【图像处理】基于Zernike矩的亚像素边缘检测理论及MATLAB实现

代码和图片下载

1 边缘检测理论

【参考文献】：亚像素边缘检测技术研究_张美静

2 MATLAB实现

function zernike7(I)

I=imread('Pic1_3.bmp');
subplot(221)
imshow(I)
title('原图像');
% 7*7Zernike模板
M00=...
[
       0	0.0287	0.0686	0.0807	0.0686	0.0287	0
    0.0287	0.0815	0.0816	0.0816	0.0816	0.0815	0.0287
    0.0686	0.0816	0.0816	0.0816	0.0816	0.0816	0.0686
    0.0807	0.0816	0.0816	0.0816	0.0816	0.0816	0.0807
    0.0686	0.0816	0.0816	0.0816	0.0816	0.0816	0.0686
    0.0287	0.0815	0.0816	0.0816	0.0816	0.0815	0.0287
       0	0.0287	0.0686	0.0807	0.0686	0.0287	0
];
M11R=...
[
       0	-0.015	-0.019	0	0.019	0.015	  0
    -0.0224	-0.0466	-0.0233	0	0.0233	0.0466	0.0224
    -0.0573	-0.0466	-0.0233	0	0.0233	0.0466	0.0573
    -0.069	-0.0466	-0.0233	0	0.0233	0.0466	0.069
    -0.0573	-0.0466	-0.0233	0	0.0233	0.0466	0.0573
    -0.0224	-0.0466	-0.0233	0	0.0233	0.0466	0.0224
       0	-0.015	-0.019	0	0.019	0.015	  0
];
M11I=...
[
       0	-0.0224	-0.0573	-0.069	-0.0573	-0.0224	  0
    -0.015	-0.0466	-0.0466	-0.0466	-0.0466	-0.0466	-0.015
    -0.019	-0.0233	-0.0233	-0.0233	-0.0233	-0.0233	-0.019
       0	   0	   0	   0	   0	   0	  0
    0.019	0.0233	0.0233	0.0233	0.0233	0.0233	0.019
    0.015	0.0466	0.0466	0.0466	0.0466	0.0466	0.015
       0	0.0224	0.0573	0.069	0.0573	0.0224	  0
];
M20=...
[
       0	0.0225	0.0394	0.0396	0.0394	0.0225	0
    0.0225	0.0271	-0.0128	-0.0261	-0.0128	0.0271	0.0225
    0.0394	-0.0128	-0.0528	-0.0661	-0.0528	-0.0128	0.0394
    0.0396	-0.0261	-0.0661	-0.0794	-0.0661	-0.0261	0.0396
    0.0394	-0.0128	-0.0528	-0.0661	-0.0528	-0.0128	0.0394
    0.0225	0.0271	-0.0128	-0.0261	-0.0128	0.0271	0.0225
       0	0.0225	0.0394	0.0396	0.0394	0.0225	0
];


if length(size(I))==3 I=rgb2gray(I); end
I=im2bw(I,0.6);
K=double(I);
[m n]=size(K);
xs=double(zeros(m,n));
ys=double(zeros(m,n));

% 卷积运算
A11I=conv2(M11I,K);
A11R=conv2(M11R,K);
A20=conv2(M20,K);

% 截掉多余部分
A11I=A11I(4:end-3,4:end-3);
A11R=A11R(4:end-3,4:end-3);
A20=A20(4:end-3,4:end-3);

J=zeros(size(K));
boundary=J;
theta=atan2(A11I,A11R);%计算theta

%计算边缘的三个参数
A11C=A11R.*cos(theta)+A11I.*sin(theta);
l=A20./A11C;
k=1.5*A11C./((1-l.^2).^1.5);
e=abs(l)>1/3.5;
k(e)=0;

%边缘判断条件
a=abs(l)max(I(:))/10;
% a,b分别为距离和边缘强度判断结果
J(a&b)=1;
%将图像的最边缘去除
% boundary(2:end-1,2:end-1)=1;
% J(~boundary)=0;
format short
% [x,y]=find(J==1);%边缘的像素级坐标
% O=[x y];
% Z=[x+l(find(J==1)).*cos(theta(find(J==1))) y+l(find(J==1)).*sin(theta(find(J==1)))];%亚像素坐标
% % fprintf('%.4f %.4f\n',Z');

[L,num]=bwlabel(J,8);%对二值图像进行标记
%自动化搜索连通域
s=zeros(1,num);
for i=1:num
   s(i)=size(find(L==i),1);
end
[bwL,label]=sort(s,'descend');
if label(1)