Applying vector median filter on RGB image based on matlab

前言：

最近想看看矢量中值滤波（Vector median filter， VMF）在GRB图像上的滤波效果，意外的是找了一大圈却发现网上没有现成的code，所以通过matab亲自实现了一个，需要学习的朋友可以拿过去用。本文的核心是VMF的matlab实现，最后通过在RGB图像上应用举例说明。

VMF的数学表达：

含有N个矢量的集合{C₁，C₂，...C_N}，它的VMF结果如下所示：

其中，C_VM1表示距离所有其他向量的距离和最小的那个向量。而距离可以自己定义，常用的欧氏距离，曼哈顿距离等等。

matlab code：

%   向量中值滤波,根据欧式距离进行滤波，将RGB图像中每个像素位置的三个颜色作为一个向量整体处理。

% pdist函数解释
% Pairwise distance between pairs of objects
% Syntax
% D = pdist(X)
% D = pdist(X,distance)
% Description
%
% D = pdist(X)
% 计算 X 中各对行向量的相互距离(X是一个m-by-n的矩阵). 这里 D 要特别注意，
% D 是一个长为m(m–)/2的行向量.可以这样理解 D 的生成：首先生成一个 X 的距离方阵，
% 由于该方阵是对称的，且对角线上的元素为0，所以取此方阵的下三角元素，按照Matlab中矩阵的按列存储原则，
% 此下三角各元素的索引排列即为(,), (,), ..., (m,), (,), ..., (m,), ..., (m,m–).
% 可以用命令 squareform(D) 将此行向量转换为原距离方阵.(squareform函数是专门干这事的，其逆变换是也是squareform。)
%
% D = pdist(X,distance) 使用指定的距离.

vectors_set = rand(,);%向量集合中的每一行是一个向量，一共含有5个向量

dist = pdist(vectors_set,'euclidean');%使用欧式距离计算向量之间的距离
dist = squareform(dist);%还原回矩阵的形式
dist = sum(dist,);%求出每个向量到其他所有向量的距离和
indx = find(dist==min(dist));%找到距离和最小的向量的index
median_vec = vectors_set(indx,:) %根据index找出中值向量

RGB图像上的应用：

%   向量中值滤波,根据欧式距离进行滤波，可以用于RGB图像的去噪。

clc;    % Clear command window.
clear;    % Delete all variables.
close all;    % Close all figure windows except those created by imtool.
imtool close all;    % Close all figure windows created by imtool.
workspace;    % Make sure the workspace panel is showing.
fontSize = ;
% Read in a standard MATLAB color demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
baseFileName = 'peppers.png';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
if ~exist(fullFileName, 'file')
    % Didn't find it there.  Check the search path for it.
    fullFileName = baseFileName; % No path this time.
    if ~exist(fullFileName, 'file')
        % Still didn't find it.  Alert user.
        errorMessage = sprintf('Error: %s does not exist.', fullFileName);
        uiwait(warndlg(errorMessage));
        return;
    end
end
rgbImage = imread(fullFileName);
subplot(, , );
imshow(rgbImage);
title('Original color Image', 'FontSize', fontSize);
subplot(, , );
noisyRGB = imnoise(rgbImage,'salt & pepper', .);
imshow(noisyRGB);
title('Image with Salt and Pepper Noise', 'FontSize', fontSize);
subplot(, , );
resortedImage = noisyRGB;

[h,w,bands] = size(rgbImage);%彩色图像的大小
win_radius = ;%滤波窗口半径大小
win_size = (*win_radius+).^;%滤波窗口的大小
for i =  + win_radius : h -
    for j =  + win_radius : w-
        vectors_set = reshape(rgbImage(i-win_radius:i+win_radius,j-win_radius:j+win_radius,:),win_size,,bands);%将窗口内的向量进行变形
        vectors_set = reshape(permute(vectors_set,[,,]),bands,[])';%将向量矩阵变为每一行为一个向量的模式
        [n,d] = size(vectors_set);%n是向量个数，d是向量维度
        % pdist
        % Pairwise distance between pairs of objects
        % Syntax
        % D = pdist(X)
        % D = pdist(X,distance)
        % Description
        %
        % D = pdist(X)
        % 计算 X 中各对行向量的相互距离(X是一个m-by-n的矩阵). 这里 D 要特别注意，
        % D 是一个长为m(m–1)/2的行向量.可以这样理解 D 的生成：首先生成一个 X 的距离方阵，
        % 由于该方阵是对称的，且对角线上的元素为0，所以取此方阵的下三角元素，按照Matlab中矩阵的按列存储原则，
        % 此下三角各元素的索引排列即为(2,1), (3,1), ..., (m,1), (3,2), ..., (m,2), ..., (m,m–1).
        % 可以用命令 squareform(D) 将此行向量转换为原距离方阵.(squareform函数是专门干这事的，其逆变换是也是squareform。)
        %
        % D = pdist(X,distance) 使用指定的距离.distance可以取下面圆括号中的值，用红色标出！
        dist = pdist(vectors_set,'euclidean');
        dist = squareform(dist);
        dist = sum(dist,2);
        indx = find(dist==min(dist));
        median_vec = vectors_set(indx,:);
        resortedImage(i,j,:)= median_vec(1,:);
    end
end

imshow(resortedImage);
title('Restored Image', 'FontSize', fontSize);

