Hough Transform

The Standard Hough Transform (SHT) is designed to detect straight lines in images. The SHT uses the parametric representation of a line:

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

theta is the angle of the perpendicular projection from the origin to the line, measured in degrees clockwise from the positive x-axis. rho is the parallel offset from the origin to the line along a vector perpendicular to the line. The magnitude of rho is equivalent to the perpendicular distance between the origin and the line. The following image depicts how theta and rho are defined relative to the perpendicular projection of a line.

You can perform the Hough transform of a binary image by using the hough function. The hough function returns a parameter space matrix whose rows and columns correspond to these rho and theta values, respectively. For every combination of rho and theta, the SHT calculates the line with those parameters and returns the sum of all true pixels in the input binary image along that line.

After you calculate the Hough transform, you can find peak values in the parameter space matrix by using the houghpeaks function. These peaks represent potential lines in the input image. However, a peak does not guarantee a line in the input image, because a peak could result from an accumulation of many short co-linear line segments.

To get more information about the line segments contributing to peaks in the Hough matrix, you can use the houghlines function. For each line segment that corresponds to a peak, the houghlines function returns the (x, y) coordinates of the two endpoints of the line segment and the values of theta and rho for the line. The houghlines function reduces the effect of noise in the input binary image by automatically connecting line segments with small gaps between them. You can use the information about endpoints to identify the longest lines in an image or to display the line segments over the input image. For an example, see Detect Lines and Highlight Longest Segment Using Hough Transform.