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 = 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');
end
end
end
%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');
end
end
% 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);%rho
c1=peaks(count,2); %theta
rho1=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 grid
grid1=[x1' y1'];grid2=[x2' y2'];grid3=[x3' y3'];
%computer the covariance
theta=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 column
YfreqDomain=fft(L3);
L=abs(YfreqDomain)/h;
L1=L(1:rho,:);L2=L(rho+1:rho*2-1,:);
Ra=flipud([L2
L1]);
NormalRa=abs(Ra)/max(max(abs(Ra)));
%Peak Detection
H = 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');
end
end
figure;
imshow(nImg/255,[]);
title('Multi-Layer Fourier');
hold on;
for count=1:size(peaks,1)
r1a=peaks(count,1);%rho
c1=peaks(count,2); %theta
rho1=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;
end
if 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);
end
x =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 pairs
xy = [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 threshold
fillgap_idx = find(dist_sq > fillgap_sq);
idx = [0; fillgap_idx; size(xy,1)];
for p = 1:length(idx) - 1
p1 = xy(idx(p) + 1,:); % offset by 1 to convert to 1 based index
p2 = xy(idx(p + 1),:); % set the end (don't offset by one this time)
linelength_sq = sum((p2-p1).^2);
if linelength_sq >= minlength_sq
numlines = numlines + 1;
lines(numlines).point1 = p1;
lines(numlines).point2 = p2;
lines(numlines).theta = theta(peaks(k,2));
lines(numlines).rho = rho(peaks(k,1));
end
end
end %for k = 1:size(peaks,1)
else
error('type = 1 or type = 2');
end %if type
end %function radonlines
function [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 radonpixels
function [r_new,c_new] = reSortRadonPixels(r,c)
if isempty(r)
r_new = r;
c_new = c;
return;
end
r_range = max(r) - min(r);
c_range = max(c) - min(c);
if r_range > c_range
sorting_order = [1,2];
else
sorting_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) >= threshold
peaks = [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;
else
done = 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1
idx = 2;
if nargin > 1
if ~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 pairs
done = false;
while ~done
input = 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 > nargin
error(message('images:houghpeaks:valForhoughpeaksMissing', inputStr))
end
switch inputStr
case '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))
end
if (any(nhood > size(h)))
error(message('images:radonpeaks:tooBigNHoodSize', inputStr))
end
otherwise
%should never get here
error(message('images:radonpeaks:internalError'))
end
if idx >= nargin
done = true;
end
idx=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
end
if 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