PROJECT 03-02 [Multiple Uses] Histogram Equalization

  1. Write a computer program for computing the histogram of an image.
  2. Implement the histogram equalization technique discussed in Section 3.3.1.
  3. Download Fig. 3.8(a) and perform histogram equalization on it.

As a minimum, your report should include the original image, a plot of its histogram, a plot of the histogram-equalization transformation function, the enhanced image, and a plot of its histogram. Use this information to explain why the resulting image was enhanced as it was.

变换函数是：$s_k=T(r_k)=(L-1)\sum_{j=0}^kp_r(r_j)=(L-1)\sum_{j=0}^k\frac{n_j}{n}$，其中$k=0,1,\ldots,L-1$

我想做一些加强，针对彩色图片做直方图均衡化。查了一些网上资料，就是对三维RGB图像的三种颜色分别做一次灰度均衡。

    I=imread('MizunoAi.jpg');
    subplot(2,3,1);imshow(I);title('原始图像');subplot(2,3,4);imhist(I);
    c=histeq(I);
    subplot(2,3,2);imshow(c);title('直方均衡化·调库');subplot(2,3,5);imhist(c);
    c=cat(3,histogram(I(:,:,1)),histogram(I(:,:,2)),histogram(I(:,:,3)));
    subplot(2,3,3);imshow(c);title('直方均衡化');subplot(2,3,6);imhist(c);
function J=histogram(I)
    J=I;
    [n,m]=size(I);
    a=zeros(1,256);
    b=zeros(1,256);
    for i=1:n
        for j=1:m
            a(1,I(i,j)+1)=a(1,I(i,j)+1)+1;
        end
    end
    sum=0;
    for i=1:256
        sum=sum+a(1,i);
        b(1,i)=255*sum/(m*n);
    end
    for i=1:n
        for j=1:m
            d=J(i,j)+1;
            J(i,j)=b(1,d);
        end
    end
end

运行结果如下，同时输出调用matlab自己的直方图均衡函数的结果作为对比，发现自己写的图像均衡偏绿…不过右侧阴影处的细节变得清晰了。

运行结果

PROJECT 03-05 Enhancement Using the Laplacian

  1. Use the programs developed in Projects 03-03 and 03-04 to implement the Laplacian enhancement technique described in connection with Eq. (3.7-5). Use the mask shown in Fig. 3.39(d).
  2. Duplicate the results in Fig. 3.40. You will need to download Fig. 3.40(a).
    clear;clc;
    I=imread('MizunoAi.jpg');
    subplot(1,3,1);imshow(I);title('原始图像');
    c=I-imfilter(I,fspecial('laplacian',0),'replicate');
    subplot(1,3,2);imshow(c);title('拉普拉斯变换·调库');
    c=cat(3,laplacian(I(:,:,1)),laplacian(I(:,:,2)),laplacian(I(:,:,3)));
    subplot(1,3,3);imshow(c);title('拉普拉斯变换');
function J=laplacian(I1)
    I=im2double(I1);
    [m,n]=size(I);
    A=zeros(m,n);
    for i=2:m-1
        for j=2:n-1
            A(i,j)=I(i+1,j)+I(i-1,j)+I(i,j+1)+I(i,j-1)-4*I(i,j);
        end
    end
    J=I-A;
end

运行结果如下，同时输出调用matlab自己的拉普拉斯方法的结果作为对比。

运行结果

PROJECT 03-06 Unsharp Masking

  1. Use the programs developed in Projects 03-03 and 03-04 to implement highboost filtering, as given in Eq. (3.7-8). The averaging part of the process should be done using the mask in Fig. 3.34(a).
  2. Download Fig. 3.43(a) and enhance it using the program you developed in (a). Your objective is to choose constant A so that your result visually approximates Fig. 3.43(d).

这里使用拉普拉斯变换得到模糊图像。

伽马变换

    close all;clc;clear all;
    I=imread('MizunoAi.jpg');
    subplot(1,2,1);imshow(I);title('原始图像');
    c=cat(3,unsharpMasking(I(:,:,1)),unsharpMasking(I(:,:,2)),unsharpMasking(I(:,:,3)));
    subplot(1,2,2);imshow(c);title('非锐化掩蔽');
function J=unsharpMasking(I)
    J = I + imfilter(I, fspecial('laplacian',0));
end

运行结果

    close all;clc;clear all;
    I=imread('MizunoAi.jpg');
    subplot(1,3,1);imshow(I);title('原始图像');
    c=cat(3,gamma(I(:,:,1),2),gamma(I(:,:,2),2),gamma(I(:,:,3),2));
    subplot(1,3,2);imshow(c);title('伽马变换，gamma=2');
    c=cat(3,gamma(I(:,:,1),0.5),gamma(I(:,:,2),0.5),gamma(I(:,:,3),0.5));
    subplot(1,3,3);imshow(c);title('伽马变换，gamma=0.5');
function J=gamma(I1,g)
    I = double(I1);
    [row,col] = size(I);
    J = zeros(row,col);
    for i = 1:row
        for j = 1:col
            J(i,j) = I(i,j).^g;
        end
    end
    J = mat2gray(J);
end

运行结果