# Voxel-based 3D Point Cloud Semantic Segmentation: Unsupervised Geometric and Relationship Featuring vs Deep Learning Methods

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## Abstract

**:**

_{1}-score (> 85%) for planar-dominant classes that are comparable to state-of-the-art deep learning.

## 1. Introduction

- a new interoperable point cloud data clustering approach that account variability of domains for higher-end applications;
- a novel point cloud voxel-based featuring developed to accurately and robustly characterize a point cloud with local shape descriptors and topology pointers. It is robust to noise, resolution variation, clutter, occlusion, and point irregularity; and,
- a semantic segmentation framework to efficiently decompose large point clouds in related Connected Elements (unsupervised) that are specialized through a graph-based approach: it is fully benchmarked against state-of-the-art deep learning methods. We specifically looked at parallelization-compatible workflows.

## 2. Related Works

#### 2.1. Point Cloud Feature Extraction

#### 2.2. Semantic Segmentation Applied to Point Clouds

## 3. Materials and Methods

#### 3.1. Voxelisation Grid Constitution

#### 3.2. Feature Extraction

#### 3.2.1. Low-Level Shape-Based Features (SF1)

#### 3.2.2. Connectivity and Relationship Features (SF2)

Algorithm 1. Voxel Relation Convexity/Concavity Tagging |

Require: A voxel ${\mathcal{V}}_{i}$ and its direct vicinity ${\left\{{\mathcal{V}}_{j}\right\}}_{j=1}^{26}$ expressed as a graph $\u210a$. |

1. For each ${\mathcal{V}}_{j}\ne \varnothing $ do2. ${\alpha}_{\mathcal{V}}\leftarrow $ angle between normal of voxels 3. if ${\alpha}_{\mathcal{V}}<0$ then4. ${\u212f}_{ij}(\u210a)\leftarrow $ edge between ${\mathcal{V}}_{i}$ and ${\mathcal{V}}_{j}$ is tagged as Concave 5. else ${\u212f}_{ij}(\u210a)\leftarrow $ edge between ${\mathcal{V}}_{i}$ and ${\mathcal{V}}_{j}$ is tagged as Convex6. end if7. end for8. end9. return $(\u210a)$ |

- Pure Horizontal relationship: For ${\mathcal{V}}_{i}$, if an adjacent voxel ${\mathcal{V}}_{j}$ has a $\overrightarrow{{v}_{3}}$ colinear to the main direction (vertical in gravity-based scenes), then the edge $\u212f\left({v}_{i},{v}_{j}\right)$ is tagged $\mathcal{H}\mathcal{r}$. If two adjacent nodes ${v}_{i}$ and ${v}_{j}$ hold an $\mathcal{H}\mathcal{r}$ relationship and both $\overrightarrow{{v}_{3}}$ are not colinear, they are connected by a directed edge, ${\u212f}_{d}\left({v}_{i},{v}_{j}\right)$, where ${v}_{i}$ is the starting node. In practice, voxels that are near horizontal surfaces hold this relationship.
- Pure Vertical relationship: For ${\mathcal{V}}_{i}$, if an adjacent voxel ${\mathcal{V}}_{j}$ has a $\overrightarrow{{v}_{3}}$ orthogonal to the main direction (vertical in gravity-based scenes), then the edge $\u212f\left({v}_{i},{v}_{j}\right)$ is tagged $\mathcal{V}\u212f$. If two adjacent nodes ${v}_{i}$ and ${v}_{j}$ are connected through $\mathcal{V}\mathcal{r}$ and both $\overrightarrow{{v}_{3}}$ are coplanar but not colinear, then they are connected by a directed edge, ${\u212f}_{d}\left({v}_{i},{v}_{j}\right)$. In the case that we are in a gravity-based scenario, they are further refined following $\overrightarrow{{v}_{1}}$ and $\overrightarrow{{v}_{2}}$ axis. These typically includes voxels that are near vertical surfaces.
- Mixed relationship: For ${\mathcal{V}}_{i}$, if within its 26-connectivity neighbours, the node ${v}_{i}$ presents $\mathcal{V}\u212f$ and $\mathcal{H}\mathcal{r}$ edges, then ${v}_{i}$ is tagged as $\mathcal{M}\mathcal{r}$. In practice, voxels near both horizontal and vertical surfaces hold this relationship.
- Neighbouring relationship. If two voxels do not hold one of these former constraining relationships but are neighbours, then the associated nodes are connected by an undirected edge without tags.

