Crack Detection and Feature Extraction of Heritage Buildings via Point Clouds: A Case Study of Zhonghua Gate Castle in Nanjing

Abstract

Zhonghua Gate Castle is on the tentative list for Chinese World Cultural Heritage. Due to long-term sunshine, rain erosion, and man-made damage, its surface appears to have different degrees of cracks and other diseases. This paper centers on Zhonghua Gate Castle; terrestrial laser scanning is used to obtain the exterior wall point cloud data. A crack detection method based on point cloud data curved surface reconstruction is proposed. It involves data preprocessing, crack detection, and the analysis of crack features. This method initially uses data preprocessing techniques to improve data quality. These techniques include removing ground points and super-voxel segmentation. Subsequently, local surface reconstruction was employed to address the issue of missing point cloud data within cracks and the Euclidean clustering algorithm was used for precise crack identification. The article provides a detailed analysis of the geometric characteristics of cracks. They involve the calculation of length, width, and area. The results of the experiment demonstrate that the method could successfully identify cracks and extract geometric features and has millimeter-level accuracy compared to actual crack sizes.

1. Introduction

Ancient buildings are a crucial component of cultural heritage. They not only serve as a witness to history but also embody the national spirit and cultural tradition. These architectural marvels, with their intricate designs and historical significance, hold immense value for society. Over time, various pathologies inevitably emerge in these heritage structures, posing significant threats to their structural integrity [1]. Among these pathologies, cracks are the most prevalent and have a profound impact on structural safety. Cracks adversely affect ancient architecture’s beauty, structural integrity, durability, and earthquake resistance [2]. The relevant authorities maintain a strict and proactive stance when faced with the deterioration of heritage buildings [3]. They know that any negligence may lead to irreparable cultural losses, so they attach great importance to detecting and repairing pathologies such as cracks. Therefore, the detection and repair of diseases such as cracks are of importance. Crack information and characteristics not only provide a crucial basis for the structural safety assessment of heritage buildings but also offer precise guidance for their restoration [4].

Traditionally, crack detection in heritage structures has been conducted through manual inspection, crack monitoring rulers, vibrating wire meters, and instruments such as theodolites, levels, and radar [4,5]. While these methods can provide intuitive detection results, they suffer from limitations due to human subjective judgment and measurement errors inherent in the equipment. Consequently, they are unable to meet the current demand for high-precision and high-efficiency detection.

In recent years, technological innovations have introduced novel solutions to the historical field of building conservation. Terrestrial laser scanning (TLS), an emerging non-contact measurement technique, has been increasingly adopted in this field [6]. TLS rapidly acquires three-dimensional(3D) coordinate data via high-speed laser scanning, accurately capturing the surface topography of heritage structures. Compared to traditional methods, TLS offers not only a faster detection speed but also higher precision, capturing intricate details that might otherwise be missed [7]. The advantages of TLS are especially evident in addressing the complexities of historical building pathologies. By generating detailed point cloud data, this technology enables a comprehensive analysis of the building’s surface, making it possible to identify even the smallest cracks. This level of detail is critical for assessing structural integrity and formulating effective repair strategies. However, despite its numerous advantages, TLS technology also presents challenges. The inability to reflect signals from deep cracks results in a lack of internal crack information. Furthermore, point clouds often display uneven density and non-structured patterns, complicating the accurate and efficient extraction of crack data.

Motivated by the need for more precise and efficient crack detection methods in ancient buildings, this study aims to explore and optimize the use of TLS technology. The objective is to overcome the limitations of existing technologies and to develop a method for high-precision automatic extraction of crack information from point cloud data. Figure 1 shows the point cloud model of Zhonghua Gate Castle. By achieving this, the study seeks to provide a scientific basis for cultural relic protection, offering precise guidance for the restoration of ancient buildings and ensuring that these invaluable historical structures are preserved for future generations.

2. Related Work

Currently, the crack detection methods based on two-dimensional(2D) images have been relatively mature but their extraction accuracy is largely affected by the quality of the image itself; various external conditions may cause interference to them [8]. With the advancement in 3D laser scanning technology, the application of LiDAR in the detection of ancient building pathologies, especially in crack extraction, has become increasingly widespread. Point cloud-based crack extraction techniques primarily fall into two categories: methods based on geometric features and methods based on deep learning.

