详解Harris角点检测及代码实现

来源：互联网发布：js断点调试debugger 编辑：程序博客网时间：2024/05/22 14:10

转自：http://blog.csdn.net/dandan_397/article/details/42110719

1. 首先，我们不禁要问什么是harris角点？

对于角点，到目前为止还没有明确的数学定义。但是你可以认为角点就是极值点，即在某方面属性特别突出的点。一般的角点检测都是对有具体定义的、或者是能够具体检测出来的兴趣点的检测。这意味着兴趣点可以是角点，是在某些属性上强度最大或者最小的孤立点、线段的终点，或者是曲线上局部曲率最大的点。

通俗的来说，在一副图像中，我们可以认为角点是物体轮廓线的连接点（见图1），当拍摄视角变化的时候，这些特征点仍能很好地保持稳定的属性。

图1 corner

角点在保留图像图形重要特征的同时，可以有效地减少信息的数据量，使其信息的含量很高，有效地提高了计算的速度，有利于图像的可靠匹配，使得实时处理成为可能。它的各种应用，这里我就不再赘述了。

2. 如何检测出harris角点？

图2 角点检测的基本思想

角点检测最原始的想法就是取某个像素的一个邻域窗口，当这个窗口在各个方向上进行小范围移动时，观察窗口内平均的像素灰度值的变化（即，E(u,v)，Window-averaged change of intensity）。从上图可知，我们可以将一幅图像大致分为三个区域（‘flat’，‘edge’，‘corner’），这三个区域变化是不一样的。

其中，u,v是窗口在水平，竖直方向的偏移，

这里可以先简单复习一下泰勒级数展开的知识，因为马上就用到啦，

这是一维的情况，对于多元函数，也有类似的泰勒公式。

对I(x+u,y+v)进行二维泰勒级数展开，我们取一阶近似，有

图中蓝线圈出的部分我们称之为结构张量（structure tensor），用M表示。

讲到这里，先明确一点，我们的目的是什么？我们的目的是寻找这样的像素点，它使得我们的u，v无论怎样取值，E(u,v)都是变化比较大的，这个像素点就是我们要找的角点。不难观察，上式近似处理后的E(u,v)是一个二次型，而由下述定理可知，

令E(u,v)=常数，我们可用一个椭圆来描绘这一函数。

椭圆的长短轴是与结构张量M的两个特征值相对应的量。通过判断的情况我们就可以区分出‘flat’，‘edge’，‘corner’这三种区域，因为最直观的印象：

corner：在水平、竖直两个方向上变化均较大的点，即Ix、Iy都较大；
edge ：仅在水平、或者仅在竖直方向有较大的点，即Ix和Iy只有其一较大；
flat ：在水平、竖直方向的变化量均较小的点，即Ix、Iy都较小；

而结构张量M是由Ix，Iy构成，它的特征值正好可以反映Ix，Iy的情况，下面我以一种更容易理解的方式来讲述椭圆的物理意义。

这样是不是更清楚了呢^_^......，因此我们可以得出结论：

当然，大牛们并没有止步于此，这样通过判断两个变量的值来判断角点毕竟不是很方便。于是他们想出了一种更好的方法，对，就是定义角点响应函数R（corner response function），

针对三种区域，R的取值如何呢？

至此，我们就可以通过判断R的值来判断某个点是不是角点了。

3. harris角点检测算法步骤

值得注意的是，在实际情况中，用来判断R的阈值依赖于实际图像的尺寸、纹理等因素，由于其不具有直观的物理意义，它的取值很难确定。通常我们采用间接的方法来判断R：通过选择图像中R值最大的前n个像素点作为特征点，再对提取到的特征点进行K*K邻域的非极大抑制处理就可以了。

