Zijian Zhang, Jicang Wu
College of Surveying and Geo-Informatics, Tongji University, Shanghai, China.
DOI: 10.4236/jcc.2024.126014   PDF    HTML   XML   226 Downloads   832 Views   Citations

Abstract

To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-scale feature descriptors. First, we select the optimal dual-scale descriptors from a range of feature descriptors. Next, we segment the facade according to the threshold value of the chosen optimal dual-scale descriptors. Finally, we use RANSAC (Random Sample Consensus) to fit the segmented surface and optimize the fitting result. Experimental results show that, compared to commonly used facade segmentation algorithms, the proposed method yields more accurate segmentation results, providing a robust data foundation for subsequent 3D model reconstruction of buildings.

Keywords

3D Laser Scanning Point Clouds, Building Facade Segmentation, Point Cloud Processing, Feature Descriptors

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1. Introduction

With the development of LiDAR (Light Detection and Ranging) technology and the advancement of the “smart city” concept, constructing LoD (Level of Detail) models of urban buildings using ground laser scanning systems has become a research hotspot among scholars both domestically and internationally. Ground LiDAR systems are widely used in urban 3D modeling due to their advantages of fast data acquisition, high precision, and non-contact measurement. These systems are also one of the key methods for data acquisition in the field of 3D modeling [1]-[3].

The primary facade of a building refers to the continuous surface in the building’s point clouds that contains the most points. This surface is usually a wall without windows, representing the basic form of the building and serving as a key basis for constructing the building’s LoD model. Extracting the primary facade is a prerequisite for building the LoD model. Accurately segmenting the primary facade of a building based on ground laser scanning systems is currently a significant research challenge. For most buildings, their structure is a simple planar form, meaning that the building is composed of four faces. For these types of buildings, a single surface fitting can yield the primary facade. However, for more complex buildings, the facade is composed of multiple intersecting planar segments. A single surface fitting cannot capture all the walls, leading to structural omissions and consequently affecting the accuracy of the subsequent LoD model. To address this issue, it is necessary to segment the building facade point clouds to precisely extract the primary facade [4].

The purpose of point clouds segmentation is to divide point clouds data into multiple homogeneous regions, where the points within the same region have similar or identical features (such as normal vectors, curvature, etc.). Currently, segmentation based on point clouds, both domestically and internationally, primarily focuses on the local neighborhood characteristics and geometric features of the point clouds [5]-[8]. Wang Y et al. proposed an urban point clouds segmentation method based on Gaussian maps. This method maps the normal vectors of the point clouds to a Gaussian map and clusters them, then groups the clustering results to identify planes, cylinders, and other shapes in the scene. However, relying solely on normal vectors results in point clouds with similar normal vectors being classified into the same category, failing to achieve refined segmentation results [9]. Wang W et al. implemented the segmentation of indoor building scenes based on an improved RG (RG) algorithm. This approach enhances traditional RG performance through more accurate normal vector estimation and strengthened RG criteria. However, for different datasets, the method still requires adjusting the normal vector angle and curvature thresholds, lacking a more universal threshold reference value [10]. Jampani V et al. converted facade point clouds into facade images and performed classification based on the pixels in the image. This method is simple and efficient, effectively transforming the point clouds segmentation problem into an image classification problem. However, the method becomes less applicable when building facades are complex [11].

Based on the aforementioned research, the current issues in the field of building facade point clouds segmentation can be summarized as follows: 1) poor segmentation accuracy; 2) low applicability of segmentation methods; and 3) lack of universal parameter threshold references. To address these issues, we propose a method (ODSFD) for extracting building primary facades based on optimal dual-scale feature descriptors. ODSFD first utilizes public datasets and simulated data to select the optimal dual-scale descriptors from numerous proposed feature descriptors, providing key threshold values as general references for users. Next, a facade segmentation algorithm is constructed based on the proposed dual-scale descriptors. Finally, experiments are conducted using self-collected data to verify the accuracy and feasibility of ODSFD. According to the final quantitative results, the proposed method not only achieves high segmentation accuracy but is also applicable to complex building facades composed of multiple small patches.

