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

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) == 3Img = 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:MaxSigmanImg = 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');endendlines = 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');endend% 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');endend% 显示检测到的直线type = 1;if type == 1radonlines(nImg,theta,rho',peaks,type);elseif type == 2lines = radonlines(EdImg,theta,rho',peaks,type,20,40,2);if ~isempty(lines)figure;imshow(nImg);title('Radon变换');for iter = 1:length(lines)hold on;xy = [lines(iter).point1;lines(iter).point2];plot(xy(:,1),xy(:,2),'LineWidth',1,'Color','green');endendend%基于Fourier变换的Radon变换直线检测shiftImg = fftshift(nImg);fftImg = FractionalFT(shiftImg,1,1); % 进行fourier变换Center = round(0.5*size(fftImg)); %中心坐标gridfftImg = [(-0.5*size(fftImg,1):0.5*size(fftImg,1)-1)',(-0.5*size(fftImg,2):0.5*size(fftImg,2)-1)'];MaxRho = sqrt(sum(sum((0.5*size(fftImg)).^2)));Nrho = round(MaxRho);Ntheta = length(0:0.5:179.5);de=59;di=26;ax = [1,1,1];ay = ax;fftImg = xvMappingOpt(gridfftImg,gridfftImg,gridfftImg,fftImg,fftImg,fftImg,Nrho,Ntheta+1,ax,ay,de,di,Center(1),Center(2));fftImg = fftImg(1:Nrho,1:Ntheta);conjfftImg = flipud(conj(fftImg));TwofftImg = [conjfftImg;fftImg(2:end,:)];radonImg = fft(TwofftImg);radonImg = abs(radonImg)/size(fftImg,1);L1 = radonImg(1:size(fftImg,1),:);L2 = radonImg(size(fftImg,1)+1:2*size(fftImg,1)-1,:);Ra = flipud([L2;L1]);
%     NormalRa = abs(Ra)/max(max(abs(Ra)));%     % 峰值个数%     Numpeaks = 3;%检测的峰值为2xNumpeaks的数组, rho = peaks(:,2), theta = peaks(:,1)peaks = radonpeaks(abs(Ra)*10000,Numpeaks,'Threshold',0.1*10000*ceil(max(max(abs(Ra)))),'Nhood',Nhood);%显示检测到的峰值if ~isempty(peaks)figure;imshow(log(abs(Ra) + 1),[]);for iter = 1:size(peaks,1)hold on;scatter(peaks(iter,2),peaks(iter,1),'r');endend% 显示检测到的直线[h,w,ncolor]=size(nImg);r=0.5*sqrt(2)*w;Factor = Nrho/size(Img,1);centery=floor(h*0.5)+1;centerx=floor(w*0.5)+1;r=0.5*sqrt(2)*w;figure;imshow(nImg/255,[]);title('Single-Layer Fourier'); hold on;for count=1:size(peaks,1)r1a=peaks(count,1);%rhoc1=peaks(count,2); %thetarho1=Factor*(r1a-Nrho-1)/Nrho*r;%为什么要乘以0.5？