Algorithm 1 Hierarchical Sparse Label Propagation

Input: M pelvic-bone-aligned training images and their segmentation groundtruths {(Ii, Si), i = 1,…, M}, and the new treatment image Inew to be segmented.

Output: The final prostate probability map Sfinal of Inew.

1. Perform sparse label fusion based on Equations 4 and 6 to calculate SM A from registered training images, and initialize $S_{\mathit{fuse}}^1=S_{MA}$.

2. Initialize ${\delta }_p^1=0.95$ and ${\delta }_n^1=0.05$.

3. Initialize ψ1 = ∅.

4. FOR voxels $\overrightarrow{x}\in I_{\mathit{new}}$

5.    IF $S_{\mathit{fuse}}^1\left(\overrightarrow{x}\right)\ge {\delta }_p^1$ or $S_{\mathit{fuse}}^1\left(\overrightarrow{x}\right)\le {\delta }_n^1$

6.      ${\Psi }^1={\Psi }^1\cup \overrightarrow{x}$.

7.    END IF

8. END FOR

9. FOR k = 2 to K

10.     FOR voxels $\overrightarrow{x}\notin {\Psi }^{k-1}$

11.        Calculate $S_{\mathit{context}}^k\left(\overrightarrow{x}\right)$ by Equation 9.

12.        Update $S_{\mathit{fuse}}^k\left(\overrightarrow{x}\right)$ by Equation 8.

13.     END FOR

14.     Set ψk = ∅.

15.     Update ${\delta }_p^k$ and ${\delta }_n^k$ by Equation 7.

16.     FOR voxels $\overrightarrow{x}\in I_{\mathit{new}}$

17.        IF $S_{\mathit{fuse}}^k\left(\overrightarrow{x}\right)\ge {\delta }_p^k$ or $S_{\mathit{fuse}}^k\left(\overrightarrow{x}\right)\le {\delta }_n^k$

18.          ${\Psi }^k={\Psi }^k\cup \overrightarrow{x}$.

19.        END IF

20.     END FOR

21. END FOR

22. Set $S_{\mathit{final}}=S_{\mathit{fuse}}^k$.

23. Return Sfinal.