2. Methodology

2.1. Research Objective

The ODSFD we propose for extracting building primary facades is based on the features of points. The feature descriptor of a point clouds is a digital representation of the point’s geometric characteristics. Points with different attributes possess distinct features. As shown in Figure 1, regular points (RP) represent the planar parts of the point clouds, while sharp points (SP) represent the points where different planes intersect. Therefore, distinguishing between regular and sharp points enables the segmentation of different planes.

2.2. Feature Descriptors of Point Clouds

To distinguish between regular and sharp points, we generate feature descriptors based on eigenvalues. These descriptors effectively characterize the regular or sharp features of points, such as linearity, planarity, sphericity, anisotropy, eigenentropy, omnivariance, surface variation, and verticality. Depending on the geometric significance of the feature descriptors, they can be classified into two categories: dimensional feature descriptors and statistical feature descriptors. These descriptors are crucial for distinguishing between regular and sharp points and are widely used in current geometric feature analysis [12] [13]. To compute these descriptors, we first calculate the eigenvalues of the points. The eigenvalues of a point P_i are typically derived from the covariance matrix of all points within a specified radius around the point. We calculate the eigenvalues of the point clouds based on PCA (Principal Component Analysis) [14] [15], expressed as Equation (1):

$Q_P=\frac{1}{N}{\displaystyle \underset{i=1}{\overset{N}{\sum }}\left(P_i-\bar{P}\right)}{\left(P_i-\bar{P}\right)}^{{\rm T}}$ . (1)

where, Q_p represents the covariance matrix of all points within a certain radius of point P_i; N is the total number of points in this neighborhood, i = 1, 2, ..., N; $\bar{P}$ is the mean of all points in the neighborhood, and it can be expressed as Equation (2):

$\bar{P}=\frac{1}{N}{\displaystyle \underset{i=1}{\overset{N}{\sum }}{P}_i}$. (2)

Based on the covariance matrix, we can calculate the eigenvalues of point P_i and further obtain its feature descriptors. The expressions for each descriptor are as Table 1:

where, L_linearity represents the linearity of point; P_planarity represents the planarity of point; S_sphericity represents the sphericity of point; A_anisotropy represents the anisotropy of point; E_eigenentropy represents the eigenentropy of point; O_ominvariance represents the omnivariance of point; S_{surface_variation} represents the surface variation of point; V_verticality represents the verticality of point; ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$ represent the normalized eigenvalues of point, and ${\lambda }_1\ge {\lambda }_2\ge {\lambda }_3$; $\stackrel{\to }{e_3}$ represent the eigenvectors corresponding to the smallest eigenvalue ${\lambda }_3$ .

Although these descriptors have certain capabilities to characterize the sharpness of points, experimental verification and analysis are still needed to determine which descriptors are more effective in distinguishing between regular and sharp points. For instance, linearity represents the linear characteristics of points in their neighborhoods, such as the point clouds of lampposts in urban areas, which tends to have a linearity close to 1. Planarity and anisotropy represent the planar characteristics of points in their neighborhoods, such as the planarity of building facades, which tends to be close to 1. Sphericity represents the degree of dispersion of points in their neighborhoods, such as the high sphericity of points in a tree leaf point clouds. Eigenentropy, omnivariance, surface variation, and verticality can all predict the position of points in the entire point set.

Under normal circumstances, multi-scale descriptors have better sharp point extraction performance compared to single descriptor. However, when the difference in accuracy is not significant, multi-scale computation can significantly increase algorithm complexity and computational costs [16]. Therefore, to reduce algorithm complexity and provide reference values, we analyze and select two descriptors through experiments to form optimal dual-scale descriptors.