theta1=(c1-1)/Ntheta*180;if rho1 <= 0 && theta1 <= 90 % 直线在左下角theta2 = 90-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);elseif rho1 < 0 && theta1 > 90% 直线在右下角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);elseif rho1 > 0 && theta1 < 90 % 直线在右上角theta2 = 90 - theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);else% 直线在左上角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);end x =centerx-size(Img,2):centerx+size(Img,2);y = slope*(x-x1) + y1;plot(x,y,'g')end% 多层fourier变换直线检测ax=[];ay=[];I1=double(nImg);I1=fftshift(I1);[h,w]=size(I1);x0=-w*0.5:w*0.5-1;y0=-h*0.5:h*0.5-1;centery=floor(h*0.5)+1;centerx=floor(w*0.5)+1;a1=0.8;a2=0.9;x1=a1*x0;y1=a2*y0;ax=[ax a1];ay=[ay a2];f1=FractionalFT(I1,a1,a2);a1=0.9;a2=0.7;x2=x0*a1;y2=y0*a2;ax=[ax a1];ay=[ay a2];f2=FractionalFT(I1,a1,a2);a1=1;a2=1;x3=x0*a1;y3=y0*a2;ax=[ax a1];ay=[ay a2];f3=FractionalFT(I1,a1,a2);%creat gridgrid1=[x1' y1'];grid2=[x2' y2'];grid3=[x3' y3'];%computer the covariancetheta=Ntheta;rho=Nrho;de=59;di=26;%thL=0.5*dr; thH=10*dr;%0.8*sigma;L1=xvMappingOpt(grid1,grid2,grid3,f1,f2,f3,rho,theta+1,ax,ay,de,di,centery,centerx);L1=L1(1:rho,1:theta);L2=flipud(conj(L1));%L3=cat(1,L2,L1);L3=[L2;L1(2:rho,:)];%忽略重复的0度,并且相当于求了共轭% %perform 1D FFT for each columnYfreqDomain=fft(L3);L=abs(YfreqDomain)/h;L1=L(1:rho,:);L2=L(rho+1:rho*2-1,:);Ra=flipud([L2L1]);NormalRa=abs(Ra)/max(max(abs(Ra)));%Peak DetectionH = log(abs(Ra)+1)*10000;peaks=radonpeaks(H,Numpeaks,'threshold',ceil(0.0001*max(H(:))),'Nhood',Nhood);%显示检测到的峰值if ~isempty(peaks)figure;imshow(log(abs(Ra) + 1),[]);for iter = 1:size(peaks,1)hold on;scatter(peaks(iter,2),peaks(iter,1),'r');endendfigure; imshow(nImg/255,[]);title('Multi-Layer Fourier'); hold on; for count=1:size(peaks,1)r1a=peaks(count,1);%rhoc1=peaks(count,2); %thetarho1=Factor*(r1a-Nrho-1)/Nrho*r;%为什么要乘以0.5？theta1=(c1-1)/Ntheta*180;if rho1 <= 0 && theta1 <= 90 % 直线在左下角theta2 = 90-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);elseif rho1 < 0 && theta1 > 90% 直线在右下角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);elseif rho1 > 0 && theta1 < 90 % 直线在右上角theta2 = 90 - theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);else% 直线在左上角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);end x =centerx-size(Img,2):centerx+size(Img,2);y = slope*(x-x1) + y1;plot(x,y,'g')end %for itersigma
end
% end%for iterimage% % 读入图像
% % 实验1 peaks = houghpeaks(R,Numpeaks,'Nhood',[51,51]);
% Img = imread('paper.png');
%
% % 实验2 peaks = houghpeaks(R,Numpeaks,'Nhood',[51,51]);
% % Img = imread('ThreeLine.bmp');
% % Img = 255 - Img;
%
% % 实验3 peaks = houghpeaks(R,Numpeaks,'Nhood',[11,11]);
% % Img = imread('SevenLine.png');
% if size(Img,3) == 3
%     Img = rgb2gray(Img);
% end

