WORD-LENGTH CONSIDERATIONS ON THE HARDWARE IMPLEMENTATION OF 2-DIMENSIONAL MALLATS WAVELET TRANSFORM

Two-dimensional discrete wavelet transforms (DWTs) have become a very powerful tool in computer vision. When implementing DWT in hardware, f inite precision arithmetic introduces quantization errors. The hardwar e designer must look for the optimum register length which, while ensu ring the minimum accuracy criteria, would also lead to a high-speed im plementation with a small chip area. We obtain expressions to characte rize the mean and the variance of the quantization errors produced in the calculation of DWT components. The theoretical results have been c ompared with the experimental ones obtained from algorithm simulation on the Lena test image. Since the maxima representation proposed by Ma llat and Zhong is defined from both the amplitude and position of the discrete maxima, the effects of quantization in the maxima amplitude a nd maxima position are analyzed. Besides the quantization error, anoth er potential source of error is the hardware implementation of the ari thmetic operations that appears in the algorithm. We have analyzed the effect of replacing the square root using one of the Filip's approxim ations. (C) 1996 Society of Photo-Optical Instrumentation Engineers.