How to downsample a image matrix using left and right downsampling matrices

[tenveer]

HI all

i am just stuck with a unique problem ...

What i want is to downsample a matrix (image matrix) using two left
and right matrices....
e.g if i have a 100 by 100 image matrix X what i want is to downsample
X to 25 by 25 matrix Y using two downsampling matrices U and V which
are on left and right respectively i.e Y=U*X*V

than what will the contents of the U and V matrices.

Any help will be appreciated

[online...@gmail.com]

在 2009年6月16日星期二UTC+8下午9时54分50秒，tenveer写道：

Hi there,

I'm happen to see this problem. Here it goes;


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function [ LR ] = matrix_downsampling( HR , window)
%matrix_downsampling_for_CCD_imaging This function is used to down sampling
%the input high rate image to low rate image combination window is
%determed by the reduce window.
% Detailed explanation goes here


[M, N]=size(HR); %输入矩阵的尺寸
[p, q]=size(window); %用于采样的窗口。由于模拟CCD的光强成像，窗口内为数据加和。

% 这里需要对M×N是否为p×q的整数倍进行判断。
% 如果不是整数倍，需要对原始图像进行填充。
r=mod(p-mod(M,p),p);c=mod(q-mod(N,q),q); %r,c为行列需要填充的个数
%p-mod(M,p)是为了求要填充的行数
%但当M正好是p倍数时，p-mod(M,p)为p
%而实际上不需要填充，故再做一次mod
HR_paded=padarray(HR, [r c], 'replicate', 'post'); %此填充方式参见冈萨雷斯matlab的P71

% 计算低速数据的输出矩阵结构
[M, N]=size(HR_paded); %新的M，N
m=M/p;n=N/q;

% 生成降速窗口的向量元
vp=ones(1,p);
vq=ones(1,q);

% 生成降速变换矩阵。CL为行降速变换矩阵，CR为列降速变换矩阵。
CL=kron(eye(M/p),vp);
CR=kron(eye(N/q),vq).';

% 对高速矩阵进行降速运算，及在原始矩阵的p*q大小的栅格单元内求和
LR=CL*HR_paded*CR;

end

%%%%%%%%%%%%%%%%%%%%%

here is the example to use this function as following:


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Out_LR=matrix_downsampling(In_HR,ones(10,10));
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

this example shows that the In_HR is down sampling by a window in 10 by 10.