Radon变换直线检测代码：

function lines = radonlines(varargin)
%RADONLINES Extract line segments based on Radon transform.
%
%   LINES = HOUGHLINES(...,PARAM1,VAL1,PARAM2,VAL2) sets various
%   parameters. Parameter names can be abbreviated, and case
%   does not matter. Each string parameter is followed by a value
%   as indicated below:
%
%   'FillGap'   Positive real scalar.
%               When HOUGHLINES finds two line segments associated
%               with the same Hough transform bin that are separated
%               by less than 'FillGap' distance, HOUGHLINES merges
%               them into a single line segment.
%
%               Default: 20 直线进行合并
%
%   'MinLength' Positive real scalar.
%               Merged line segments shorter than 'MinLength'
%               are discarded.
%
%               Default: 40 直线的最短长度
%
%   Class Support
%   -------------
%   BW can be logical or numeric and it must be real, 2-D, and nonsparse.
% Author: HSW
% Date: 2015/4/21
% HARBIN INSTITUTE OF TECHNOLOGY
%
center = floor((0.5*size(varargin{1})));
centery = center(1);
centerx = center(2);
theta = varargin{2};
rho = varargin{3};
peaks = varargin{4};
type = varargin{5}; % 选择画直线还是画线段
if isempty(peaks)disp('no peaks');return;
endif type == 1% 画直线figure;imshow(varargin{1});hold on;for iter = 1:size(peaks,1)rho1 = rho(peaks(iter,1));theta1 = theta(peaks(iter,2));if rho1 <= 0 && theta1 <= 90% 直线在左下角theta2 = 90-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);elseif rho1 < 0 && theta1 > 90% 直线在右下角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);elseif rho1 > 0 && theta1 < 90% 直线在右上角theta2 = 90 - theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);else% 直线在左上角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);endx =centerx-size(varargin{1},2):centerx+size(varargin{1},2);y = slope*(x-x1) + y1;plot(x,y,'g')end
elseif type == 2% 画线段fillgap = varargin{6};minlength = varargin{7};delta = varargin{8};minlength_sq = minlength^2;fillgap_sq = fillgap^2;numlines = 0;[y,x] = find(varargin{1});nonzeropix = [x,y] - 1;lines = struct([]);for k = 1:size(peaks,1)[r,c] = radonpixels(nonzeropix,theta,rho,delta,peaks(k,:),center);if isempty(r)continue;end% Compute distance^2 between the point pairsxy = [c r]; % x,y pairs in coordinate system with the origin at (1,1)diff_xy_sq = diff(xy,1,1).^2;dist_sq = sum(diff_xy_sq,2);% Find the gaps larger than the thresholdfillgap_idx = find(dist_sq > fillgap_sq);idx = [0; fillgap_idx; size(xy,1)];for p = 1:length(idx) - 1p1 = xy(idx(p) + 1,:); % offset by 1 to convert to 1 based indexp2 = xy(idx(p + 1),:); % set the end (don't offset by one this time)linelength_sq = sum((p2-p1).^2);if linelength_sq >= minlength_sqnumlines = numlines + 1;lines(numlines).point1 = p1;lines(numlines).point2 = p2;lines(numlines).theta = theta(peaks(k,2));lines(numlines).rho = rho(peaks(k,1));endendend %for k = 1:size(peaks,1)
elseerror('type = 1 or type = 2');
end %if typeend %function radonlinesfunction [r,c] = radonpixels(nonzeropix,theta,rho,delta,peak,center)
x = nonzeropix(:,1);
y = nonzeropix(:,2);
centery = center(1);
centerx = center(2);
rho1 = rho(peak(1));
theta1 = theta(peak(2));
if rho1 <= 0 && theta1 <= 90% 直线在左下角theta2 = 90-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);
elseif rho1 < 0 && theta1 > 90% 直线在右下角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);
elseif rho1 > 0 && theta1 < 90% 直线在右上角theta2 = 90 - theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx + rho1*cos(theta1*pi/180);
else% 直线在左上角theta2 = 270-theta1;theta1 = 180-theta1;slope = tan((theta2)*pi/180);y1 = centery - rho1*sin(theta1*pi/180);x1 = centerx - rho1*cos(theta1*pi/180);
end
idx = find(abs(slope*(x-x1) + y1 - y) <= delta); %进行直线拟合
r = y(idx) + 1;
c = x(idx) + 1;
[r,c] = reSortRadonPixels(r,c);
end% function radonpixelsfunction [r_new,c_new] = reSortRadonPixels(r,c)if isempty(r)r_new = r;c_new = c;return;
endr_range = max(r) - min(r);
c_range = max(c) - min(c);if r_range > c_rangesorting_order = [1,2];
elsesorting_order = [2,1];
end
[rc_new] = sortrows([r,c],sorting_order);
r_new = rc_new(:,1);
c_new = rc_new(:,2);
end % function reSortRadonPixels

