The Image Processing Toolbox™ supports functions that enable you to use the Hough transform to detect lines in an image.

The `hough`

function implements the Standard Hough Transform (SHT).
The Hough transform is designed to detect lines, using the parametric representation of
a line:

rho = x*cos(theta) + y*sin(theta)

The variable `rho`

is the distance from the origin to the line along
a vector perpendicular to the line. `theta`

is the angle between the
x-axis and this vector. The `hough`

function generates a parameter
space matrix whose rows and columns correspond to these `rho`

and
`theta`

values, respectively.

After you compute the Hough transform, you can use the `houghpeaks`

function to find peak values in the parameter space. These peaks represent potential
lines in the input image.

After you identify the peaks in the Hough transform, you can use the
`houghlines`

function to find the endpoints of the line segments
corresponding to peaks in the Hough transform. This function automatically fills in
small gaps in the line segments.

This example shows how to detect lines in an image using the H`ough`

transform.

Read an image into the workspace and, to make this example more illustrative, rotate the image. Display the image.

I = imread('circuit.tif'); rotI = imrotate(I,33,'crop'); imshow(rotI)

Find the edges in the image using the `edge`

function.

```
BW = edge(rotI,'canny');
imshow(BW);
```

Compute the Hough transform of the binary image returned by `edge`

.

[H,theta,rho] = hough(BW);

Display the transform, `H`

, returned by the `hough`

function.

figure imshow(imadjust(rescale(H)),[],... 'XData',theta,... 'YData',rho,... 'InitialMagnification','fit'); xlabel('\theta (degrees)') ylabel('\rho') axis on axis normal hold on colormap(gca,hot)

Find the peaks in the Hough transform matrix, `H`

, using the `houghpeaks`

function.

`P = houghpeaks(H,5,'threshold',ceil(0.3*max(H(:))));`

Superimpose a plot on the image of the transform that identifies the peaks.

x = theta(P(:,2)); y = rho(P(:,1)); plot(x,y,'s','color','black');

Find lines in the image using the `houghlines`

function.

lines = houghlines(BW,theta,rho,P,'FillGap',5,'MinLength',7);

Create a plot that displays the original image with the lines superimposed on it.

figure, imshow(rotI), hold on max_len = 0; for k = 1:length(lines) xy = [lines(k).point1; lines(k).point2]; plot(xy(:,1),xy(:,2),'LineWidth',2,'Color','green'); % Plot beginnings and ends of lines plot(xy(1,1),xy(1,2),'x','LineWidth',2,'Color','yellow'); plot(xy(2,1),xy(2,2),'x','LineWidth',2,'Color','red'); % Determine the endpoints of the longest line segment len = norm(lines(k).point1 - lines(k).point2); if ( len > max_len) max_len = len; xy_long = xy; end end % highlight the longest line segment plot(xy_long(:,1),xy_long(:,2),'LineWidth',2,'Color','red');