 1988.
[17] P. L. Zador, "Asymptotic quantization error of continuous signals and the quantization dimension,"IEEE Trans. Inform. Theory, vol. IT-28, p. 139, 1982.

Index Terms:
picture processing; computer vision; error statistics; algorithm reliability; hexagonal sensory configurations; quantization error; average error; error distribution; spatial samplings; computer vision; error statistics; picture processing
Citation:
B. Kamgar-Parsi, B. Kamgar-Parsi, "Quantization Error in Hexagonal Sensory Configurations," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 14, no. 6, pp. 665-671, June 1992, doi:10.1109/34.141556
Usage of this product signifies your acceptance of the Terms of Use.