Methods based on geometric features primarily use differences in geometric characteristics between cracks and surrounding areas, such as crack gradient, normal vector, curvature, and density [9,10,11]. Researchers have employed multiple techniques in their studies on directly extracting cracks based on geometric features. Using local geometric features of point clouds, such as covariance, normal vectors, and curvature, to identify damaged points in the point cloud is the most direct and effective method [12,13]. Cao [14] enhanced the edge detection method through fractional differencing to achieve 3D crack identification and studied a plane fitting technique based on dynamic thresholds to calculate crack depth. Gu [15] employed statistical filtering and Euclidean clustering segmentation to identify regions of interest and then used the least squares plane fitting approach to ascertain the nature and extent of surface defects. Paulina [16] combined geometric and radiometric data from point clouds to detect cracks. To overcome the limitations of direct extraction methods, such as accuracy, automation, and adaptability to complex scenarios, researchers have begun combining geometric features with algorithms like clustering. Some algorithms such as Random Sample Consensus (RANSAC), region growth, and Euclidean clustering are considered the most classic approaches [17,18,19,20]. Furthermore, Zhang [21] achieved the effective detection and evaluation of reinforced concrete column damage through a series of complex calculation steps, including horizontal stratification, boundary line comparison, curve fitting, and interpolation calculation. Li [22] integrated the M-estimator Sample Consensus (MSAC) algorithm and the K-Nearest Neighbors (KNN) method to detect crack points by fitting planes and segmenting the point cloud. On the other hand, due to the relative maturity of image processing technology, converting point clouds into images for processing has become another effective method for extracting cracks. A common approach involves projecting the point cloud onto an image plane. Jiang [23] used planar triangulation modeling and inverse distance weighting point cloud rasterization methods to generate a grid surface and extracted cracks based on their shape features. Phan [24] extracted crack and damage points by calculating the normal vectors of points and the intensity gradients of adjacent points and then converted them into a binary image for processing. Zhong [25] loosely converted MLS data into a regular grid structure to adopt mature image-based crack extraction methods. Additionally, morphological methods applied to point clouds can also effectively detect cracks on building surfaces. Yang [26] focused on the Canny method using reflectivity intensity values to extract cracks in tunnel structures, an automatic and intelligent crack recognition and extraction method that combines dilation and the Canny algorithm. Zhou [27] proposed improved opening and closing operations to simultaneously detect concave and convex defects and designed a flexible filtering window increment strategy based on surface curvature.

Furthermore, it is worth mentioning that in recent years, with the rapid development of deep learning and neural networks, many researchers have used them to study the semantic classification of point clouds [28]. For example, Chen used an unsupervised learning framework and anomaly detection algorithms to accurately segment crack areas from point clouds, complementing the significant expansion graph convolutional network developed by Ma [29,30] and fully demonstrating the efficiency and accuracy of deep learning in detecting cracks in heritage buildings. Kim and Hu further improved the real-time performance and accuracy of crack detection by optimizing models and precisely registering images with LiDAR point clouds [31,32]. In terms of data processing, Nguyen used crack point cloud upsampling methods and the public point cloud dataset created by Bolourian, along with semantic segmentation methods, to collectively provide richer and more accurate data resources for crack detection [33,34]. Meanwhile, to address the deep learning model’s reliance on extensive annotated data, Feng used a semi-supervised approach and Zhang’s model correlating crack region pixel values with two-way travel time. These approaches have successfully alleviated the pressure of data labeling [35,36]. Additionally, Dong’s research on three-dimensional point cloud segmentation of road potholes and Pathak’s crack identification using Faster-RCNN have also provided new perspectives and solutions for the detection of cracks in heritage buildings [37,38]. There are studies focusing on combining systematic and periodic visual inspection with automated recognition of typical bridge defects to facilitate the evaluation of defect evolution over time, especially for reinforced concrete (RC) bridges, using deep learning (DL) methods and techniques to interpret prediction results [39]. To reduce the time and effort required for initial risk screening, some studies have adopted deep learning-based object detectors, such as YOLOv5, to automatically identify defects and damages in existing bridge elements [40]. In order to assess the efficacy of various crack extraction techniques, Feng [41] compared various methods including the identification and extraction of cracks based on first-order derivatives of height data, the extraction of crack points based on the difference between ideal and actual contours, surface fitting methods, local surface roughness algorithms, and machine learning.

In general, the above methods typically require the collection and processing of point cloud information, such as surface condition, geometric shape, point cloud density, and laser reflectance intensity of cracks. In real situations, point clouds may also contain cracks with uneven intensity, stains, and sensor noise. Data quality highly depends on factors such as the scanning range from the laser sensor to the target, the incidence angle of the laser beam, and the material characteristics of the target. This results in certain limitations when using geometric features to identify crack candidates. Deep learning-based crack extraction methods require large sample sets and training time, which reduces the efficiency of road surface point cloud extraction. In addition, there is a lack of relevant datasets and experiments to prove the effectiveness and robustness of these algorithms.

