數字圖像處理實驗（一）（鄰域平均法濾波、中值濾波等）

內容摘要

最近，做數字圖像處理實驗，簡單記錄一下幾個挺有意思的圖像處理方法。本篇主要介紹領域平均法和中值濾波法去除圖像噪聲，求圖像SNR和PSNR及其matlab實現代碼。

鄰域平均法

簡單來說，就是對於每一個像素點都取它周圍一圈的平均值，來降低一些像素值突變的點（即噪聲點）的影響。當然，一個明顯的結果就是，圖片會一定程度上變模糊，於是有人提出“超限領域平均法”，即如果某個像素的灰度值大於其鄰域像素的平均值，且達到一定水平，則判斷該像素爲噪聲，繼而用鄰域像素的均值取代這一像素值。
代碼實現如下，使用方法參見主程序註釋。

% 鄰域均值法去燥
function Img_average_filter=Average_filter(varargin) 
narginchk(1,3);         
Img_in = varargin{1};
Temp = [1 1 1;1 1 1;1 1 1]; % 默認模板
Threshold = 0;              % 默認閾值
if nargin == 2
    Temp = varargin{2};
elseif nargin == 3
    Temp = varargin{2};
    Threshold = varargin{3};
end
[n, m] = size(Img_in);
Img_raw = int32(Img_in);
[L1, L2] = size(Temp);
LL=sum(sum(Temp));
Img_average_filter = int32(zeros(n-L1+1, m-L2+1));  % 捨棄邊緣信息
for i = (L1+1)/2:n-(L1-1)/2
    for j = (L2+1)/2:m-(L2-1)/2
        Img_raw_sub = Img_raw(i-(L1-1)/2:i+(L1-1)/2, j-(L2-1)/2:j+(L2-1)/2);
        SUM = sum(sum(Img_raw_sub.*int32(Temp)));
        ave = SUM/LL;
        if Threshold ~= 0
            if abs(Img_raw(i,j)-ave) > Threshold
                Img_average_filter(i-(L1-1)/2, j-(L2-1)/2) = ave;
            else
                Img_average_filter(i-(L1-1)/2, j-(L2-1)/2) = Img_raw(i,j);
            end
        else
            Img_average_filter(i-(L1-1)/2, j-(L2-1)/2) = ave;
        end
    end
end

中值濾波

簡單來說，就是對於每一個像素點，取其周圍像素值的中值，來代替該像素點的灰度值，當然，同樣也可以加上一個閾值條件。
代碼實現如下，使用方法參見主程序註釋。

% 中值濾波法去燥
function Img_med_filter=Med_filter(varargin)
narginchk(1,3);           
Img_in = varargin{1};
L = 3;                      % 默認滑動窗口尺寸
Threshold = 0;              % 默認閾值
if nargin == 2
    L = varargin{2};
elseif nargin == 3
    L = varargin{2};
    Threshold = varargin{3};
end
[n, m] = size(Img_in);
Img_raw = int32(Img_in);
Img_med_filter = int32(zeros(n-L+1, m-L+1)); % 棄邊緣信息
for i = (L+1)/2:n-(L-1)/2
    for j = (L+1)/2:m-(L-1)/2
        Img_raw_sub = reshape(Img_raw(i-(L-1)/2:i+(L-1)/2, j-(L-1)/2:j+(L-1)/2), 1, L*L);
        Img_raw_sub = sort(Img_raw_sub);
        ave = Img_raw_sub((L*L+1)/2);
        if Threshold ~= 0
            if abs(Img_raw(i,j)-ave) > Threshold
                Img_med_filter(i-(L-1)/2, j-(L-1)/2) = ave;
            else
                Img_med_filter(i-(L-1)/2,j-(L-1)/2) = Img_raw(i,j);
            end
        else
            Img_med_filter(i-(L-1)/2, j-(L-1)/2) = ave;
        end
    end
end

