直线检测——Radon变换/霍夫变换/基于快速傅里叶变换的直线检测_傅里叶检测直线

1. 直线检测

1.1. Radon直线检测原理

基于Radon变换的直线检测的目的就是检测根据角度变化时出现的“局部峰值”，即可以确定直线的方向，同时，峰值大小能够确定直线上点的个数

1.2. Hough 直线检测原理

将直线利用极坐标表示时，一条直线即可通过角度和长度确定，通过对角度和长度计算累计图，寻找峰值点即可确定一条直线：

1.3. 正弦图合击-分进直线检测

2. 实现代码

%LineDetection.m
%Author: HSW
%Date: 2015/4/21
%HARBIN INSTITUTE OF TECHNOLOGY
%
%Set Matlab
close all;
clear all;
clc;
% Add Path
addpath(genpath('MultiLayerLineUtil\'));
addpath(genpath('SingleLayerLineUtil\'));
addpath(genpath('RadonLineUtil\'));
% 测试图像路径和结果保存路径
ImageFilePath = 'TestImage\';
SaveFilePath = 'Results\';
type = ['*.png';'*.bmp';'*.jpg'];
MaxSigma = 1;
sigmastep = 0.05;
% 考虑是否需要设置Neighborstep 和 MaxNeighbor，因为每张图都不一样
% ，特别是随着噪声的增大时，Neighbor需要增大可能更好
Neighborstep = 5;
MaxNeighbor = 60;
Neighbor = 11;

%比较算法如下
%1. 标准Hough变换直线检测
%2. 标准Radon变换直线检测
%3. 基于Fourier变换的Radon变换直线检测
%4. 基于MultiLayer Fourier变换的Radon变换直线检测
%5. 零填充Fourier变换的Radon变换直线检测（扩大图像）

% imgdir = dir(fullfile(ImageFilePath,type(1,:))); %修改为type(2,:)
% 处理.bmp格式图片, type(3,:),处理.jpg格式图片，这里是为了批处理（但是这里不需要）
% for iterimage = 1:length(imgdir)
% Img = imread(fullfile(ImageFilePath,imgdir(iterimage).name));
% Img = imread(fullfile(ImageFilePath,'NewLine2.png'));Nhood = [51,51];   Numpeaks = 1; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'NewOneLine.png'));Nhood = [51,51];   Numpeaks = 1; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'OneLine1.png'));Nhood = [51,51];   Numpeaks = 1; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'OneLine.png'));Nhood = [51,51];   Numpeaks = 1; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'Line30_256.png')); Nhood = [31,31];   Numpeaks = 30; %注意修改peaks的数目
Img = imread(fullfile(ImageFilePath,'Line30_512.png')); Nhood = [31,31];   Numpeaks = 31; %注意修改peaks的数目
% Img = 255-imread(fullfile(ImageFilePath,'house.png'));Nhood = [51,51];   Numpeaks = 11; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'half.png'));Nhood = [51,51];   Numpeaks = 1; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'paper.png'));Nhood = [11,11];   Numpeaks = 3; %注意修改peaks的数目
% Img = imread(fullfile(ImageFilePath,'5line.png'));Nhood = [31,31];   Numpeaks = 5; %注意修改peaks的数目
if size(Img,3) == 3
    Img = rgb2gray(Img);
end
NextPow1 = nextpow2(size(Img,1));
NextPow2 = nextpow2(size(Img,2));
if abs(size(Img,1) - 2^NextPow1) > abs(size(Img,1) - 2^(NextPow1 - 1))
    NextPow1 = NextPow1 -1;
end
if abs(size(Img,2) - 2^NextPow2) > abs(size(Img,2) - 2^(NextPow2 - 1))
    NextPow2 = NextPow2 - 1;
end
NextPow = max(NextPow1,NextPow2);
Img = imresize(Img,[2^NextPow, 2^NextPow],'bicubic');

for itersigma = 1:MaxSigma
    nImg = double(Img) + (itersigma - 1)*randn(size(Img)); %添加噪声
   
    % 标准Hough变换直线检测
    EdImg = edge(nImg,'canny');
    %     title('待检测图像');
    [R,theta,rho] = hough(EdImg,'ThetaResolution',1);
    
    % 峰值个数
  
    %检测的峰值为2xNumpeaks的数组, rho = peaks(:,2), theta = peaks(:,1)
    peaks = houghpeaks(R,Numpeaks,'Threshold',0.1*max(R(:)),'Nhood',Nhood);
    
    %显示检测到的峰值
    if ~isempty(peaks)
        figure;
        %         subplot(1,3,2);
        imshow(R,[]);
        title('正弦图像');
        for iter = 1:size(peaks,1)
            hold on;
            scatter(peaks(iter,2),peaks(iter,1),'r');
        end
    end
    
    lines = houghlines(EdImg,theta,rho,peaks,'FillGap',5,'MinLength',7);
    
    if ~isempty(lines)
        figure;
        imshow(nImg/255,[]);
        hold on;
        title('Hough变换');
        for iter = 1:length(lines)            
            xy = [lines(iter).point1;lines(iter).point2];
            plot(xy(:,1),xy(:,2),'LineWidth',1,'Color','green');
        end
    end
 
    % 标准Radon变换直线检测
    EdImg = edge(nImg,'sobel');
    % 角分辨率
    theta = 0:0.5:179.5;
    %进行Radon变换
    [R,rho] = radon(EdImg,theta);
    
    %检测的峰值为2xNumpeaks的数组, rho = peaks(:,2), theta = peaks(:,1)
    peaks = radonpeaks(R,Numpeaks,'Threshold',0,'Nhood',Nhood);
    %显示检测到的峰值
    if ~isempty(peaks)
        figure; 
        imshow(R,[]);
        title('正弦图');
        for iter = 1:size(peaks)
            hold on;
            scatter(peaks(iter,2),peaks(iter,1),'r');
        end
    end
    
    % 显示检测到的直线
    type = 1;
    if type == 1
        radonlines(nImg,theta,rho',peaks,type);
    elseif type == 2
        lines = radonlin