#### 3.3. Connected Element Constitution and Voxel Refinement

#### 3.4. Graph-based Semantic Segmentation

## 4. Dataset

^{−9}m from one another) add an extra bias. However, it was chosen, as it is a big dataset that provides a high variability of scene organization and it is currently used for benchmarking new algorithms. It is a very interesting opportunity to evaluate the robustness of our approach and to study the impact of features and their robustness to hefty point cloud artefacts. We remind the readers that the goal is to obtain relevant semantic patches constituting Connected Elements in a Smart Point Cloud Infrastructure.

## 5. Results

#### 5.1. Metrics

- True Positive (TP): Observation is positive and is predicted to be positive.
- False Negative (FN): Observation is positive but is predicted negative.
- True Negative (TN): Observation is negative and is predicted to be negative.
- False Positive (FP): Observation is negative but is predicted positive.

_{1}-score can be interpreted as a weighted harmonic mean of the precision and recall, thus giving a good measure of how well the classifier performs. Indeed, global accuracy metrics are not appropriate evaluation measures when class frequencies are unbalanced, which is the case in most scenarios, both in real indoor and outdoor scenes, since they are biased by the dominant classes. In general, the Intersection-Over-Union (IoU) metric tends to penalize the single instances of bad classification more than the F1-score, even when they can both agree that this one instance is bad. Thus, the IoU metric tends to have a “squaring” effect on the errors relative to the F1-score. Henceforth, the F1-score in our experiments gives an indication on the average performance of our proposed classifier, while the IoU score measures the worst-case performance.

#### 5.2. Quantitative and Qualitative Assessments

#### 5.2.1. Feature Influence

_{1}-scores, which are superior for all classes up to +37 points.

#### 5.2.2. Full S3DIS Benchmark

_{1}-score of 0.72. These are relatively good metrics considering the complexity of the test dataset, and the naïve classification approach. The largest improvement margin is linked to the ‘door’ and ‘bookcase’ classes as identified earlier and confirmed in Table 11. While for horizontal planar-dominant classes being ceiling and floor, the F

_{1}-scores of 0.92 and 0.96 give little place for improvement. It orients future work toward problematic cases handling (presented in Appendix B), and irregular structures targeting. The wall class detection scores of 0.79 gives a notable place for improvements, aiming both at a more precise and coherent classification approach. While table and chair precision are relatively good, their recall rate orients future work to better account for the full number of positive samples ignored with the present classification iteration. Looking at the normalized confusion matrix (denominator: 695 878 620 points in S3DIS), a large proportion of false positives are given to the clutter concerning all classes, which also demands a better precision in the recognition approach.

#### 5.3. Implementation and Performances Details

## 6. Discussion

#### 6.1. Strengths

#### 6.2. Limitations and Research Directions

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

IoU for Area-5 | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

PointNet [25] | 88.8 | 97.33 | 69.8 | 0.05 | 10.76 | 58.93 | 52.61 | 40.28 | 33.22 |

SegCloud [48] | 90.06 | 96.05 | 69.86 | 0 | 23.12 | 70.4 | 75.89 | 58.42 | 41.6 |

SPG [49] | 91.49 | 97.89 | 75.89 | 0 | 52.29 | 77.4 | 86.35 | 65.49 | 50.67 |

Ours | 85.78 | 92.91 | 71.32 | 0 | 7.54 | 31.15 | 29.02 | 23.48 | 21.91 |

## Appendix B

## Appendix C

F1-score | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

Area-1 | 0.97 | 0.96 | 0.80 | 0.66 | 0.24 | 0.48 | 0.48 | 0.26 | 0.47 |

Area-2 | 0.85 | 0.94 | 0.70 | 0.15 | 0.22 | 0.11 | 0.12 | 0.26 | 0.32 |

Area-3 | 0.98 | 0.98 | 0.78 | 0.61 | 0.21 | 0.41 | 0.61 | 0.38 | 0.50 |

Area-4 | 0.90 | 0.97 | 0.78 | 0.00 | 0.12 | 0.25 | 0.40 | 0.24 | 0.35 |

Area-5 | 0.92 | 0.96 | 0.83 | 0.00 | 0.14 | 0.48 | 0.45 | 0.38 | 0.36 |

Area-6 | 0.95 | 0.97 | 0.78 | 0.58 | 0.24 | 0.54 | 0.53 | 0.28 | 0.43 |

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**Figure 1.**Voxel-based three-dimensional (3D) semantic segmentation. From left to right: Raw point cloud, feature engineering, Connected Elements extraction, Classified point cloud.

