Detecting lines in images with the Hough transform

In our human-made world, planar and linear structures abound. As a result, straight lines are frequently visible in images. These are meaningful features that play an important role in object recognition and image understanding. The Hough transform is a classic algorithm that is often used to detect these particular features in images. It was initially developed to detect lines in images and, as we will see, it can also be extended to detect other simple image structures.

Getting ready

With the Hough transform, lines are represented using the following equation:

The ρ parameter is the distance between the line and the image origin (the upper-left corner), and θ is the angle of the perpendicular to the line. In this representation, the lines visible in an image have a θ angle between 0 and π radians, while the ρ radius can have a maximum value that equals the length of the image diagonal. Consider, for example, the following set of lines:

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