实验结果：

总结：算法的实现并不复杂，但是运算时间较长，可以进一步优化。

另外：在针对RGB图像的矢量滤波上面，有一种做法是color plane by color plane的做法，虽然已经不算是vector median filter-based的方法了，但是效果还好，可以借鉴

matlab code:

%
% 一个plane一个plane的单独处理

clc;    % Clear command window.
clear;    % Delete all variables.
close all;    % Close all figure windows except those created by imtool.
imtool close all;    % Close all figure windows created by imtool.
workspace;    % Make sure the workspace panel is showing.
fontSize = ;
% Read in a standard MATLAB color demo image.
folder = fullfile(matlabroot, '\toolbox\images\imdemos');
baseFileName = 'peppers.png';
% Get the full filename, with path prepended.
fullFileName = fullfile(folder, baseFileName);
if ~exist(fullFileName, 'file')
    % Didn't find it there.  Check the search path for it.
    fullFileName = baseFileName; % No path this time.
    if ~exist(fullFileName, 'file')
        % Still didn't find it.  Alert user.
        errorMessage = sprintf('Error: %s does not exist.', fullFileName);
        uiwait(warndlg(errorMessage));
        return;
    end
end
rgbImage = imread(fullFileName);
% Get the dimensions of the image.  numberOfColorBands should be = .
[rows columns numberOfColorBands] = size(rgbImage);
% Display the original color image.
subplot(, , );
imshow(rgbImage);
title('Original color Image', 'FontSize', fontSize);
% Enlarge figure to full screen.
set(gcf, 'Position', get(,'Screensize'));
% Extract the individual red, green, and blue color channels.
redChannel = rgbImage(:, :, );
greenChannel = rgbImage(:, :, );
blueChannel = rgbImage(:, :, );
% Display the individual red, green, and blue color channels.
subplot(, , );
imshow(redChannel);
title('Red Channel', 'FontSize', fontSize);
subplot(, , );
imshow(greenChannel);
title('Green Channel', 'FontSize', fontSize);
subplot(, , );
imshow(blueChannel);
title('Blue Channel', 'FontSize', fontSize);
% Generate a noisy image.  This has salt and pepper noise independently on
% each color channel so the noise may be colored.
noisyRGB = imnoise(rgbImage,'salt & pepper', .);
subplot(, , );
imshow(noisyRGB);
title('Image with Salt and Pepper Noise', 'FontSize', fontSize);
% Extract the individual red, green, and blue color channels.
redChannel = noisyRGB(:, :, );
greenChannel = noisyRGB(:, :, );
blueChannel = noisyRGB(:, :, );
% Display the noisy channel images.
subplot(, , );
imshow(redChannel);
title('Noisy Red Channel', 'FontSize', fontSize);
subplot(, , );
imshow(greenChannel);
title('Noisy Green Channel', 'FontSize', fontSize);
subplot(, , );
imshow(blueChannel);
title('Noisy Blue Channel', 'FontSize', fontSize);
% Median Filter the channels:
redMF = medfilt2(redChannel, [ ]);
greenMF = medfilt2(greenChannel, [ ]);
blueMF = medfilt2(blueChannel, [ ]);
% Find the noise in the red.
noiseImage = (redChannel ==  | redChannel == );
% Get rid of the noise in the red by replacing with median.
noiseFreeRed = redChannel;
noiseFreeRed(noiseImage) = redMF(noiseImage);
% Find the noise in the green.
noiseImage = (greenChannel ==  | greenChannel == );
% Get rid of the noise in the green by replacing with median.
noiseFreeGreen = greenChannel;
noiseFreeGreen(noiseImage) = greenMF(noiseImage);
% Find the noise in the blue.
noiseImage = (blueChannel ==  | blueChannel == );
% Get rid of the noise in the blue by replacing with median.
noiseFreeBlue = blueChannel;
noiseFreeBlue(noiseImage) = blueMF(noiseImage);
% Reconstruct the noise free RGB image
rgbFixed = cat(, noiseFreeRed, noiseFreeGreen, noiseFreeBlue);
subplot(, , );
imshow(rgbFixed);
title('Restored Image', 'FontSize', fontSize);

实验结果：