**Figure 2.**Visual patterns on points from left to right: Not grouped; Proximity criterion; Similarity criterion; Common cluster region; Linear criterion; Parallel criterion: Symmetry criterion.

**Figure 3.**Methodological workflow for the constitution of Connected Elements and knowledge-based classification. A point cloud goes through seven serialized steps (diamonds) to obtain a fully classified dataset (red square).

**Figure 4.**Point Cloud and its extracted voxel structure, where each octree level represents the grid voxels, each subdivided in subsequent eight voxel children.

**Figure 5.**Feature transfer between octree levels. We note that each non-empty node describes a voxel which can then permit a point-level access for example to compute feature sets (here, a planar voxel and a corresponding SF1 sample, and a transition voxel and its corresponding SF1 sample).

**Figure 7.**Direct voxel-to-voxel topology in a 26-connectivity graph. Considered voxel ${\mathcal{V}}_{i}$ is red, direct connections are either vertex.touch (grey), edge.touch (yellow), or face.touch (orange).

**Figure 8.**Relationship tagging in the voxel-space. (

**a**) represent a mixed relationship $\mathcal{M}\mathcal{r}$, (

**b**) a pure vertical relationship $\mathcal{V}\mathcal{r}$, and (

**c**) a pure horizontal relationship $\mathcal{H}\mathcal{r}$.

**Figure 9.**S3DIS points within categorized voxels. (

**a**) Full transition voxels, (

**b**) vertical group of points, (

**c**) horizontal group of points, and (

**d**) mixed group of points.

**Figure 11.**Elements detection and categorization. A point cloud is search for Primary Elements (PE), the rest is searched for Secondary elements (SE). The remaining from this step is searched for transition elements (TE), leaving remaining elements (RE). TE permits extracting graphs through SF2 analysis with PE, SE, and RE.

**Figure 13.**Different graphs generated on voxel categories. (

**a**) Connected Elements (CEL) graph, (

**b**) PE graph, (

**c**) SE graph, (

**d**) TE graph, and (

**e**) RE graph.

**Figure 14.**(

**a**) Raw point cloud; (

**b**) {PE, SE, TE, RE} groups of voxels; (

**c**) Connected Elements; and, (

**d**) Classified point cloud.

**Figure 16.**Problematics cases which often include point cloud artefacts such as heavy noise, missing parts, irregular shape geometries, mislabelled data.

**Figure 17.**Normalized Confusion matrix of our semantic segmentation approach over the full S3DIS dataset.

**Figure 18.**Results of the semantic segmentation on a room sample. (

**a**) RGB point cloud, (

**b**) Connected Elements, (

**c**) Ground Truth, and (

**d**) Results of the semantic segmentation.

Eigen-Based Feature | Description | |
---|---|---|

${\lambda}_{1},{\lambda}_{2},{\lambda}_{3}$ | Eigen values of ${\mathcal{V}}_{i,j,k}$ where ${\lambda}_{1}>{\lambda}_{2}>{\lambda}_{3}$ | |

$\overrightarrow{{v}_{1}},\text{}\overrightarrow{{v}_{2}},\text{}\overrightarrow{{v}_{3}}$ | Respective Eigen vectors of ${\mathcal{V}}_{i,j,k}$ | |

$\overrightarrow{{v}_{3}}$ | Normal vector of ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{a}$ | Anisotropy of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{e}$ | Eigen entropy of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{l}$ | Linearity of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{o}$ | Omnivariance of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{p}$ | Planarity of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{s}$ | Sphericity of voxel ${\mathcal{V}}_{i,j,k}$ | |

${\lambda}_{v}$ | Surface variation of voxel ${\mathcal{V}}_{i,j,k}$ |

Geometrical Feature | Description | |
---|---|---|

$\overline{{\mathcal{V}}_{i}{}_{x}},\overline{{\mathcal{V}}_{i}{}_{y}},\overline{{\mathcal{V}}_{i}{}_{z}}$ | Mean value of points in ${\mathcal{V}}_{i,j,k}$ respectively along $\overrightarrow{{e}_{x}},\overrightarrow{{e}_{y}},\overrightarrow{{e}_{z}}$ | |

${\sigma}_{i}{{}_{x}}^{2},{\sigma}_{i}{{}_{y}}^{2},{\sigma}_{i}{{}_{z}}^{2}$ | Variance of points in voxel ${\mathcal{V}}_{i,j,k}$ | |