求信噪比SNR和峯值信噪比PSNR

function SNR(Img_raw, Img_noise, Img_filter)
Img_raw_signal = double(0);
Img_noise_signal = double(0);
Img_filter_signal = double(0);
[n0, m0] = size(Img_raw);
[n1, m1] = size(Img_filter);
stx = (n0-n1)/2+1; edx = n0-stx+1;
sty = (m0-m1)/2+1; edy = m1-sty+1;
for i = stx:edx
    for j = sty:edy
        Img_raw_signal = Img_raw_signal+Img_raw(i,j)*Img_raw(i,j);
        Img_noise_signal = Img_noise_signal+(Img_raw(i,j)-Img_noise(i,j))*(Img_raw(i,j)-Img_noise(i,j));
        Img_filter_signal = Img_filter_signal+(Img_raw(i,j)-Img_filter(i-stx+1,j-sty+1))*(Img_raw(i,j)-Img_filter(i-stx+1,j-sty+1));
    end
end
Img_raw_snr = 10.0*log10(double(Img_raw_signal/Img_noise_signal));
Img_raw_psnr = 10.0*log10(double(n1*m1*255.0*255.0/Img_noise_signal));
Improved_snr = 10.0*log10(double(Img_noise_signal/Img_filter_signal));
Img_filter_snr = 10.0*log10(double(Img_raw_signal/Img_filter_signal));
Img_filter_psnr = 10.0*log10(double(n1*m1*255.0*255.0/Img_filter_signal));
disp('Input image snr = ');
disp(Img_raw_snr);
disp('Input image psnr = ');
disp(Img_raw_psnr);
disp('Improved snr = ');
disp(Improved_snr);
disp('Output image snr = ');
disp(Img_filter_snr);
disp('Output image psnr = ');
disp(Img_filter_psnr);

主程序入口

% ex_main.m  主程序入口
clc,clear;
% 原始圖像處理
Img_raw = imread('lena.jpg');
figure(1);
[n, m, c] = size(Img_raw);
if c ~= 1
    Img_raw = rgb2gray(Img_raw);
end
subplot(2, 2, 1);
imshow(Img_raw);
title('原始灰度圖像');

% 加噪聲
% 加‘salt & pepper’噪聲
Img_noise = imnoise(Img_raw, 'salt & pepper', 0.03);
% 加‘speckle’噪聲
% Img_noise = imnoise(Img_raw, 'speckle'); 
% Img_noise = Img_raw;
subplot(2, 2, 2);
imshow(Img_noise);
title('原始噪聲圖像');

% 可選鄰域均值法常用模板
% Temp=[1 1 1;1 1 1;1 1 1];
% Temp=[1 1 1;1 2 1;1 1 1];
% Temp=[1 2 1;2 4 2;1 2 1];
% Temp=[1 1 1;1 0 1;1 1 1];
Temp=[1 1 1 1 1;1 1 1 1 1;1 1 1 1 1;1 1 1 1 1;1 1 1 1 1];

% 鄰域平均法去噪聲 
% Average_filter(圖片像素矩陣，模板，閾值) 
% 用法：
% Average_filter(Img_noise);      
% Average_filter(Img_noise, Temp);
% Average_filter(Img_noise, Temp, 35);
% 含有閾值T，即爲閾值爲T的超限領域平均法
Img_average_filter=Average_filter(Img_noise, Temp, 35);
subplot(2, 2, 3);
imshow(uint8(Img_average_filter));
title('鄰域平均法去噪聲');
disp('Average_filter');
% 求SNR和PSNR
SNR(int32(Img_raw), int32(Img_noise), int32(Img_average_filter));

% 中值濾波法去噪聲 
% Med_filter(圖片像素矩陣，滑動窗口尺寸，閾值) 
% 用法：
% Med_filter(Img_noise);
% Med_filter(Img_noise, 3);
% Med_filter(Img_noise, 3, 35);
Img_med_filter=Med_filter(Img_noise);
subplot(2, 2, 4);
imshow(uint8(Img_med_filter));
title('中值濾波法去噪聲');
disp('Med_filter');
% 求SNR和PSNR
% SNR(原始圖像，噪聲圖像，濾波後圖像)
SNR(int32(Img_raw), int32(Img_noise), int32(Img_med_filter));

Lena圖片