2.3. Segmentation Algorithm of ODSFD

Assuming that the obtained optimal dual-scale feature descriptors are D₁ and D₂, and their threshold reference values are v₁ and v₂ respectively, we can use these dual-scale descriptors and their reference values to distinguish between regular and sharp points in the point clouds and construct the ODSFD algorithm. The ODSFD is based on the traditional RG algorithm, but unlike the traditional RG algorithm, the threshold values of its two key parameters usually remain constant across different datasets. The ODSFD steps are as follows:

1) For the point clouds to be segmented, sort the points based on their D₁ values, and select the point with the minimum D₁ as the initial seed point. Add this initial seed point to the seed point set;

2) Calculate the difference of D₂ between each neighboring point of the seed point and the seed point. If the difference is less than v₂, classify the neighboring point and reevaluate the difference between its D₁ value and the seed point’s D₁. Otherwise, do not classify the neighboring point;

3) If the difference of D₁ is less than v₁, add the neighboring point to the seed point set; otherwise, classify the neighboring point but do not add it to the seed point set;

4) Remove the current seed point from the seed point set and continue to “grow” with the new seed point, repeating steps b) to c). Continue this process until the seed point set is empty, indicating that the growth of this class is complete. All classified points form one class;

5) For the remaining unclassified points, repeat steps a) to d) until all points are classified.

However, due to the complexity of real building structures or the incomplete accuracy of the given empirical parameters, over-segmentation issues still exist. The RANSAC algorithm, one of the most common algorithms in point clouds fitting, not only provides a good plane fitting effect but also offers better noise resistance compared to least squares fitting. To address the over-segmentation problem, this paper proposes the following optimization methods and constraints based on the RANSAC algorithm for fitting the segmentation results [17] [18]. The schematic diagram is shown in Figure 2:

1) For each segmented point sets S = {S₁, S₂, …, S_n} perform plane fitting using the RANSAC;

2) For point set S_i, extract all points from the original point set that are within 0.05 m of the fitted plane and designate this point set as a new set C_i, C_i may contain points that are in the same plane as S_i but belong to different classes;

3) Use the DBSCAN (Density-Based Spatial Clustering of Applications with Noise) algorithm to segment point set C_i and obtain point sets G = {G₁, G₂, …, G_m} [19] [20]. From point set G = {G₁, G₂, …, G_m}, select the point set hose centroid is closest to a distance S_i from the centroid. This point set represents the set of face in the original point clouds corresponding to the segmented point set S_i;

4) After all segmented point sets S = {S₁, S₂, …, S_n} have been fitted, determine if the number of duplicate points between any two sets of faces is greater than 90% of the total number of points in the set with fewer points. If so, merge the points within the two faces, and delete duplicate points until no more faces can be merged.

By using the above method, not only has the over-segmentation problem in the segmentation process been improved, but also the robustness of the ODSFD algorithm has been enhanced. Additionally, further denoising of the point clouds has been achieved.

3. Experiments and Analysis

We designed three experiments to select the optimal dual-scale descriptors and validate the feasibility of the ODSFD. These experiments are the descriptor segmentation experiment (Experiment 1), the optimal dual-scale descriptors threshold reference experiment (Experiment 2), and the ODSFD facade segmentation experiment (Experiment 3). Experiment 1 is used to select the optimal dual-scale descriptors, Experiment 2 is used to determine the threshold reference values of the optimal dual-scale descriptors, and Experiment 3 is used to verify the ODSFD algorithm’s ability in facade segmentation. In each experiment, we conducted a detailed analysis of the results. Next, we will introduce these three experiments separately.

3.1. Descriptor Segmentation Experiment

1) Experimental data

To find the optimal dual-scale feature descriptors that distinguish between regular and sharp points, it is necessary to evaluate the segmentation capabilities of each descriptor. We selected three sets of data for the experiments, which come from the Semantic 3D public dataset and synthetic data. Two sets of measured data come from Semantic 3D, and one set is synthetic data. The synthetic data is generated based on model, so the point distribution is relatively regular. The three sets of data are named Shice_1, Shice_2, and Moni_1. The schematic diagram and detailed information of the three sets of data are shown in Figure 3 and Table 2, respectively.

