# Segmentation Based Classification of 3D Urban Point Clouds: A Super-Voxel Based Approach with Evaluation

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

#### 2.1. Segmentation of 3D Data

#### 2.1.1. Specialized Features and Surface Discontinuities

#### 2.1.2. Graph Clustering

#### 2.1.3. Geometrical Primitives

#### 2.1.4. Markov Random Fields

#### 2.2. Classification of 3D Data

#### 2.2.1. Discriminate Models and Model Fitting

#### 2.2.2. Features Based

## 3. Voxel Based Segmentation

#### 3.1. Voxelisation of Data

1: | repeat |

2: | Select a 3D point for voxelisation |

3: | Find all neighboring points to be included in the voxel using r-NN within the specified maximum voxel length |

4: | Transform voxel into s-voxel by first finding and then assigning to it all the properties found by using PCA, including surface normal. |

5: | until all 3D points are used in a voxel |

6: | repeat |

7: | Specify an s-voxel as a principal link |

8: | Find all secondary links attached to the principal link |

9: | until all s-voxels are used |

10: | Link all principal links to form a chain removing redundant links in the process |

#### 3.2. Transformation of Voxels into Super-Voxels

**V**_{X,Y,Z}: geometrical center of the voxel;**V**_{R,G,B}: mean R, G, & B value of constituting 3D points;- Var(R, G, B): maximum of the variance of R, G & B values;
**V**_{I}: mean laser reflectance intensity value of constituting 3D points;- Var(I): variance of laser reflectance intensity values;
- s
_{X,Y,Z}is the voxel size along each axis X, Y & Z; - Surface normals: A surface normal is calculated using PCA (Principal Component Analysis). The PCA method has been proved to perform better than the area averaging method [32] to estimate the surface normal. Given a point cloud data set $\mathcal{D}={\left\{{x}_{i}\right\}}_{i=1}^{n}$, the PCA surface normal approximation for a given data point p ∈ $\mathcal{D}$ is typically computed by first determining the k-Nearest Neighbors, x
_{k}∈ $\mathcal{D}$, of p. Given the K neighbors, the approximate surface normal is then the eigenvector associated with the smallest eigenvalue of the symmetric positive semi-definite matrix$$\mathbf{P}=\sum _{k=1}^{K}{({x}_{k}-\overline{p})}^{T}({x}_{k}-\overline{p})$$The estimated surface normal is ambiguous in terms of sign; to account for this ambiguity it is homogenized using the dot product. Yet for us the sign of the normal vector is not important as we are more interested in the orientation. A surface normal is estimated for all the points belonging to a voxel and is then associated with that particular voxel.

#### 3.3. Clustering by Link-Chain Method

**V**

_{P}be a principal link and

**V**

_{n}be the n

^{th}secondary link. Each

**V**

_{n}is linked to

**V**

_{P}if and only if the following three conditions are fulfilled:

**V**_{PX,Y,Z},**V**_{nX,Y,Z}are the geometrical centers;**V**_{PR,G,B},**V**_{nR,G,B}are the mean R, G & B values;**V**_{PI},**V**_{nI}are the mean laser reflectance intensity values;- w
_{C}is the color weight equal to the maximum value of the two variances Var(R, G, B), i.e., max(**V**_{PVar(R,G,B)},**V**_{nVar(R,G,B)}); - w
_{I}is the intensity weight equal to the maximum value of the two variances Var(I).

_{D}is the distance weight given as $\frac{\left({\mathbf{V}}_{{P}_{{s}_{X,Y,Z}}}+{\mathbf{V}}_{{n}_{{s}_{X,Y,Z}}}\right)}{2}$. Here s

_{X,Y,Z}is the voxel size along X, Y & Z axis respectively. c

_{D}is the inter-distance constant (along the three dimensions) added depending upon the density of points and also to overcome measurement errors, holes and occlusions, etc. The value of c

_{D}needs to be carefully selected depending upon the data (see Section 6.5 for more details on the selection of this value). The orientation of normals is not considered in this stage to allow the segmentation of complete 3D objects as one entity instead of just planar faces.

## 4. Classification of Segmented Objects

**a.****Surface normals:**The orientation of the surface normals is found essential for the classification of ground and building faces. For ground object the surface normals are predominantly (threshold values greater than 80%) along Z-axis (height axis), whereas for building faces the surface normals are predominantly (threshold values greater than 80%) parallel to the X-Y axis (ground plane), see Figure 4.**b.****Geometrical center and barycenter:**The height difference between the geometrical center and the barycenter along with other properties is very useful in distinguishing objects like trees and vegetation, etc., where h(`barycenter − geometrical center`) > 0, with h being the height function.**c.****Color and intensity:**Intensity and color are also an important discriminating factor for several objects.**d.****Geometrical shape:**Along with the abovementioned descriptors, geometrical shape plays an important role in classifying objects. In 3D space, where pedestrians and poles are represented as long and thin with poles being longer, cars and vegetation are broad and short. Similarly, as roads represent a low flat plane, the buildings are represented as large (both in width and height) vertical blocks (as shown in Figure 5). The values for these comparison threshold on the shape and size for each of the object types are set accordingly.

