$T_f$

The number of failures that can be tolerated. The running time must be finite, regardless of whether the correct results are obtained.

$T_r$

The ratio threshold of co-circle pixels. It is used to replace the global threshold

$T_g$

The number of pixels at the edge of circle, $T_g=2\pi r{T}_r$ , r is the radius of possible circle.

$T_a$

The threshold of distance. The distance between any two agent pixels of the possible circle should be larger than $T_a$ .

$T_d$

The distance threshold for co-circle. It means that the fourth selected pixel is closed to the possible circle, which is determined by the other three pixels.

$T_c$

The number of circles that we want to detect in image.

$T_{rL}$

The minimal radius that the possible circle should fit.

$T_{rU}$

The maximal radius that the possible circle should fit.