To overcome these limitations, this paper proposes a new method that combines super-voxel segmentation, surface reconstruction, Euclidean clustering, and convex hull algorithms to achieve the automatic extraction of cracks on the surface of heritage buildings. Aiming at the aforementioned issues, this paper adopts local surface reconstruction technology combined with super-voxel segmentation to fill in missing point data in the crack area. Combining with the Euclidean clustering algorithm, cracks are identified. The concave–convex algorithm is used to calculate the area of triangular facets within the convex hull, obtaining geometric features such as the length, width, and area of the crack. Subsequently, the proposed method was experimentally verified and compared with the traditional total station extractor method for crack extraction. This method effectively addresses the issue of difficulty in feature extraction due to missing information inside cracks. The research ideas and methods of the article are described in Section 3. In Section 4, specific tests and experiments are carried out and experimental results and analysis are presented. The results and scientific validity of the method proposed in this paper are discussed in Section 5. The summary and prospect of the article are given in Section 6.

3. Materials and Methods

Cracks on the surface of heritage buildings not only affect the overall aesthetics but also more seriously threaten the structural stability and, moreover, could lead to safety accidents. This study takes Zhonghua Gate Castle as the research object, uses a TLS to obtain the point clouds of Zhonghua Gate Castle, and researches the crack detection and feature extraction methods based on those point clouds. The technical route is shown in Figure 2.

3.1. Preprocessing of Point Clouds

During the initial analysis of the point clouds model of the wall, it was discovered that many cracks were occluded by vegetation. This made crack detection and analysis difficult. Due to the corrosion and detachment of bricks on the wall surface, the wall surface is not smooth, which means that the point clouds of the wall surface do not exhibit clear planarity. This makes the extraction of cracks more complicated. In the preprocessing stage, three key steps are taken to deal with these challenges: (1) the Cloth Simulation Filter (CSF) is used to remove ground points; (2) the super-voxel segmentation is applied to divide the point clouds into multiple modules; and (3) the RANSAC algorithm is used to fit planes to each module and remove vegetation point clouds based on the distance from the point clouds to the fitted plane.

3.2. Removal of Ground Points

The CSF is a typical method employed for noise removal and the extraction of valuable information from point clouds [42]. This algorithm is based on the physical modeling of point clouds, resembling the motion simulation of cloth, thus eliminating noisy points. Traditional filtering algorithms mostly differentiate between objects and ground points based on differences in slope and elevation changes, while the “cloth” filtering algorithm takes a completely new approach by flipping the point clouds. Assuming a piece of cloth is dropped from above under the influence of gravity, the final position of the cloth represents the current terrain, enabling the separation of ground and non-ground points. It is shown in Figure 3. In this paper, the proposed processing method not only reduces interference from non-target objects in crack detection but also enhances the visibility and clarity of detailed crack features within the point cloud. Meanwhile, CSF filtering is effective in reducing both false positives and false negatives, enabling a more precise quantitative analysis. This provides reliable data support for subsequent crack assessment and maintenance work.

The black solid line on the bottom represents the original measurement, which is flipped, and the blue dashed line represents the fabric, which can reflect the ups and downs of the terrain. The core of the CSF algorithm can be calculated as follows:

$$m{\displaystyle \frac{\partial X(t)}{\partial t^2}}=F_{ext}(X,t)+F_{\mathrm{int}}(X,t)$$

(1)

where $X$ represents the position of the particles in the “cloth” at time $t$, $F_{ext}(X,t)$ represents the external drivers (gravity, collisions, etc.), and $F_{\mathrm{int}}(X,t)$ represents the internal drivers (internal connections between particles). Therefore, it can be concluded that both $F_{ext}(X,t)$ and $F_{\mathrm{int}}(X,t)$ factors impact the position of the “cloth” particles. Separation between ground and non-ground is achieved through identification under both internal and external driving forces.

3.3. Super-Voxel Segmentation

After removing the ground points, the number of points in the wall point cloud model is too large and the fitting of the whole wall plane using the least square method is not ideal. In this paper, the Voxel Cloud Connectivity Segmentation (VCCS) method is used to segment the point clouds [43], dividing the wall surface into multiple modules. Compared to traditional methods based on images, super-voxel segmentation performs better in handling object boundaries. Furthermore, it uses a spatial octree structure and directly performs segmentation on the point clouds through the region growing with K-means clustering.