2) Evaluation metrics

We use Precision, Recall, and F1 score as evaluation metrics for the experimental results. The expressions for these three metrics are as Equations (3)-(5):

$Precision=\frac{TP}{TP+FP}$ . (3)

$Recall=\frac{TP}{TP+FN}$ . (4)

$F1-Score=2\ast \frac{Recall\ast Precision}{Recall+Precision}$ . (5)

where, TP (True Positives) is the number of correctly classified sharp points; FP (False Positives) is the number of regular points incorrectly classified as sharp; FN (False Negatives) is the number of sharp points incorrectly classified as regular.

3) Experimental methodology

We categorize the point clouds within the scene into two classes: sharp points and regular points. To intuitively analyze the segmentation capabilities of various feature descriptors, we use the RF (Random Forest) algorithm for data classification. We calculate the classification results of single descriptor, dual-scale descriptors combining any two descriptors, and multi-scale descriptors, and select the optimal dual-scale descriptors based on the classification results. For the reference datasets, sharp points extracted by manually adjusting the angle threshold parameter of RG are used as the standard values for sharp points, while the remaining points are used as the standard values for regular points. The segmentation results of the standard datasets are shown in Figure 4.

Regarding the RF parameter settings, due to the significant difference in the number of regular and sharp points, we aim to reduce the impact of different class data sizes on the classification results. For each of the three datasets, we manually select 4000 sharp points and n * 4000 regular points as the training dataset to ensure a uniform ratio of each class in the dataset (where n is the ratio of regular points to sharp points obtained from the reference dataset). Additionally, we select 30% of the points from the training set as the test set to analyze the classification ability of the descriptors.

The number of decision trees and the minimum number of leaf nodes also affect the algorithm’s complexity and accuracy. We set the number of decision trees to 100 and the minimum number of leaf nodes to 5, considering both classification accuracy and computational complexity.

4) Results and analysis

Figure 5 displays the classification results of three datasets when considering both single descriptor and all combinations of dual-scale descriptors. The results are presented in the form of a score matrix, where the diagonal elements represent the classification results of the single descriptor.

The experimental results indicate that compared to single descriptor, dual-scale descriptors show significant improvements in Precision, Recall, and

F1-score, demonstrating the effectiveness of the proposed method. Among all dual-scale descriptor combinations, the combination of feature descriptor S_sphericity and feature descriptor S_{surface_variation} performs the best in terms of F1-score (0.959, 0.835, and 0.973 respectively) and achieves the best Precision in Moni_1 (0.988). For the Shice_1, this combination achieves a Precision of 0.969, which, although not the highest among all combinations, is only 0.003 lower than the highest Precision of 0.972. Therefore, we select S_sphericity and S_{surface_variation} as the optimal dual-scale feature descriptors.

Table 3 presents the detailed classification results for the three datasets using single feature descriptor, optimal dual-scale feature descriptors, and all descriptors considered.

The results from Table 3 indicate that, for all three datasets, single descriptors exhibit significantly lower Precision, Recall, and F1-scores compared to the selected optimal dual-scale descriptors. Specifically, for Shice_1, the optimal dual-scale descriptors improve Precision by 0.018, Recall by 0.019, and F1-score by 0.019 compared to the highest single-scale descriptor values. For Shice_2, the improvements are 0.085 in Precision, 0.109 in Recall, and 0.101 in F1-score. For Moni_1, the improvements are 0.008 in Precision, 0.005 in Recall, and 0.008 in F1-score.

The improvements for the three metrics are significant for the measured data, with Shice_2 showing a F1-score improvement of nearly 12%, while the improvements are smaller for the simulated data. This is because the simulated data is more regular and has uniform point density, leading to good classification results for both single and dual-scale descriptors. However, in practical data collection processes, point clouds density is often uneven. Therefore, in terms of practical application considerations, this experiment also demonstrates that the optimal dual-scale descriptors obtained through this method have higher practical value.

