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Optical Engineering

Word length considerations on the hardware implementation of two-dimensional Mallat's wavelet transform
Author(s): Jose I. Artigas; Luis A. Barragan; J. R. Beltran; Eduardo Laloya; Juan C. Moreno; Denis Navarro; Armando Roy
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Paper Abstract

Two-dimensional discrete wavelet transforms (DWTs) have become a very powerful tool in computer vision. When implementing DWT in hardware, finite precision arithmetic introduces quantization errors. The hardware designer must look for the optimum register length which, while ensuring the minimum accuracy criteria, would also lead to a high-speed implementation with a small chip area. We obtain expressions to characterize the mean and the variance of the quantization errors produced in the calculation of DWT components. The theoretical results have been compared with the experimental ones obtained from algorithm simulation on the Lena test image. Since the maxima representation proposed by Mallat and Zhong is defined from both the amplitude and position of the discrete maxima, the effects of quantization in the maxima amplitude and maxima position are analyzed. Besides the quantization error, another potential source of error is the hardware implementation of the arithmetic operations that appears in the algorithm. We have analyzed the effect of replacing the square root using one of the Filip’s approximations.

Paper Details

Date Published: 1 April 1996
PDF: 15 pages
Opt. Eng. 35(4) doi: 10.1117/1.600608
Published in: Optical Engineering Volume 35, Issue 4
Show Author Affiliations
Jose I. Artigas, Univ. de Zaragoza (Spain)
Luis A. Barragan, Univ. de Zaragoza (Spain)
J. R. Beltran, Univ. de Zaragoza (Spain)
Eduardo Laloya, Univ. de Zaragoza (Spain)
Juan C. Moreno, Univ. de Zaragoza (Spain)
Denis Navarro, Univ. de Zaragoza (Spain)
Armando Roy, Univ. de Zaragoza (Spain)

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