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Evaluation of Quantization Error in Computer Vision
September 1989 (vol. 11 no. 9)
pp. 929-940

Due to the important role that digitization error plays in the field of computer vision, a careful analysis of its impact on the computational approaches used in the field is necessary. The authors develop the mathematical tools for the computation of the average (or expected) error due to quantization. They can be used in estimating the actual error occurring in the implementation of a method. Also derived is the analytic expression for the probability density of error distribution of a function of an arbitrarily large number of independently quantized variables. The probability that the error of the function will be within a given range can thus be obtained accurately. The tools developed can be used in the analysis of the applicability of a given algorithm.

[1] F. R. Bevington,Data Reduction and Error Analysis for the Physical Sciences. New York: McGraw-Hill, 1969.
[2] Y. Beers,Introduction to the Theory of Error. Reading, MA: Addison-Wesley, 1957.
[3] R. V. Hogg and E. A. Tanis,Probability and Statistical Inference. New York: Macmillan, 1983.
[4] A. Rosenfeld and A. Kak,Digital Picture Processing, New York: Academic, 1976.
[5] S. D. Blostein and T. S. Huang, "Error analysis in stereo determination of 3-D point positions,"IEEE Trans. Patt. Anal. Machine Intell., vol. PAMI-9, pp. 752-765, Nov. 1987; errata in vol. PAMI-10, pp. 765, Sept. 1988.
[6] B. Kamgar-Parsi and R. D. Eastman, "Calibration of a stereo system with small relative angles," inProc. IEEE Comput. Soc. Conf. Computer Vision and Pattern Recognition, 1988, p. 44.
[7] B. Kamgar-Parsi, "Minimization of the quantization error in stereo," inProc. DARPA Image Understanding Workshop, 1987, p. 671.
[8] B. Kamgar-Parsi, B. Kamgar-Parsi, and W. A. Sander, III, "Quantization error in computer vision: Comparison between square and hexagonal pixels,"IEEE Trans. Pattern Anal. Machine Intell., submitted for publication.
[9] E. M. Reingold, J. Nievergelt, and N. Deo,Combinatorial Algorithms: Theory and Practice. Englewood Cliffs, NJ: Prentice-Hall, 1977, Algorithm 5.5.

Index Terms:
error estimation; quantization error; computer vision; probability density; error distribution; computer vision; computerised picture processing; error statistics; probability
Citation:
B. Kamgar-Parsi, B. Kamgar-Parsi, "Evaluation of Quantization Error in Computer Vision," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 11, no. 9, pp. 929-940, Sept. 1989, doi:10.1109/34.35496
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