## 5. Evaluation Metrics

_{i}, i ∈ {1, ⋯ , N}, be the total number of s-voxels distributed into objects belonging to N number of different classes, i.e., this serves as the ground truth, and let t

_{ji}, i ∈ {1, ⋯ , N}, be the total number of s-voxels classified as a particular class of type-j and distributed into objects belonging to N different classes (for example an s-voxel classified as part of the building class may actually belong to a tree). Then the ratio S

_{jk}(j is the class type as well as the row number of the matrix and k ∈ {1, ⋯ , N}) is given as:

_{jk}are calculated for each type of class and are used to fill up each element of the confusion matrix, row by row (refer to tables in Section 6.1 for instance). Each row of the matrix represents a particular class.

**True Positive**rate**TP**= S_{11}(i.e., the diagonal of the matrix represents the**TP**s)**False Positive**rate $\mathbf{FP}=\sum _{m=2}^{N}{S}_{1m}$**True Negative**rate**TN**= (1 −**FP**)**False Negative**rate**FN**= (1 −**TP**)

**TP**s gives the Segmentation ACCuracy (

**SACC**), similar to the voxel scores recently introduced by Douillard et al. [35]. The effects of unclassified s-voxels are automatically incorporated in the segmentation accuracy. Using the above values, the Classification ACCuracy (

**CACC**) is given as:

**CACC**is calculated for all N types of classes of objects present in the scene. Overall Classification ACCuracy (

**OCACC**) can then be calculated as

**OSACC**) can also be calculated. The values of T

_{i}and t

_{ji}used above are laboriously evaluated by hand matching the voxelised data output and the final classified s-voxels and points.

## 6. Results

- 3D data sets of Blaise Pascal University;
- 3D Urban Data Challenge data set [36].

#### 6.1. 3D Data Sets of Blaise Pascal University

_{D}= 0.25 m.

#### 6.2. 3D Urban Data Challenge Data Set

_{D}= 0.15 m were used for this data set. Results (image results will be available in our website along with performance measures for comparison, after paper acceptance) of different scenes from this data set are shown in Figures 9, 10 and 11 and Tables 5, 6 and 7.

#### 6.3. Comparison of Results with Existing Evaluation Methods

#### 6.4. Performance Evaluation and Discussion

**OCACC**) was found to be slightly better than the segmentation accuracy (

**OSACC**). Not taking anything away from the segmentation method, one of the main reasons is that the 5 types of objects chosen for classification are distinctly different and that if the segmentation is good, classification becomes easier and a simple method like the one proposed is sufficient.

**SACC**and

**CACC**). These results show that in most of the cases, the buildings, roads and poles have been classified the best with consistent scores of

**SACC**and

**CACC**higher than 90%, except in the case of data set 3 in which the building classification accuracy

**CACC**is slightly deteriorated due to a large overlapping tree that is wrongly classified as a building rather than a tree. This is also reflected in the low Homogeneity value of 0.670 obtained when calculating V-measure for this data set. The classification of cars is generally good and the results are consistent but they are slightly hampered due to occlusions in some scenes (data set 3:

**CACC**86.3%, Scene B:

**CACC**89.5%). In case of trees, the

**SACC**and

**CACC**are found to vary the most. This is mainly due to the fact that the proposed classification method is based on local descriptors and geometrical features, which in the case of trees are very difficult to define (due to large variation of shapes, sizes and types). Thus, where the proposed algorithm succeeded in classifying smaller trees of more classical shapes with higher

**SACC**and

**CACC**scores, it produced low

**SACC**and

**CACC**scores of 68% and 79.4% respectively for Scene B. The Recall and Precision scores obtained during the calculation of F-measure for the tree class of this scene were found to be similarly low as well (0.682 and 0.614 respectively).

#### 6.5. Effect of Voxel Size on Classification Accuracy and Choice of Optimal Values

_{D}also needs to be adjusted accordingly.

_{D}were varied from 0.1 m to 1.0 m on data set 1 and corresponding classification accuracy was calculated. The results are shown in Figure 12(a). Then for the same variation of maximum voxel size and c

_{D}, the variation in processing time was studied as shown in Figure 12(b).