The process of super voxel iteration generation involves local K-means clustering, taking into account both connectivity and flow direction. The specific process is as follows:

(1)

Initial seed point selection: start with the voxel closest to each cluster center and consider neighboring voxels in turn;

(2)

Adjacent voxel evaluation: for each adjacent voxel, the following distance formula is used for evaluation and the characteristic distance between the adjacent voxel and the current super voxel center is calculated as follows:

$$D=\sqrt{w_c{D}_c^2+{\displaystyle \frac{w_s{D}_s^2}{3R_{seed}^2}}+w_n{D}_n^2}$$

(2)

(3)

Minimum distance mark: if the calculated distance D is minimum, the adjacent voxel is marked as belonging to the current super voxel and that adjacent voxel is added to the search sequence of the corresponding label;

(4)

Iterative processing: iterative processing of the next super-voxel, with the seed voxel as the center, expanding outward, is defined as the same time level of all super-voxels. This process continues until reaching the search volume edge of each voxel or there are no other neighboring points that can be traversed.

3.4. Removing of Vegetation

After super-voxel segmentation divides the wall surface point clouds into multiple modules with a tendency toward planar structures, the Random Sample Consensus algorithm (RANSAC) is used to fit planes to each module, effectively removing vegetation by measuring the distance between vegetation points and the fitted planes. Sufficient points are selected from the point clouds for plane fitting. These points can be randomly selected or preprocessed and filtered to exclude outliers. An initial plane model is formed by randomly selecting points. This plane can be represented as follows:

$$Ax+By+Cz+D=0$$

(3)

where, $A$, $B$, $C$, and $D$ are the parameters of the model and $x,y,z$ are the 3D coordinates of each point.

The distance from each point in the data to the fitted plane is calculated. If the distance is smaller than the threshold, label these points as inliers consistent with the plane model. The number of inliers under the fitted plane is calculated and whether the number of inliers has reached a predetermined minimum is estimated. If there are enough inliers, the model is considered effective. Re-estimate the plane parameters using all inliers and use fitting methods such as least squares to improve the accuracy of the model. The above steps are repeated several times in order to search for multiple possible plane models. The model with the most inliers from all iterations is selected as the best-fitting plane and then the parameters of the best-fitting plane and the inliers on the plane can be obtained. Due to the vegetation being attached to the wall surface, it is not on the same plane as the wall surface, so the above algorithm can effectively remove vegetation points as outliers.

3.5. Crack Detection

In the stage of crack detection, it is very important to recover the point clouds inside the crack. The restoration of point clouds inside the cracks was achieved through a process of curved surface reconstruction in this study. The process of curved surface reconstruction is in Figure 4.

The basic idea of the Alpha-shape algorithm is to roll a circle with a radius of $\alpha$ around a given set of discrete points $S$. When $\alpha$ is properly chosen, the circle will not roll inside $S$, the points that intersect with the circle are the edge contour points of $S$, and the trace of the rolling circle is the boundary line of $S$. Taking any two points within the point set $S$, a circle with a radius of $\alpha$ is drawn through these two points. If there are no other points inside the circle, it can be considered as part of the borderline.

The convex hull of the point clouds is created by convex hull calculations on the input point clouds in this paper. The convex hull is used to identify local concave–convex regions in the point clouds. The computation of concave–convex polygons involves removing one or more convex parts from the entire convex hull. These convex parts are determined by specifying the parameter $\alpha$, which determines the smoothness of the concave polygons generated on the convex hull. A smaller $\alpha$ will generate concave polygons that are closer to the convex hull, while a larger $\alpha$ will generate smoother concave polygons. The final output is the mesh format of the concave–convex polygons, which is used to establish the surface model of the wall.

The point cloud data after curved surface reconstruction is used as the target point clouds and the difference segmentation operation is performed by comparing the point clouds before and after curved surface reconstruction. Each point in the source point clouds is traversed and the square of its Euclidean distance to all points in the target point clouds is calculated. If the Euclidean distance between a source point and any point in the target point clouds is less than or equal to the threshold, the source point is considered a non-differing point. If the threshold is set as the square of the maximum distance between corresponding points in the source point clouds and target point clouds, it could be calculated as follows:

$$d^2={(p_x-P_x)}^2+{(p_y-P_y)}^2+{(p_z-P_z)}^2$$

(4)

where $d$ represents the distance between the source points and the target points, $p$ refers to the point in the source point cloud, and $p$ refers to the point in the target point cloud.