Compared to the scenario where all eight descriptors are considered, the optimal dual-scale descriptors show slightly lower Precision, Recall, and F1-scores. Specifically, for Shice_1, the multi-scale descriptors improve Precision by 0.011, Recall by 0.014, and F1-score by 0.012 compared to the optimal dual-scale descriptors. For Shice_2, the multi-scale descriptors improve Precision by 0.002, Recall by 0.027, and F1-score by 0.025. For Moni_1, Precision improves by 0.002, Recall by 0.010, and F1-score by 0.005.

Although the multi-scale descriptors show improvements in all three metrics, the improvements are not significant for both measured and simulated data, while the computational complexity increases significantly. In the implementation of the algorithm, suitable parameters need to be provided for all eight descriptors, whereas the dual-scale descriptors only require two parameters. In conclusion, the proposed dual-scale descriptors greatly reduce the computational cost with a minor sacrifice in segmentation accuracy. Subsequent experiments will analyze the distribution of S_sphericity and S_{surface_variation} values for regular and sharp points and provide reference thresholds.

3.2. Optimal Dual-Scale Descriptors Threshold Reference Experiment

1) Experimental data

To obtain more generalizable reference thresholds for distinguishing sharp points from regular points, the same three datasets used in Experiment 3.1 were employed in this experiment.

2) Results and analysis

Compute the S_sphericity and S_{surface_variation} values for regular and sharp points in the standard datasets of the three groups of data, and arrange the S_sphericity and S_{surface_variation} values of the two types of points in ascending order. The resulting curve is shown in Figure 6, where the x-axis represents the point number and the y-axis represents the S_sphericity and S_{surface_variation} values for each point.

From Figure 6, we can see that the S_sphericity and S_{surface_variation} values of regular and sharp points in the three datasets exhibit similar distribution trends for the dual-scale descriptors values. In both the measured and simulated data, the majority of regular points have low S_sphericity and S_{surface_variation} values, close to 0, with only about 1% of regular points having relatively high S_sphericity and S_{surface_variation} values. Similarly, the majority of sharp points have high S_sphericity and S_{surface_variation} values. For Shice_1 and Shice_2, only about 5% of sharp points have S_sphericity values less than 0.02 and S_{surface_variation} values less than 0.01, while in Moni_1, only about 1% of sharp points have S_sphericity values less than 0.02 and S_{surface_variation} values

less than 0.01.The 1% or 5% discrepancy in regular and sharp points could be attributed to two reasons. Firstly, it could be due to errors in the standard datasets themselves, as the classification of regular and sharp points in the standard datasets is determined by manually adjusting the normal vector angle threshold, which may introduce some human error. Secondly, it could be due to suboptimal radius settings for computing the feature values of some points, leading to errors in the computed feature values and further affecting the calculation of the feature descriptors.

From these three sets of data, it can be seen that effective differentiation between regular and sharp points can be achieved when the S_sphericity threshold is set to 0.02 and the S_{surface_variation} threshold is set to 0.01.

3.3. ODSFD Facade Segmentation Experiment

1) Experimental data

The experimental data in this experiment are from two facades of a library at a university in Shanghai, China. The data was acquired using a Riegl VZ-400 terrestrial laser scanner. Each facade consists of multiple planar segments of varying sizes. The two facades are named Face_1 and Face_2. The schematic diagrams of the two facades and detailed information about the point clouds data are shown in Figure 7 and Table 4, respectively.

2) Evaluation metrics

The evaluation metrics for the experiment are Precision, Recall, and F1-score.

3) Experimental methodology

In the segmentation process of the two facades, the S_sphericity and S_{surface_variation} thresholds are set to 0.02 and 0.01, respectively. To validate the effectiveness and accuracy of ODSFD, we use manually segmented results as the standard dataset. We compare our method with RG algorithms (with normal vector angle thresholds of 5˚ and 10˚) and the RANSAC algorithm applied to the same two facades.