4. Matlab 代码实现

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% ori_im =double(imread('lena.jpg'));     % 读取图像 
ori_im = imread('pig.jpg');
% ori_im = imread('Baboon.bmp');
% figure,
% imshow(ori_im),
% title('the original image')
ori_gray = rgb2gray(ori_im);
% fx = [5 0 -5;8 0 -8;5 0 -5];          % 高斯函数一阶微分，x方向(用于改进的Harris角点提取算法) 
fx = [-2 -1 0 1 2];                     % x方向梯度算子(用于Harris角点提取算法) 
Ix = filter2(fx,ori_gray);                % x方向滤波 
% fy = [5 8 5;0 0 0;-5 -8 -5];          % 高斯函数一阶微分，y方向(用于改进的Harris角点提取算法) 
fy = [-2;-1;0;1;2];                     % y方向梯度算子(用于Harris角点提取算法) 
Iy = filter2(fy,ori_gray);                % y方向滤波 
Ix2 = Ix.^2; 
Iy2 = Iy.^2; 
Ixy = Ix.*Iy; 
clear Ix; 
clear Iy; 
%% 考虑到图像一般情况下的噪声影响，采用高斯滤波去除噪声点
h= fspecial('gaussian',[7 7],2);      % 产生7*7的高斯窗函数，sigma=2 
Ix2 = filter2(h,Ix2); 
Iy2 = filter2(h,Iy2); 
Ixy = filter2(h,Ixy); 
height = size(ori_gray,1); 
width = size(ori_gray,2); 
result = zeros(height,width);         % 纪录角点位置，角点处值为1 
%% 计算角点的响应函数R（即用一个值来衡量这个点是否是角点）,并标记角点（R(i,j)>0.01*Rmax,且R(i,j)为3x3邻域局部最大值）
k=1;
lambda=zeros(height*width,2);
R = zeros(height,width); 
for i = 1:height 
    for j = 1:width 
        M = [Ix2(i,j) Ixy(i,j);Ixy(i,j) Iy2(i,j)];             % auto correlation matrix 
        K = det(M);                          %求行列式
        H = trace(M);                        %求迹
%         R(i,j) = det(M)-0.06*(trace(M))^2;   
        R(i,j) = K-0.06*H^2;
        lambda(k,:)=[K H];
        k=k+1;
    end; 
end; 
figure,
plot(lambda(:,1),lambda(:,2),'.');
ylabel('trace');xlabel('det');
%%
cnt = 0; 
for i = 2:height-1 
    for j = 2:width-1 
        % 进行非极大抑制，窗口大小3*3 
        if  R(i,j) > R(i-1,j-1) && R(i,j) > R(i-1,j) && R(i,j) > R(i-1,j+1) && R(i,j) > R(i,j-1) && R(i,j) > R(i,j+1) && R(i,j) > R(i+1,j-1) && R(i,j) > R(i+1,j) && R(i,j) > R(i+1,j+1) 
            result(i,j) = 1; 
            cnt = cnt+1; 
        end; 
    end; 
end; 
Rsort=zeros(cnt,1); 
[posr, posc] = find(result == 1); 
for i=1:cnt 
    Rsort(i)=R(posr(i),posc(i)); 
end; 
[Rsort,ix]=sort(Rsort,1); 
Rsort=flipud(Rsort); 
ix=flipud(ix); 
ps=120; 
posr2=zeros(ps,1); 
posc2=zeros(ps,1); 
pos=zeros(ps,1); 
for i=1:ps 
    posr2(i)=posr(ix(i)); 
    posc2(i)=posc(ix(i)); 
    pos(i)= (posr2(i)-1)*width+posc2(i);
end; 
hold on,
plot(lambda(pos,1),lambda(pos,2),'r*');
legend('flat & edges','corners')
figure,
imshow(ori_im); 
hold on; 
plot(posc2,posr2,'g.'); 

来自CODE的代码片
harris.m

实验结果：

再附一张中间结果图，det(M) 与trace(M)的分布图，便于大家更好地理解R，

我在上面做了一些标记，

欢迎大家一起学习交流！

C.Harris, M.Stephens. “A Combined Corner and Edge Detector”. 1988

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详解Harris角点检测及代码实现

来自CODE的代码片harris.m

来自CODE的代码片
harris.m