Realization principle of cumulative graph of OPENCV Hough circle transformation. You can get any score you want.

Here, I will tell you how to use a technique similar to the standard Hough transform to detect circles (which is very important in computer vision applications). This article assumes that you know how the Hough transform works, or that you have understood the previous articles in this series (Hough transform).

Parameterization

A circle can be completely described by three pieces of information: the center (a, b) and the radius. (The center consists of two parts, so there are three parts.)

x = a + Rcosθ

y = b + Rsinθ

When θ changes from 0 to 360, a complete circle with radius r will be generated.

Therefore, using the circular Hough transform, we expect to find the triplets of (x, y, r), which are probably circles in the image. In other words, we want to find three parameters. Therefore, the parameter space is 3D … which means that if you don't take your time, things will get very bad. Even if your programming language uses virtual memory, out-of-memory errors are common.

So let's start with something simple.

Suppose r is known.

First, let's assume that you are looking for a circle with a specific radius, that is, r is known. The equation for each circle is:

x = a + Rcosθ

y = b + Rsinθ

Therefore, every point in xy space is equivalent to a circle in ab space (r is not a parameter, we already know). This is because by rearranging the equations, we get:

a = x 1–rcosθ

b = y 1–rsinθ

For a specific point (x 1, y 1). θ scans from 0 to 360 degrees.

So, the flow of events is like this:

Load image

Detect edges and generate binary images

For each "edge" pixel, a circle is generated in ab space.

For each point on the circle in ab space, a "vote" is made in the accumulator unit.

The cell with more votes is the center.

When r is unknown.

When the radius is unknown, the simplest solution is to guess. Suppose R = 1 and run the same algorithm. Then run it again assuming R = 2. Suppose R = 3… ... and so on.

What is the upper limit of r? A safe limit is the length of the diagonal of the image. There cannot be a circle with a radius greater than or equal to the diagonal on the image.