362
V. L. Kondarattsev et al.
edges is defined by the vertices belonging to polygons, i.e., if two vertices belong
to the same polygon, then there is an edge in the graph between them. Then, the
set of connected polygons is formed as the set of connectivity components of an
undirected graph G [10]:
M n,m = (V n , F m ) =
k
∪
i=1
M n i ,m i =
k
∪
i=1
V n i , F m i
,
F m i ∩ F m j = ∅, i, j = 1, . . . , k, i = j,
where k is the number of connectivity components of graph G, V n i are the vertices
that belong to the connectivity component with number i, F m i are the polygons
that are formed by vertices from V n i .
3. For each set of vertices V n i of model M n i ,m i =
V n i , M m i
, we compute its
geometrical median m i [11]:
m i = arg min
y∈R 3
x∈V n
y − x, i = 1, . . . , k.
4. Let us set the parameter α ∈ [0; 1] is the ratio of the maximum assumed number
of vertices in noise objects to the number of scan vertices, β ∈ [0; 1] is the ratio of
the minimum distance of the geometric median from the center of the bounding
box B
M n,m
.
5. Compute d
max
=
x
1
max −x
1
min
2
2 +
x
2
max −x
2
min
2
2 .
6. Let ‘us create a set of objects of interest S = ∅.
7. For each model M n i ,m i =
V n i , F m i
with i = 1, . . . , k :
a. If n i > α · n and (m1−d
max
1 )
2 +(m 2 −d
max
2 )
2
d max
≤ β, then we add M n i ,m i to the set
S: S = S ∪
M n i ,m i
.
8. We will get a new model M
k,l =
V
k , F
l
, where V
k =
(V,F)∈S
V, F
l =
(V,F)∈S
F.
The result of applying this algorithm to the scan with the removed floor obtained
at the previous stage is shown in Fig. 24.3.
As a result, the F m function consists of algorithms: removing the reference surface
and removing noise along with extraneous objects. The implementation of these two
algorithms is available on our GitHub page [12].
24.4.2 Point Cloud Classification
As mentioned above, we chose the implementation of the LDGCNN architecture to
classify the selected model. The model was trained from scratch based on the Model
Net 40 dataset, which, like most other 3D datasets, consists of models drawn by 3D
V. L. Kondarattsev et al.
edges is defined by the vertices belonging to polygons, i.e., if two vertices belong
to the same polygon, then there is an edge in the graph between them. Then, the
set of connected polygons is formed as the set of connectivity components of an
undirected graph G [10]:
M n,m = (V n , F m ) =
k
∪
i=1
M n i ,m i =
k
∪
i=1
V n i , F m i
,
F m i ∩ F m j = ∅, i, j = 1, . . . , k, i = j,
where k is the number of connectivity components of graph G, V n i are the vertices
that belong to the connectivity component with number i, F m i are the polygons
that are formed by vertices from V n i .
3. For each set of vertices V n i of model M n i ,m i =
V n i , M m i
, we compute its
geometrical median m i [11]:
m i = arg min
y∈R 3
x∈V n
y − x, i = 1, . . . , k.
4. Let us set the parameter α ∈ [0; 1] is the ratio of the maximum assumed number
of vertices in noise objects to the number of scan vertices, β ∈ [0; 1] is the ratio of
the minimum distance of the geometric median from the center of the bounding
box B
M n,m
.
5. Compute d
max
=
x
1
max −x
1
min
2
2 +
x
2
max −x
2
min
2
2 .
6. Let ‘us create a set of objects of interest S = ∅.
7. For each model M n i ,m i =
V n i , F m i
with i = 1, . . . , k :
a. If n i > α · n and (m1−d
max
1 )
2 +(m 2 −d
max
2 )
2
d max
≤ β, then we add M n i ,m i to the set
S: S = S ∪
M n i ,m i
.
8. We will get a new model M
k,l =
V
k , F
l
, where V
k =
(V,F)∈S
V, F
l =
(V,F)∈S
F.
The result of applying this algorithm to the scan with the removed floor obtained
at the previous stage is shown in Fig. 24.3.
As a result, the F m function consists of algorithms: removing the reference surface
and removing noise along with extraneous objects. The implementation of these two
algorithms is available on our GitHub page [12].
24.4.2 Point Cloud Classification
As mentioned above, we chose the implementation of the LDGCNN architecture to
classify the selected model. The model was trained from scratch based on the Model
Net 40 dataset, which, like most other 3D datasets, consists of models drawn by 3D