It goes without saying that image recognition is an essential issue in computer science, especially with the unprecedented growth of deep learning. Its has various applications, from cat face for google to my subject which is mesoscale eddy identification. However, today I am going to introduce a relatively classic method for detect basic geometric entites such as lines and circles, and a popular algorithm in physical oceanography, the Hough transform.

## Theory

Apparrently, each line in an plane can be described as:

$$
y = kx + b.
$$

However, the parameter k is nonlinear correlated with the angle \(\theta\), as follows:

$$
y = (-\frac{\cos\theta}{\sin\theta})x+\frac{r}{\sin\theta},
$$

Thus, we have:

$$
r = x\cos\theta+y\sin\theta.
$$

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