Circles

We can extend the Hough transform to other shapes that can be expressed parametrically. For example, a circle of

fixed radius can be described fully by the location of its center (x, y).

Think of each feature (edge) point on the circle as saying, ”if I’m on the circle, the center must be in one of these

places”. It turns out that the locus of these votes is itself a circle.

But what about circles of unknown size? In this case, we need a third parameter: the radius of the circle. So, we can

parameterize circles of arbitrary size by (x, y, r). Instead of casting votes in a circular pattern into a two-dimensional

accumulator, we cast votes in circles of successively larger size in a three-dimensional accumulator.