${\mathcal{V}}_{\mathcal{A}p}$ | Area of points in ${\mathcal{V}}_{i,j,k}$ along $\overrightarrow{{n}_{\mathcal{V}}}$ ($\overrightarrow{{v}_{3}}$) | |

${\mathcal{V}}_{\mathcal{A}}$ | Area of points in ${\mathcal{V}}_{i,j,k}$ along $\overrightarrow{{e}_{z}}$ | |

$m$ | Number of points in ${\mathcal{V}}_{i,j,k}$ | |

${V}_{\mathcal{V}}$ | Volume occupied by points in ${\mathcal{V}}_{i,j,k}$ | |

${D}_{\mathcal{V}}$ | point density within voxel ${\mathcal{V}}_{i,j,k}$ |

**Table 3.**Relational features of the SF2 feature set for three-dimensional (3D) structural connectivity.

Relational Feature | Description |
---|---|

${g}_{26}\left(i\right)$ | Graph of voxel entity $i$ and its neighbours retaining voxel topology (vertex.touch, edge.touch, face.touch) |

${F}_{g}$ | Geometrical difference |

${g}_{26-cc}\left(i\right)$ | ${g}_{26}\left(i\right)$ retaining Convex/Concave tags. |

${g}_{26-cc-p}\left(i\right)$ | ${g}_{26-cc}\left(i\right)$ retaining planarity tags ($\mathcal{H}\mathcal{r},\mathcal{V}\mathcal{r},\mathcal{M}\mathcal{r}$). |

Area-1 | Area-2 | Area-3 | Area-4 | Area-5 | Area-6 | |
---|---|---|---|---|---|---|

#Points | 43 956 907 | 470 023 210 | 18 662 173 | 43 278 148 | 78 649 818 | 41 308 364 |

Area (m²) | 965 | 1100 | 450 | 870 | 1700 | 935 |

Rooms (nb) | 44 | 40 | 23 | 47 | 68 | 48 |

Method | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Others |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

Area 1 | 56 | 45 | 235 | 62 | 87 | 70 | 156 | 91 | 123 |

Area 2 | 82 | 51 | 284 | 62 | 94 | 47 | 546 | 49 | 92 |

Area 3 | 38 | 24 | 160 | 14 | 38 | 31 | 68 | 42 | 45 |

Area 4 | 74 | 51 | 281 | 4 | 108 | 80 | 160 | 99 | 106 |

Area 5 | 77 | 69 | 344 | 4 | 128 | 155 | 259 | 218 | 183 |

Area 6 | 64 | 50 | 248 | 69 | 94 | 78 | 180 | 91 | 127 |

Full S3DIS | 391 | 290 | 1552 | 215 | 549 | 461 | 1369 | 590 | 676 |

Method | Zone | Time (min) | CEL number | mIOU | oAcc | F1-score |
---|---|---|---|---|---|---|

SF1 | Room | 0.7 | 214 | 0.53 | 0.73 | 0.77 |

Area 1 | 42.4 | 10105 | 0.35 | 0.58 | 0.63 | |

SF1SF2 | Room | 1.0 | 125 | 0.83 | 0.95 | 0.95 |

Area 1 | 55.0 | 5489 | 0.47 | 0.75 | 0.75 |

**Table 7.**Quantitative CEL segmentation compared to nominal number of elements per class for both a room (Conference room) and area (area 1).

CEL Number | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase |
---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | |

Room 1 | 1 | 1 | 4 | 1 | 1 | 1 | 13 | 1 |

Tagged CEL | 1 | 1 | 4 | 1 | 1 | 1 | 11 | 1 |

Area 1 | 56 | 44 | 235 | 62 | 87 | 70 | 156 | 91 |

Tagged CEL | 52 | 44 | 146 | 47 | 23 | 67 | 129 | 70 |

**Table 8.**Global per-class metrics concerning the Area-1 of the S3DIS dataset. SF1 alone and combined SF1SF2 are compared.

