Question

I am just being adventurous and taking my first baby step toward computer vision. I tried to implement the Hough Transformation on my own but I just don’t get the whole picture. I read the wikipedia entry, and even the original “use of the hough transformation to detect lines and curves in pictures” by richard Duda and Peter Hart, but didn’t help.

Can someone help explaining to me in a more friendly language?

Answer 1

It’s more common to think of a line in rectangle coordinates, i.e. y = mx + b. As the Wikipedia article states, a line can also be expressed in polar form. The Hough transform exploits this change of representation (for lines, anyway. The discussion can also be applied to circles, ellipses, etc.).

The first step in the Hough transform is to reduce the image to a set of edges. The Canny edge-detector is a frequent choice. The resulting edge image serves as the input to the Hough process.

To summarize, pixels “lit” in the edge image are converted to polar form, i.e. their position is represented using a direction theta and a distance r – instead of x and y. (The center of the image is commonly used as the reference point for this change of coordinates.)

The Hough transform is essentially a histogram. Edge pixels mapping to the same theta and r are assumed to define a line in the image. To compute the frequency of occurrence, theta and r are discretized (partitioned into a number of bins). Once all edge pixels have been converted to polar form, the bins are analyzed to determine the lines in the original image.

It is common to look for the N most frequent parameters – or threshold the parameters such that counts smaller than some n are ignored.

I’m not sure this answer is any better than the sources you originally presented – is there a particular point that you are stuck on?