What is the Hough line transform?

In the world of autonomous cars, enhanced medical diagnosis, and facial recognition, computer vision is the backbone concept supporting these real-life applications. Computer vision is the field of artificial intelligence that helps the computer understand and interpret the information in any picture or video. This kind of technology has played a crucial role in the evolution of how we communicate with computers. Thanks to the advancement of artificial intelligence in deep learning and neural networks, improvements in computer vision have skyrocketed. Other supporting techniques have helped in the field of computer vision, such as:

• Image segmentation involves dividing an image into separate regions or segments for individual analysis.

• Object detection identifies specific objects within an image, with advanced techniques capable of recognizing multiple objects using bounding boxes.

• Facial recognition goes beyond object detection to identify and differentiate specific individuals within images.

• Edge detection focuses on identifying the outer boundaries of objects or landscapes to improve image understanding.

• Pattern detection recognizes recurring shapes, colors, and visual elements in images.

• Image classification categorizes images into distinct classes or categories.

• Feature matching is a pattern detection method that finds similarities between images to aid in classification.

Similar to these techniques, the Hough line transform is a reliable technique to isolate distinct features of a particular shape within an image. Shifting gears, let's explore the main focus of this Answer, the Hough line transform.

What is the Hough line transform?

As previously mentioned, Hough line transform is a computer vision technique to detect straight lines in an image. It transforms the image space into a parameter space called the Hough space. This allows for the identification of lines based on their geometric properties. But before we apply the Hough line technique, we have to use the edge detection algorithm. This is so we can procure an edge image that will be the input for the Hough line algorithm.

Read up in detail about line detection using Hough line transform.

Edge detection algorithm

Edge detection is an image processing method used to locate areas in a digital image where there are abrupt changes in brightness, resulting in discontinuities. These discontinuities, referred to as edges or boundaries, mark the regions where the image brightness undergoes rapid variations. There are many methods used for edge detection, and some of the most commonly used are listed below:

• Canny algorithm

• Laplacian algorithm

• Prewitt algorithm

Hough space

We can learn more about the algorithm through the understanding of Hough space. The Hough Space is a two-dimensional plane with a horizontal axis representing the slope (a) and a vertical axis representing the intercept (b) of a line on the edge image. 

In the Hough Transform algorithm, a line on the edge image corresponds to a point in the Hough Space, defined by its slope and intercept. Conversely, an edge point on the edge image can generate multiple lines in the Hough Space. The Hough Space is utilized in the algorithm to determine the presence of lines in the edge image.

How does Hough line work

The Hough line transform depends on the Hough space, which is a 2D plane. This means there are different coordinate systems we can use, such as

Cartesian coordinate system

Polar coordinate system

We use the polar coordinate system for the Hough line transform. In general, for any point $(x,y)$, we can find out the lines going through it through the polar coordinate formula. This also represents that each pair (r,θ) represents each line passing through the point. Usually, when we plot these lines going through the point, we get a sinusoidal curve. When we do the same operation of plotting all the points in an image, if the curves of two different points intersect, that means that both points belong to the same line.

The Hough line transform works by keeping track of the intersection points between curves at every point in the edge image. If the intersections exceed a threshold, it declares it a line. In other words, the line can be detected by finding the number of intersections between curves just as it shows in the above illustration. The more curves intersect, the more points the line represented by that intersection has. We can define a threshold for the minimum number of intersections needed to detect a line.

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Conclusion 

The Hough Line Transform is a feature extraction method used in image analysis, computer vision, and digital image processing. It detects straight lines in an image by finding the intersections of curves in a parameter space.