As part of an image recognition project I was working on today I was introduced to the Hough transform. This transform is useful for finding lines and other regular shapes (circles, ellipses) in an image. Every pixel on the image is sampled, and an accumulator array (whose dimension is equal to the number of parameters in the shape: line=2, circle=3, ellipse=5) is used to tabulate votes based on edges in that pixels neighborhood. This description shows several nice image pairs.

The similar Radon transform is in some sense a continuous version of the Hough transform, and used in tomography. The complex form of the Radon transform is the Penrose transform, which is somehow important in twistor theory.