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. 2021 May 26;21(11):3703. doi: 10.3390/s21113703

Algorithm 2. Filtering based on NKNN

Input:

S_{f} (n_{f} \times 3 p o i n t s)

Output:

S_{o} (n_{o} \times 3 p o i n t s), S_{g} (n_{g} \times 3 p o i n t s)

1:

C o n s t r u c t t h e K - D t r e e o f S_{f}

2: for

e a c h p o i n t

do

3:

C a l c u l a t e t h e k n e a r e s t n e i g h b o r s

4:

p_{i} = (x_{1}, x_{2}, \dots, x_{n})

5: end for

6: for

n e i g h b o r s o f e a c h p o i n t

do

7:

μ_{j} = \frac{1}{k} \sum_{j = 1}^{k} x_{j}

8:

{\tilde{x}}_{j} = x_{j} - μ_{j}

9:

C = [{\tilde{x}}_{1}, {\tilde{x}}_{2}, \dots, {\tilde{x}}_{k}]

10:

C o m p u t e S V D : U Σ V^{T} = C C^{T}

11:

v_{i} \leftarrow T h e e i g e n v e c t o r o f t h e m i n i m u m e i g e n v a l u e i n U

12: end for

13: for

p i c k v_{i} \in Ω a t r a n d o m

do

14: for

e a c h v_{j} \in Ω

do

15:

θ = \frac{v_{i} v_{j}}{| | v_{i} | | | | v_{j} | |}

16: if

θ < δ

then

17:

x_{i} \in S a m e c l a s s

18:

r e m o v e v_{i} i n Ω

19: end if

20: end for

21: if

Ω i s n o n e

then

22:

b r e a k

23: end if

24: end for

25: for

e a c h p o i n t x_{i}

do

26:

n c l a s s \leftarrow t h e m o s t c l a s s i n t h e n e i g h b o r h o o d

27:

x_{i} \in n c l a s s

28: end for

29: if

n c l a s s i s m a x

then

30:

G r o u n d S_{g} \leftarrow t h e p o i n t s o f n c l a s s

31: else

32:

N o i s e S_{o} \leftarrow o t h e r n c l a s s

33: end if