4) Results and analysis

The segmentation results of Face_1 using the RG algorithm (with a normal vector angle threshold of 5˚), the RG algorithm (with a normal vector angle threshold of 10˚), and the RANSAC algorithm are shown in Figures 8(a)-(c),

respectively. The segmented planes extracted by the ODSFD algorithm before optimization are shown in Figure 8(d), with the results after optimization in Figure 8(e). Similarly, for Face_2, the segmentation results using the RG algorithm (with a normal vector angle threshold of 5˚), the RG algorithm (with a normal vector angle threshold of 10˚), and the RANSAC algorithm are shown in Figures 9(a)-(c), respectively. The segmented planes extracted by the ODSFD algorithm before optimization are shown in Figure 9(d), with the results after optimization in Figure 9(e). The Precision, Recall, and F1-scores of the ODSFD algorithm and the comparison methods are summarized in Table 5.

Analysis of Table 5 reveals that the segmentation results of the traditional RG algorithm vary significantly depending on the normal vector angle threshold. A smaller angle threshold results in a higher number of segmented planes. For Face_1, the traditional RG algorithm with a 5˚ threshold segmented 243 planes, while the 10˚ threshold resulted in only 102 planes. Similarly, for Face_2, the 5˚ threshold yielded 157 planes, whereas the 10˚ threshold produced just 59 planes. Both thresholds exhibited varying degrees of over-segmentation, under-segmentation, and missed segmentation. The RANSAC algorithm’s segmentation capability was between the traditional RG algorithms with 5˚ and 10˚ thresholds, segmenting 210 planes for Face_1 and 124 planes for Face_2, but still showed issues of

over-segmentation, under-segmentation, and missed segmentation.

In terms of Precision, Recall, and F1-score, the ODSFD algorithm outperformed the other methods. For Face_1, the ODSFD algorithm achieved a Precision of 1, a Recall of 0.993, and an F1-score of 0.996. Compared to the other three methods, the ODSFD algorithm’s Precision improved by 0.103, 0.078, and 0.133, respectively; Recall improved by 0.276, 0.684, and 0.394, respectively; and the F1-score improved by 0.199, 0.533, and 0.287, respectively. The results for Face_2 were similar, with the ODSFD algorithm also achieving the best segmentation results.

From the pre-optimization results of the ODSFD, it is evident that while over-segmentation was severe, resulting in a number of segmented planes far exceeding the actual number of planes. However, post-optimization, the number of over-segmented planes significantly decreased, demonstrating the effectiveness of the proposed optimization method.

For Face_1, the ODSFD resulted in two missed planes, while Face_2 had one missed plane. This can be attributed to two main reasons: firstly, the quality of the point clouds data for these planes was relatively low, and secondly, the surfaces of these planes were highly undulating, making them more like curved surfaces than flat planes.

4. Conclusion

We focused on building facades as our research subject and proposed an ODSFD facade point clouds segmentation method based on optimal dual-scale feature descriptors by thoroughly exploring the geometric feature information of facade point clouds. First, we selected the optimal dual-scale descriptors through experiments to construct the segmentation algorithm. Then, we provided more general threshold reference values based on the distribution of descriptors. Finally, we validated the feasibility of the proposed ODSFD algorithm using measured data. From the final comparative experiments, the ODSFD algorithm demonstrated more accurate segmentation results. It was able to produce multiple fine-grained planes even for relatively complex building facades. However, the ODSFD algorithm still has shortcomings, notably severe over-segmentation before optimization, which increases the computational cost of subsequent optimizations. Additionally, the threshold reference values for the optimal dual-scale descriptors were derived from only three datasets. In the future, we plan to use more datasets to provide more convincing and accurate threshold reference values.

Acknowledgements

We are very grateful for the support of the National Natural Science Foundation of China (42074022) for our research.

Conflicts of Interest

The authors declare no conflicts of interest regarding the publication of this paper.

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