Algorithm 1: Optimization algorithm

Input: Noisy point cloud $Y^{\prime }$, number of patches m, number of nearest neighbors k,

number of adjacent patches $\epsilon$, trace constraint $C^{*}$.

Output: Denoised point cloud Y.

1     Initialize Y with $Y^{\prime }$;

2     for iter = 1, 2,… do

3     estimate normal for Y;

4     initialize m empty patches V;

5     find the adjacent $\epsilon$ patches;

6     initialize M with identity matrix;

7     compute the feature distance $s_i-s_j$ for each vertex pair(i,j);

8     solve M;

9     compute adjacency matrix W over all patches;

10         compute Laplacian matrix L;

11         solve Y with (14);

12    end