Hough transform understanding [easy to understand]

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hough Transformation concept In the computer , It is often necessary to extract some specific shapes from the picture , It is very difficult to search directly with pixels , At this time, we need to map the image from the pixel to the parameter space according to a certain algorithm .hough Change provides a transformation method from image pixel information to parameter space . For things like straight lines , round , Regular curves like ellipses hough Is a commonly used algorithm .hough The biggest advantage of the change is the tolerance of the interval in the feature edge description and the transformation is not affected by the image noise .

hough Transformation principle hough Transformation is a kind of mapping the points on the image to the accumulated parameter space , Realize the recognition of known analytic curve .

Parameter space Because of the slope of the line k There is an infinite case , here hough Transformation transforms the original image space into the parameter space represented by the polar coordinate system . Straight line y = k ∗ x + b y=k*x+b y=k∗x+b Convert to polar space ρ = x c o s θ + y s i n θ \rho=xcos\theta+ysin\theta ρ=xcosθ+ysinθ, ρ \rho ρ Represents the distance from the straight line to the origin , θ \theta θ Defines the slope of the line ( This is just about limitation , It's not the slope of a straight line ). Any straight line can pass ( ρ , θ ) (\rho,\theta) (ρ,θ) To express . Parameter space H ( ρ , θ ) H(\rho,\theta) H(ρ,θ) Represents a set of finite points . Parameter space H ( ρ , θ ) H(\rho,\theta) H(ρ,θ) Each point represents a straight line . As shown in the figure ：

Cumulative voting of parameter space It's going on hough Before the change , First, we need to extract the edge image of the image , Based on the edge image hough Transformation . There are many straight lines passing through each point of the edge image , Here's the picture ：

The representation of a straight line passing through a certain point in the parameter space is like a sine curve . In the edge image , Only the pixels representing the edge can form a straight line . Now go back to parameter space , In parameter space H ( ρ , θ ) H(\rho,\theta) H(ρ,θ) in , It will pass through every effective pixel in the edge image ( Edge pixels ) All line information of is added to H ( ρ , θ ) H(\rho,\theta) H(ρ,θ) On . such as , Pixel point ( x , y ) (x,y) (x,y) Represents a pixel that forms an edge , Traverse θ \theta θ, According to the formula ρ = x c o s θ + y s i n θ \rho=xcos\theta+ysin\theta ρ=xcosθ+ysinθ We can calculate all the passing points ( x , y ) (x,y) (x,y) Line information . For example, below ：

Here are three points in a straight line , Lines of different colors represent straight lines passing through the impasse , The table below the figure shows the parameters of the line . Express the line parameter on the curve of parameter space , As shown in the figure ：

Each curve is composed of all the parameters of the straight line passing through a point . We find three curves in (60,81) It crosses nearby , This shows that θ = 60 , ρ = 81 \theta=60,\rho=81 θ=60,ρ=81 There are three points on this line . This shows how we can start from the parameter space H ( ρ , θ ) H(\rho,\theta) H(ρ,θ) Look for line information on . take H H H As an accumulator , An accumulator that represents line information . Set a certain threshold , The line represented by the parameter point that exceeds the threshold indicates the existence of this line in the image . hough Transformation examples

RGB= imread('lines.png');
imshow(RGB),title('original image');
I = rgb2gray(RGB);
BW = edge(I, 'canny');  %   use canny Algorithm to extract edge image 
figure,imshow(BW),title('edge image');
[H, T, R]=hough(BW);  %  Calculated H For the parameter matrix ,T To limit the angle of the line ,R Is the value of the line to the origin 
figure, imshow(imadjust(mat2gray(H)), 'XData', T, ...   %  draw hough Transformed graph 
'YData', R, 'InitialMagnification', 'fit'),title('hough image');
xlabel('\theta'), ylabel('\rho');
axis on; axis normal; hold on;
colormap(hot);
peaks = houghpeaks(H,4);  %  The algorithm is used to extract a specified number of peak points , That is to find a straight line 
figure, imshow(BW);
hold on;
lines = houghlines(BW, T, R, peaks, 'FillGap',30, 'MinLength',30);

max_len = 0;
for k=1:length(lines)
xy = [lines(k).point1; lines(k).point2];
   plot(xy(:,1),xy(:,2),'LineWidth',3,'Color','b');
   plot(xy(1,1),xy(1,2),'x','LineWidth',3,'Color','yellow');
   plot(xy(2,1),xy(2,2),'x','LineWidth',3,'Color','red');

   len = norm(lines(k).point1 - lines(k).point2);
   if ( len > max_len)
      max_len = len;
      xy_long = xy;
   end
end

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reference ：《 digital image processing matlab edition 》- Zuofei 《 Digital image processing third edition 》 http://blog.csdn.net/poem_qianmo/article/details/26977557 https://en.wikipedia.org/wiki/Hough_transform http://homepages.inf.ed.ac.uk/rbf/HIPR2/hough.htm

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