_{a}is chosen for comparison purposes (along Z-axis time varies from 0 to 200T

_{a}). This makes the comparison results independent of the processor used, even though the same computer was used for all computations.

_{D}) but the computational cost increases. It is also evident that variation in value of c

_{D}has no significant impact on time t. It is also observed that after a certain reduction in voxel size, the classification result does not improve much but the computational cost continues to increase manifolds. As both

**OCACC**and time (both plotted along Z-axis) are independent, using and combining the results of the two 3D plots in Figure 12 we can find the optimal value (in terms of

**OCACC**and t) of maximum voxel size and c

_{D}depending upon the final application requirements. For our work, we have chosen a maximum voxel size of 0.3 m and c

_{D}= 0.25 m.

#### 6.6. Influence of RGB Color and Reflectance Intensity

#### 6.7. Considerations for Further Improvements

## 7. Conclusions

**OSACC**) of 87% and an overall classification accuracy (

**OCACC**) of about 90%. The results indicate that with good segmentation, a simplified classification method like the one proposed is sufficient.

_{D}) but at the cost of processing time. Thus a choice of an optimal value, as discussed, is recommended. The study also demonstrates the importance of using laser reflectance intensity values along with RGB colors in the segmentation and classification of urban environment, as they are more illumination invariant and more consistent.

## Acknowledgments

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**Figure 1.**A number of points is grouped together to form cubical voxels of maximum size 2r. The actual voxel sizes vary according to the maximum and minimum values of the neighboring points found along each axis to ensure the profile of the structure.

**Figure 2.**Clustering of s-voxels using a link-chain method is demonstrated.

**(a)**shows s-voxel 1 taken as principal link in red and all secondary links attached to it in blue;

**(b)**and

**(c)**show the same for s-voxels 2 and 3 taken as principal links;

**(d)**shows the linking of principal links (s-voxels 1, 2 & 3) to form a chain removing redundant secondary links.

**Figure 4.**(a) Normals of building—shows surface normals of building s-voxels that are parallel to the ground plane. In (b) Normals of road—it can be clearly seen that the surface normals of road surface s-voxels are perpendicular to the ground plane.

**Figure 6.**(a) 3D data points—shows 3D data points of data set 1. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 7.**(a) 3D data points—shows 3D data points of data set 3. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 8.**(a) 3D data points—shows 3D data points of data set 3. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 9.**Segmentation and classification results for a particular scene-A of scenes from 3D Urban Data Challenge 2011, image

`# ParkAvenue SW12 piece07`[36]. (a) 3D data points—shows 3D data points of data set 1. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 10.**Segmentation and classification results for a particular scene-B of scenes from 3D Urban Data Challenge 2011, image

`# ParkAvenue SW12 piece00`[36]. (a) 3D data points—shows 3D data points of data set 1. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 11.**Segmentation and classification results for a particular scene-C of scenes from 3D Urban Data Challenge 2011, image

`# ParkAvenue SW14 piece00`[36]. (a) 3D data points—shows 3D data points of data set 1. (b) Voxelisation and segmentation into objects—shows s-voxel segmentation of 3D points (along with orientation of normals). (c) Labeled points—shows classification results (labeled 3D points).

**Figure 12.**(a) Influence of voxel size on OCACC—is a 3D plot in which the effect of maximum voxel size and variation on OCACC is shown. In (b) Influence of voxel size on processing time—the effect of maximum voxel size and variation on processing time is shown. Using the two plots we can easily find the optimal value for maximum voxel size and c

_{D}.

Data Set # | Number of 3D Data Points | Number of Segmented s-voxels | Number of Segmented Objects |
---|---|---|---|

# 1 | 27, 396 | 7, 924 | 41 |

# 2 | 53, 676 | 6, 928 | 75 |

# 3 | 110, 392 | 18, 541 | 237 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.943 | 0.073 | 0 | 0 | 0 | 0.935 |

Road | 0.007 | 0.858 | 0.015 | 0.008 | 0 | 0.914 |

Tree | 0 | 0.025 | 0.984 | 0 | 0 | 0.979 |

Pole | 0 | 0.049 | 0 | 0.937 | 0 | 0.944 |

Car | – | – | – | – | – | – |

Overall segmentation accuracy: OSACC | 0.930 | |||||

Overall classification accuracy: OCACC | 0.943 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.996 | 0.007 | 0 | 0 | 0 | 0.995 |

