Algorithm 2: SP-FCM Clustering Algorithm

1. Input: Pre-processed cryo-EM image $I_p$

2. Return: Super-clustered image $I_{sc}$

3. Set number of clusters, $k$

4. Generate the 2D super-pixel over segmentation image

5.  begin/*SLIC*/

6.  Initialize the cluster centers $C_k={\left[l_k,x_k,y_k\right]}^T$

7.  Move the cluster center cluster centers to the lowest gradient position in a 3 × 3 neighborhood.

8.  Set label $l\left(i\right)=-1$ for each pixel $i$.

9.  Set distance $d\left(i\right)=\infty$ for each pixel $i$.

10.  repeat

11.   for $k=1$ to $K$ do

12.    for each pixel $i$ in $2S\times 2S$ region around $C_k$ do

13.     Compute distance D between $C_k$ and $i$.

14.     if $D<d\left(i\right)$ then

15.      Set $d\left(i\right)=D$.

16.      Set $l\left(i\right)=k$.

17.     end if

18.    end for

19.   end for

20.   Compute new cluster center ${\mathsf{\theta }}_k$.

21.   Compute residual error $E$.

22.  until $E\le threshold$

23. generate binary mask

24. end/* SLIC */

25. repeat

26.   for n = 1 to $N$ do

27.    Update membership ${\mathrm{u}}_{\mathrm{nk}}$ by taking sum of distance ratios of cluster $\mathrm{k}$ and all clusters.

28.                 $u_{nk}={\displaystyle \sum }_{i=1}^K{\left(\frac{d\left(x_n,{\theta }_k\right)}{d\left(x_n,{\theta }_i\right)}\right)}^{-\frac{1}{m-1}}$

29.       end for

30. until change in cluster centers are small

31. for k = 1 to $K$ do/* foe each clustered image */

32.    ${\mathrm{I}}_{\mathrm{sc}}\leftarrow \mathrm{Min}\left(\mathrm{Nonzero}\left({\mathrm{I}}_{\mathrm{k}}\right)\right)$/* extract the total number of the non-zero element in each cluster and select the minimum one as a final selected clustered image */

33. end for