Global Metrics Area-1 | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

SF1 IoU | 0.81 | 0.75 | 0.61 | 0.39 | 0.10 | 0.24 | 0.06 | 0.02 | 0.14 |

SF1 Precision | 0.99 | 0.99 | 0.84 | 0.67 | 0.11 | 0.96 | 0.09 | 0.15 | 0.32 |

SF1 Recall | 0.82 | 0.75 | 0.69 | 0.48 | 0.57 | 0.25 | 0.14 | 0.03 | 0.20 |

SF1 F-1 score | 0.90 | 0.86 | 0.76 | 0.56 | 0.18 | 0.39 | 0.11 | 0.05 | 0.24 |

SF1SF2 IoU | 0.95 | 0.92 | 0.67 | 0.49 | 0.14 | 0.32 | 0.32 | 0.15 | 0.31 |

SF1SF2 Precision | 0.98 | 0.95 | 0.79 | 0.88 | 0.29 | 0.9 | 0.69 | 0.2 | 0.41 |

SF1SF2 Recall | 0.97 | 0.97 | 0.82 | 0.53 | 0.2 | 0.33 | 0.37 | 0.37 | 0.56 |

SF1SF2 F-1 score | 0.97 | 0.96 | 0.8 | 0.66 | 0.24 | 0.48 | 0.48 | 0.26 | 0.47 |

**Table 9.**Benchmark results of our semantic segmentation approach against best-performing deep-learning methods.

$\overline{\mathit{I}\mathit{o}\mathit{U}}$ | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

PointNet [25] | 88 | 88.7 | 69.3 | 42.4 | 51.6 | 54.1 | 42 | 38.2 | 35.2 |

MS+CU(2) [51] | 88.6 | 95.8 | 67.3 | 36.9 | 52.3 | 51.9 | 45.1 | 36.8 | 37.5 |

SegCloud [48] | 90.1 | 96.1 | 69.9 | 0 | 23.1 | 75.9 | 70.4 | 40.9 | 42 |

G+RCU [51] | 90.3 | 92.1 | 67.9 | 44.7 | 51.2 | 58.1 | 47.4 | 39 | 41.9 |

SPG [49] | 92.2 | 95 | 72 | 33.5 | 60.9 | 65.1 | 69.5 | 38.2 | 51.3 |

KWYND [12] | 92.1 | 90.4 | 78.5 | 37.8 | 65.4 | 64 | 61.6 | 51.6 | 53.7 |

Ours | 85.4 | 92.4 | 65.2 | 32.4 | 10.5 | 27.8 | 23.7 | 18.5 | 23.9 |

**Table 10.**Benchmark results of our semantic segmentation approach against deep-learning methods without any colour information used.

Method | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter |
---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | |

PointNet | 84 | 87.2 | 57.9 | 37 | 35.3 | 51.6 | 42.4 | 26.4 | 25.5 |

MS+CU(2) | 86.5 | 94.9 | 58.8 | 37.7 | 36.7 | 47.2 | 46.1 | 30 | 31.2 |

Ours | 85.4 | 92.4 | 65.2 | 32.4 | 10.5 | 27.8 | 23.7 | 18.5 | 23.9 |

S3DIS Class Metrics | Ceiling | Floor | Wall | Beam | Door | Table | Chair | Bookcase | Clutter | Average |
---|---|---|---|---|---|---|---|---|---|---|

0 | 1 | 2 | 3 | 6 | 7 | 8 | 10 | 12 | ||

Precision | 0.94 | 0.96 | 0.79 | 0.53 | 0.19 | 0.88 | 0.72 | 0.28 | 0.33 | 0.75 |

Recall | 0.90 | 0.96 | 0.79 | 0.46 | 0.19 | 0.29 | 0.26 | 0.36 | 0.47 | 0.72 |

F1-score | 0.92 | 0.96 | 0.79 | 0.49 | 0.19 | 0.43 | 0.38 | 0.31 | 0.39 | 0.72 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Poux, F.; Billen, R. Voxel-based 3D Point Cloud Semantic Segmentation: Unsupervised Geometric and Relationship Featuring vs Deep Learning Methods. *ISPRS Int. J. Geo-Inf.* **2019**, *8*, 213.
https://doi.org/10.3390/ijgi8050213

**AMA Style**

Poux F, Billen R. Voxel-based 3D Point Cloud Semantic Segmentation: Unsupervised Geometric and Relationship Featuring vs Deep Learning Methods. *ISPRS International Journal of Geo-Information*. 2019; 8(5):213.
https://doi.org/10.3390/ijgi8050213

**Chicago/Turabian Style**

Poux, Florent, and Roland Billen. 2019. "Voxel-based 3D Point Cloud Semantic Segmentation: Unsupervised Geometric and Relationship Featuring vs Deep Learning Methods" *ISPRS International Journal of Geo-Information* 8, no. 5: 213.
https://doi.org/10.3390/ijgi8050213