Road | 0 | 0.906 | 0.028 | 0.023 | 0.012 | 0.921 |

Tree | 0 | 0.045 | 0.922 | 0 | 0 | 0.938 |

Pole | 0 | 0.012 | 0 | 0.964 | 0 | 0.976 |

Car | 0 | 0.012 | 0 | 0 | 0.907 | 0.947 |

Overall segmentation accuracy: OSACC | 0.939 | |||||

Overall classification accuracy: OCACC | 0.955 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.901 | 0.005 | 0.148 | 0 | 0 | 0.874 |

Road | 0.003 | 0.887 | 0.011 | 0.016 | 0.026 | 0.916 |

Tree | 0.042 | 0.005 | 0.780 | 0 | 0 | 0.867 |

Pole | 0 | 0.002 | 0 | 0.966 | 0 | 0.982 |

Car | 0 | 0.016 | 0.12 | 0 | 0.862 | 0.863 |

Overall segmentation accuracy: OSACC | 0.879 | |||||

Overall classification accuracy: OCACC | 0.901 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.980 | 0.002 | 0 | 0 | 0 | 0.989 |

Road | 0.002 | 0.950 | 0.002 | 0 | 0.080 | 0.933 |

Tree | 0 | 0.040 | 0.890 | 0 | 0.080 | 0.885 |

Pole | 0 | 0 | 0 | 0 | 0 | - |

Car | 0.040 | 0.020 | 0.030 | 0 | 0.900 | 0.905 |

Overall segmentation accuracy: OSACC | 0.930 | |||||

Overall classification accuracy: OCACC | 0.928 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.985 | 0.002 | 0 | 0 | 0 | 0.991 |

Road | 0.002 | 0.950 | 0.002 | 0 | 0.080 | 0.933 |

Tree | 0 | 0.012 | 0.680 | 0.080 | 0 | 0.794 |

Pole | 0 | 0.006 | 0 | 0.860 | 0.016 | 0.919 |

Car | 0.060 | 0.050 | 0.020 | 0.050 | 0.970 | 0.895 |

Overall segmentation accuracy: OSACC | 0.889 | |||||

Overall classification accuracy: OCACC | 0.906 |

Building | Road | Tree | Pole | Car | CACC | |
---|---|---|---|---|---|---|

Building | 0.955 | 0.002 | 0.005 | 0.001 | 0 | 0.976 |

Road | 0.002 | 0.950 | 0 | 0 | 0.007 | 0.970 |

Tree | 0 | 0 | 0. 800 | 0.035 | 0 | 0.882 |

Pole | 0 | 0 | 0 | 0.950 | 0 | 0.950 |

Car | 0 | 0.003 | 0 | 0 | 0.900 | 0.948 |

Overall segmentation accuracy: OSACC | 0.911 | |||||

Overall classification accuracy: OCACC | 0.945 |

**Table 8.**Classification results evaluated using three different metrics. For the calculation of V-measure the value β = 1 is used.

Data Set # | OCACC | F-measure | V-measure |
---|---|---|---|

# 1 | 0.943 | 0.922 | 0.745 |

# 2 | 0.955 | 0.942 | 0.826 |

# 3 | 0.901 | 0.831 | 0.733 |

# A | 0.928 | 0.917 | 0.741 |

# B | 0.906 | 0.860 | 0.734 |

**Table 9.**Overall segmentation and classification accuracies when using RGB-Color and reflectance intensity values.

Data Set # | Only RGB-Color | Intensity Value with RGB-Color | ||
---|---|---|---|---|

OSACC | OCACC | OSACC | OCACC | |

# 1 | 0.660 | 0.772 | 0.930 | 0.943 |

# 2 | 0.701 | 0.830 | 0.939 | 0.955 |

# 3 | 0.658 | 0.766 | 0.879 | 0.901 |

## Share and Cite

**MDPI and ACS Style**

Aijazi, A.K.; Checchin, P.; Trassoudaine, L.
Segmentation Based Classification of 3D Urban Point Clouds: A Super-Voxel Based Approach with Evaluation. *Remote Sens.* **2013**, *5*, 1624-1650.
https://doi.org/10.3390/rs5041624

**AMA Style**

Aijazi AK, Checchin P, Trassoudaine L.
Segmentation Based Classification of 3D Urban Point Clouds: A Super-Voxel Based Approach with Evaluation. *Remote Sensing*. 2013; 5(4):1624-1650.
https://doi.org/10.3390/rs5041624

**Chicago/Turabian Style**

Aijazi, Ahmad Kamal, Paul Checchin, and Laurent Trassoudaine.
2013. "Segmentation Based Classification of 3D Urban Point Clouds: A Super-Voxel Based Approach with Evaluation" *Remote Sensing* 5, no. 4: 1624-1650.
https://doi.org/10.3390/rs5041624