Algorithm 2: Proposed circle detection algorithm.

Result: $({\mathbf{c}}^{★},r^{★})$ minimizing $J_{MC}(\mathbf{c},r)$  $i=1$;  ${\mathcal{S}}_m^{(0)}=$ the set of the entire pixels in the input image;    Sort ${\left\{J_{MC}({\mathbf{c}}_j,r_j)\right\}}_{j=1}^{i-1}$ in ascending order;  $({\mathbf{c}}^{★},r^{★})=({\mathbf{c}}_1,r_1)$ with the least $J_{MC}(\mathbf{c},r)$ in the sorted set.