Tham khảo tài liệu 'robotics handbook of computer vision algorithms in image algebra part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Ể -1w 2x Re Y - - e 0 . to -1 c-a e j T o l - L. The odd indexed terms are given by e-1 a 2i i jic 44-ad .U-Ũ jtrei h giưĩvt n Jỉe ĩ 1 c - a 1 jrj i-0 1 Ỉ-1- With the information above it is easy to adapt the formulations of the one-dimension fast Fourier transforms Section for the implementation of fast one-dimensional cosine transforms. The cosine transform and its inverse are separable. Therefore fast two-dimensional transforms implementations are possible by taking one-dimensional transforms along the rows of the image followed by one-dimensional transforms along the columns 5 6 7 . Previous Table of Contents Next HOME SUBSCRIBE SEARCH FAQ SITEMAP CONTACT US Products Contact Us About Us Privacy Ad Info Home Use of this site is subject to certain Terms Conditions Copyright 1996-2000 EarthWeb Inc. All rights reserved. Reproduction whole or in part in any form or medium without express written permission of EarthWeb is prohibited. Read EarthWeb s privacy statement. n 1 u 0 it is seen that a is a weighted sum of the basis functions gu x . The weights in the sum are given by the Walsh transform. Figure shows the Walsh basis functions for n 4 and how an image is written as a weighted sum of the basis functions. Figure The Walsh basis for n 4. Thus the Walsh transform and the Fourier transform are similar in that they both provide the coefficients for the representation of an image as a weighted sum of basis functions. The basis functions for the Fourier transform are sinusoidal functions of varying frequencies. The basis functions for the Walsh transform are the elements ofdefined above. The rate of transition from negative to positive value in the Walsh basis function is analogous to the frequency of the Fourier basis function. The frequencies of the basis functions for the Fourier transform increase as u increases. However the rate at which Walsh basis functions change signs is not an increasing function of u. For Í1 b in the forward and reverse .
