Algorithm 1: SP-k-Means 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 from the super-clustered image

5. begin/* SLIC */

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

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.    Determine the closest representative, ${\theta }_k$, for $x_n$

28.    Set label for data point $n$ to $k$

29.   end for

30.   for k = 1 to K do

31.    Update cluster representative ${\theta }_k$ to the mean with cluster label $k$

32.                  ${\mathsf{\theta }}_k=\frac{{\sum }_{n=1}^N{u}_{nk}{x}_n}{{\sum }_{n=1}^N{u}_{nk}}$

33.   end for

34.  until change in cluster centers are small

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

36.   ${\mathrm{I}}_{\mathrm{sc}}\leftarrow \mathrm{Min}\left(\mathrm{Nonzero}\left({\mathrm{I}}_{\mathrm{k}}\right)\right)$/* extract the total number of the non-zero element in each cluster and select the cluster that has the minimum total number of the non-zero element */

37.   end for