If the squared Euclidean distance between a source point and any point in the target point clouds is larger than the threshold, then the source point will be marked as an outlier. All source points marked as outliers will form a new point cloud dataset, namely the crack point cloud dataset. After extracting the crack points, the noise points could be eliminated by Euclidean clustering, which can improve the accuracy of crack detection. Its main steps are as follows: inputting the point cloud data and setting the threshold of Euclidean distance $d$. Constructing a KD-tree for an efficient nearest neighbor search. Selecting one point from the unprocessed points as the seed point of the current cluster randomly. Finding all neighboring points within the threshold distance from the current seed point via the KD-tree, adding them to the current cluster, and labeling them as processed. Repeating this search and expansion process until no more points can be added to the current cluster. After each expansion, it is checked as to whether the current cluster contains a sufficient number of points. If the condition is met, save the cluster. Next, an unprocessed point is selected as the new seed point to create the next cluster. This process is repeated until all points are assigned to a cluster.

3.6. Characterization of Cracks

The features of surface cracks in heritage buildings usually include the length, width, and area. In this study, the length and width of cracks refer to the maximum longitudinal length and maximum transverse length, which can be directly calculated using the coordinates of the crack point clouds; they are shown as follows:

$$\{{\displaystyle \frac{length=\left|z_{\max }-z_{\min }\right|}{width=\left|x_{\max }-x_{\min }\right|}}$$

(5)

Regarding the crack area, the Graham scan algorithm [44] is used to reconstruct the convex hull of the crack point clouds and the area of the triangular facets within the convex hull is calculated to obtain the crack area. The basic idea of the Graham scan algorithm is to first find a point on the convex hull and then proceed counterclockwise to find each point on the convex hull starting from that point.

The detailed steps of Graham scanning algorithm are as follows:

(1)

Selecting the point $H$ with the smallest y-coordinate among all points as the base point. If there are multiple points with the smallest y-coordinate, we select the one with the smallest x-coordinate. Points with the same coordinates should be excluded;

(2)

Sorting the vectors $\stackrel{\rightharpoonup }{HP}$ formed by each point $p$ and the base point according to the angle with the x-axis. The base point is $H$ and the sorted points from smallest to largest angle are $H,K,C,D,L,F,G,E,I,B,A,J$. Then, proceed with counterclockwise scanning, as shown in Figure 5. Each border line of the convex hull in the figure is represented by $l$.

(3)

$l_{HK}$ must be on the convex hull; then, $C$ is added. Assuming $l_{KC}$ is also on the convex hull. For $H$, $K$, and $C$, their convex hull is formed by these three points. But when $D$ is added, it is found that $l_{KD}$ will be on the convex hull, so $l_{KC}$ is excluded and $C$ cannot be a convex hull point. Certainly, when a point is added, it is necessary to consider whether the previous segment is on the convex hull;

(4)

In the above figure, when $K$ is added, because $l_{HC}$ needs to rotate to the angle of $l_{HK}$ in a clockwise direction, $C$ is not on the convex hull and should be removed, while point K is retained. Then, $D$ is added because $l_{KD}$ needs to rotate to the angle of $l_{HK}$ in a counter-clockwise direction; $D$ is retained. By repeating the above steps until all points in the point set have been traversed, the convex hull is obtained.

The area of the convex hull can be calculated using the area formula of a polygon. Using the vertex coordinates of the convex hull $(x_1,y_1),(x_2,y_2),\cdots ,(x_n,y_n)$, the polygon is divided into several triangles based on the principle of vector cross product and the area of each triangle can be calculated as follows:

$$Area=0.5\times \left|(x_1{y}_2+x_2{y}_3+\cdots +x_n{y}_1)-(y_1{x}_2+y_2{x}_3+\cdots +y_n{x}_1)\right|$$

(6)

4. Experimental Analysis

In this study, a section of Zhonghua Gate Castle’s exterior wall is selected as the study object. The surveying area is 128 m long and about 22 m high, covering an area of about 2900 m². The Faro Focus 3D X330 laser scanner, manufactured by FARO Technologies Inc. in Lake Mary, Florida, United States, was used to obtain experimental data. The main parameters of data acquisition are as follows: data were scanned at intervals of 20 m, with a total of three stations; the vertical distance between the scanner and the wall is about 5 m; the resolution and quality of the scanned data are set to 1/4; the horizontal angle is set between 0° and 180°; and the vertical angle ranges from −30° to 60°. Figure 6 shows the data acquisition site.