function peaks = radonpeaks(varargin)
% RADONPEAKS Identify peaks in Radon transform.
%   PEAKS = HOUGHPEAKS(H,NUMPEAKS) locates peaks in the Hough
%   transform matrix, H, generated by the HOUGH function. NUMPEAKS
%   specifies the maximum number of peaks to identify. PEAKS is
%   a Q-by-2 matrix, where Q can range from 0 to NUMPEAKS. Q holds
%   the row and column coordinates of the peaks. If NUMPEAKS is
%   omitted, it defaults to 1.
%
%   PEAKS = HOUGHPEAKS(...,PARAM1,VAL1,PARAM2,VAL2) sets various
%   parameters. Parameter names can be abbreviated, and case
%   does not matter. Each string parameter is followed by a value
%   as indicated below:
%
%   'Threshold' Nonnegative scalar.
%               Values of H below 'Threshold' will not be considered
%               to be peaks. Threshold can vary from 0 to Inf.
%
%               Default: 0.5*max(H(:))
%
%   'NHoodSize' Two-element vector of positive odd integers: [M N].% odd 奇数
%               'NHoodSize' specifies the size of the suppression
%               neighborhood. This is the neighborhood around each
%               peak that is set to zero after the peak is identified.
%
%               Default: smallest odd values greater than or equal to
%                        size(H)/50.
%
%   Class Support
%   -------------
%   H is the output of the HOUGH function. NUMPEAKS is a positive
%   integer scalar.
%
%   Example
%   -------
%   Locate and display two peaks in the Hough transform of the
%   rotated circuit.tif image.
%
%      I  = imread('circuit.tif');
%      BW = edge(imrotate(I,50,'crop'),'canny');
%      [H,T,R] = hough(BW);
%      P  = houghpeaks(H,2);
%      imshow(H,[],'XData',T,'YData',R,'InitialMagnification','fit');
%      xlabel('\theta'), ylabel('\rho');
%      axis on, axis normal, hold on;
%      plot(T(P(:,2)),R(P(:,1)),'s','color','white');
%
%   See also HOUGH and HOUGHLINES.%   Author: HSW
%   HARBIN INSTITUTE OF TECHNOLOGY
[h, numpeaks, threshold, nhood] = parseInputs(varargin{:});
% h: radon 变换的输出
% numpeaks: 峰值的个数
% threshold: 峰值的最小值, 默认为0.5*max(H(:))
% nhood: 包含两个奇数的数组[M,N], 当峰值识别出来后,设置为0 % initialize the loop variables
done = false;
hnew = h;
nhood_center = (nhood-1)/2;% 抑制块的中心位置,例如nhood = [5,5], 则nhood_center = [2,2]
peaks = [];
% 循环搜索峰值
while ~done[dummy max_idx] = max(hnew(:)); %#ok寻找现有的最大值[p, q] = ind2sub(size(hnew), max_idx);p = p(1); q = q(1);if hnew(p, q) >= thresholdpeaks = [peaks; [p q]]; %#ok<AGROW> % add the peak to the list% Suppress this maximum and its close neighbors.p1 = p - nhood_center(1); p2 = p + nhood_center(1);q1 = q - nhood_center(2); q2 = q + nhood_center(2);% Throw away neighbor coordinates that are out of bounds in% the rho direction.[qq, pp] = meshgrid(q1:q2, max(p1,1):min(p2,size(h,1)));pp = pp(:); qq = qq(:);% For coordinates that are out of bounds in the theta% direction, we want to consider that H is antisymmetric% along the rho axis for theta = +/- 90 degrees.theta_too_low = find(qq < 1);qq(theta_too_low) = size(h, 2) + qq(theta_too_low);pp(theta_too_low) = size(h, 1) - pp(theta_too_low) + 1;theta_too_high = find(qq > size(h, 2));qq(theta_too_high) = qq(theta_too_high) - size(h, 2);pp(theta_too_high) = size(h, 1) - pp(theta_too_high) + 1;% Convert to linear indices to zero out all the values.hnew(sub2ind(size(hnew), pp, qq)) = 0; %设置为0 done = size(peaks,1) == numpeaks;elsedone = true;end
end%-----------------------------------------------------------------------------
function [h, numpeaks, threshold, nhood] = parseInputs(varargin)narginchk(1,6); % 参数个数小于1 大于6报错h = varargin{1};
% validateattributes(h, {'double'}, {'real', '2d', 'nonsparse', 'nonempty',...
%                    'finite', 'integer'}, ...
%                    mfilename, 'H', 1);
% hough变换的中h中的取值必然为非负整数,但是,radon变换中只能保证为非负的validateattributes(h, {'double'}, {'real', '2d', 'nonsparse', 'nonempty',...'finite'}, ...mfilename, 'H', 1);numpeaks = 1; % set default value for numpeaks峰值的默认值为1idx = 2;
if nargin > 1if ~ischar(varargin{2})numpeaks = varargin{2};validateattributes(numpeaks, {'double'}, {'real', 'scalar', 'integer', ...'positive', 'nonempty'}, mfilename, 'NUMPEAKS', 2);idx = 3;end
end% Initialize to empty
nhood = [];
threshold = [];% Process parameter-value pairs
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
validStrings = {'Threshold','NHoodSize'};if nargin > idx-1 % we have parameter/value pairsdone = false;while ~doneinput = varargin{idx};inputStr = validatestring(input, validStrings,mfilename,'PARAM',idx);idx = idx+1; %advance index to point to the VAL portion of the input if idx > narginerror(message('images:houghpeaks:valForhoughpeaksMissing', inputStr))endswitch inputStrcase 'Threshold'threshold = varargin{idx};validateattributes(threshold, {'double'}, {'real', 'scalar','nonnan' ...'nonnegative'}, mfilename, inputStr, idx);case 'NHoodSize'nhood = varargin{idx};validateattributes(nhood, {'double'}, {'real', 'vector', ...'finite','integer','positive','odd'},...mfilename, inputStr, idx);if (any(size(nhood) ~= [1,2]))error(message('images:radonpeaks:invalidNHoodSize', inputStr))endif (any(nhood > size(h)))error(message('images:radonpeaks:tooBigNHoodSize', inputStr))end     otherwise%should never get hereerror(message('images:radonpeaks:internalError'))endif idx >= nargindone = true;endidx=idx+1;end
end% Set the defaults if necessary
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
if isempty(nhood)nhood = size(h)/50; nhood = max(2*ceil(nhood/2) + 1, 1); % Make sure the nhood size is odd.确保nhood为奇数
endif isempty(threshold)threshold = 0.5 * max(h(:)); %设置默认值
end

3. 模型效果

3.1 Hough变换直线检测(Matlab内建函数）

3.2 Radon变换直线检测

3.3 合击-分进直线检测

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