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

Algorithm 1. GPCA outliers removed

Input:

S (n \times 3 p o i n t s)

Output:

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

1:

S = (x_{n}, y_{n}, z_{n})

2:

μ = (\frac{1}{n} \sum_{i = 1}^{n} x_{i}, \frac{1}{n} \sum_{i = 1}^{n} y_{i}, \frac{1}{n} \sum_{i = 1}^{n} z_{i})

3: for

e a c h p o i n t

p_{i} = (x_{i}, y_{i}, z_{i}) \in S

do

4:

p_{i} = p_{i} - μ

5: end for

6:

C = S

7:

Γ = \frac{1}{n} C^{T} C

8:

U Σ V^{T} = Γ

9:

V = (t_{1}, t_{2}, t_{3})

10:

Δ T = (t_{1}, t_{2})

11:

S_{q} = S Δ T

12:

b_{x} = (x_{\max} - x_{\min}) / l

13:

b_{y} = (y_{\max} - y_{\min}) / l

14: for

e a c h p o i n t

v_{i} = (x_{i}, y_{i}) \in S_{q}

do

15:

h_{x i} = r o u n d ((x_{i} - x_{\min}) / b_{x})

16:

h_{y i} = r o u n d ((y_{i} - y_{\min}) / b_{y})

17:

h_{i} = (h_{x i}, h_{y i})

18: end for

19: for

e a c h g r i d (i, j)

do

20:

C o u n t t h e n u m b e r k_{i j} o f p o i n t s i n e a c h c e l l

21: if

k_{i j} < k_{σ}

then

22:

N o i s e f \leftarrow P o i n t s i n g r i d (i, j)

23: else

24:

W a l l p o i n t s w \leftarrow P o i n t s i n g r i d (i, j)

25: end if

26: end for

27:

G e t S_{f} a n d S_{w}