${T}_{f}$ | 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. |