Algorithm 3: SP-IBC 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. Transform the intermedia 2D image map ${\mathrm{I}}_{\mathrm{m}}$ into 1D ${\mathrm{I}}_{\mathrm{v}}$ which has the intensity values of all the pixels.

26. $\mathrm{L}$← height × width where $\mathrm{L}$ is the total number of pixels in the ${\mathrm{I}}_{\mathrm{p}}$

27. ${\mathrm{V}}_{\mathrm{Max}}$← $\mathrm{Max}\left[{\mathrm{I}}_{\mathrm{v}}\right]$/* maximum values of intensity in the image */

28. ${\mathrm{V}}_{\mathrm{Min}}$← $\mathrm{Min}\left[{\mathrm{I}}_{\mathrm{v}}\right]$/* minimum values of intensity in the image */

29. K← 4/* set the number of initial cluster based on the interval size = 0.15 */

30. for $i$ = 1 to $K$ do

31.  ${\mathrm{Int}}_{\mathrm{s}}$← $\left(\frac{{\mathrm{V}}_{\mathrm{Max}}-{\mathrm{V}}_{\mathrm{Min}}}{\mathrm{K}\times 0.15}\right)\times 0.15/$* set the interval size as the vector of intensity range (max min) divided by the cluster number $\mathrm{K}$ */

32. end for

33. for $i$ = 1 to $K$ do

34.  ${\mathsf{\theta }}_{\mathrm{k}}\leftarrow {\mathrm{Int}}_{\mathrm{s}}\left[\mathrm{i}\right]$ /* initialize the cluster center based on the interval size */

35. end for

36. repeat

37.    for $i$ = 1 to $K$ do

38.    for $j$ = 1 to $L$ do

39.     $\mathrm{Cluster}\left[\mathrm{ind}\right]\leftarrow \min (\mathrm{abs}\left({\mathsf{\theta }}_{\mathrm{k}}\left[\mathrm{i}\right]-{\mathrm{I}}_{\mathrm{v}}\left[\mathrm{j}\right]\right)$/* assign ${\mathrm{x}}_{\mathrm{n}}$ the cluster $\mathrm{k}$ whose center (${\mathsf{\theta }}_{\mathrm{k}})$ is closest to ${\mathrm{x}}_{\mathrm{n}}$ according to the absolute intensity difference between the two */

40.   end for

41.  end for

42.  for $n$ = 1 to $K$ do

43.   ${\mathsf{\theta }}_{\mathrm{k}}\left[\mathrm{n}\right]\leftarrow \sum _{\mathrm{n}=1}^{\mathrm{k}}\frac{\mathrm{Cluster}\left[\mathrm{k}\right]}{\mathrm{count}\left(\mathrm{ones}\right)}$/* update the mean ${\mathsf{\theta }}_{\mathrm{k}}$ of each cluster by calculating the average intensity values of the pixels assigned to the cluster */.

44.  end for

45. until there is no change in cluster centers.