二维Walsh矩阵变换

%The function implement the 2D Walash Transform which can be used in %signal processing,pattern recognition and Genetic algorithms. The Formula of %2D Walsh Transform is defined as : %% N-1 N-1 q-1 %% ---- ---- -- %% 1 \ \ | | b[i](m)*b[q-1-i](u)+b[i](n)*b[q-1-i](v) %% W(u,v) = --- / / f(m,n) | |(-1) %% N ---- ---- | | %% m=0 n=0 i=0 %% u,v = 0,...,N-1 %% where for instance ,A[i] is the ith indices of A. %The definition : %%% f(m,n) : Two dimentional Image(Sequence) ,m,n = 0,...,N-1; %% Input image can belong to UINT8 or DOUBLE class.Also %% it must be squre! % q %%% N = 2 : where N is the size of Image %%% W(u,v) : Walsh Transform; %% b[k](u): kth bit(from LSB) in the binary representation of u; %% For instance if u = 6 where in binary it becomes 110 then %% b[0](6) = 0,b[1](6) = 1 and b[2](6) = 1, %*** You must download 'walsh1d.m' to use this function***% %** Example : %% W = walsh2d(imread('myiage.jpg')); %% Author : Ahmad poursaberi %% e-mail : a.poursaberi@ece.ut.ac.ir %% Control and Intelligent Processing Center of Excellence %% Faulty of Engineering, Electrical&Computer Department, %% University of Tehran,Iran,August 2004 %% copyright 2004 function W = walsh2d(I) warning off if length(size(size(I)))~=2 I = im2bw(imread(input('Enter Image Name '))) ; end siz = max(size(I)); q = log2(siz); if sum(ismember(char(cellstr(num2str(q))),'.'))~=0 disp(' Warning!... '); disp('The size of Vector must be in the shape of 2^N ..'); return end if isa(I,'double')==1 I = im2uint8(I); end W = I; len = length(I); for i = 1:len W2(i,:) = walsh1d(double(W(i,:))); end W = zeros(len); for j = 1:len W(:,j) = walsh1d(double(W2(:,j)'))'; end