The original point clouds contain noise, invalid data, and other redundant information. To make them suitable for experimental analysis, they must be preprocessed to clean and optimize them. The preprocessing includes three steps: (1) removing points on the ground via CSF, (2) dividing the point cloud of the wall into multiple modules with planar characteristics by the super-voxel segmentation technique, and (3) fitting planes for each module in order to remove vegetation point clouds on the surface of the wall by RANSAC. The original and preprocessed point clouds are shown in Figure 7. Figure 7a shows the point cloud model of the Zhonghua Gate Castle and it is apparent that there are numerous trees in the vicinity, which has a substantial influence on the research. Figure 7b shows the result of removing ground points from the exterior wall on the north side of the Castle and it is evident that there are multiple cracks, broken bricks, and vegetation covers on the walls. Figure 7c shows the result of super-voxel segmentation, dividing the wall surface of Figure 7b into eight modules with a tendency toward planar characteristics. Figure 7d shows the vegetation point clouds that need to be removed after plane fitting, where the red color represents vegetation point clouds and the blue color represents the point cloud model of the wall after vegetation removal.

The local curved surface reconstruction is performed on the preprocessed point clouds and the point clouds before and after curved surface reconstruction are segmented differently. The difference points are determined by comparing the squared distance of the corresponding points. These difference points are identified as crack points. The result of the difference segmentation is shown in Figure 8. In Figure 8a, the identified difference points can be observed, which include not only interior crack points but also some noise points that may cause certain interference in the analysis of crack features. To clearly display the extracted difference points, the wall point clouds are represented in red and the difference point clouds are represented in green in Figure 8b.

In order to verify the feasibility and effectiveness of the proposed method, Euclidean clustering was performed on the difference point clouds; the detection results are shown in Figure 9. As can be seen from Figure 9, there are three obvious cracks on the surface of the wall, which are numbered A, B, and C and represented by different colors. It is confirmed in the field that the shape of the cracks in Figure 9 is consistent with the actual shape of the wall cracks. It shows that the above method can effectively detect the wall cracks.

After point cloud preprocessing and crack detection, the experimental results successfully extracted 110 cracks. However, many regions of brick detachment on the wall can also be mistakenly identified as cracks. To accurately describe the characteristics of cracks, this study filtered and classified them based on their area. Specifically, cracks with a length of less than 0.1 m and an area of less than 0.05 m² were excluded from the statistical analysis of cracks. The results of the crack feature analysis are shown in

Table 1. Results of crack extraction.

Crack Area (m2)	Number of Cracks
0 < Area < 0.01	54
0.01 < Area < 0.05	5
0.05 < Area < 0.1	3

and

Table 2. Geometric characteristics of cracks.

ID	Extract Length I (m)	Extract Width I (m)	Extract Length II (m)	Extract Width II (m)	Actual Length (m)	Actual Width (m)	Area I (m2)	Area II (m²)
Crack A	0.718	0.066	0.752	0.078	0.709	0.061	0.155	0.178
Crack B	0.558	0.046	0.601	0.058	0.551	0.043	0.118	0.136
Crack C	1.285	0.309	1.312	0.333	1.289	0.305	0.533	0.556

. Table 1 shows the statistical data of classifying cracks into different levels based on their area. In Table 1, there are a total of 54 cracks with an area less than 0.01 m², 5 cracks with an area between 0.01 m² and 0.05 m², and 3 cracks with an area between 0.05 m² and 0.1 m². Table 2 compares the three representative cracks on the wall with the data obtained from field measurements using total-station without prism. The results indicate that the error between the crack features calculated by the proposed method and the actual crack is only at the millimeter level, further demonstrating the accuracy and feasibility of the method.

This research conducts a comparative analysis of crack geometric characteristics, comparing the proposed method with a point cloud-to-image conversion technique to evaluate their precision and effectiveness in crack detection and analysis. Table 2 shows two methods: Method I, the proposed approach, and Method II, which involves point cloud-to-image conversion. The point cloud-to-image conversion involves projecting 3D data onto a 2D plane and using edge detection and shape fitting to identify crack features. Table 2 shows that the proposed method achieves millimeter-level accuracy in measuring crack dimensions compared to actual metrics. This precision is achieved through a local surface reconstruction technique that effectively fills voids in crack data, complemented by the Euclidean clustering algorithm’s efficiency in crack detection. Moreover, our method demonstrates superior adaptability and robustness. The latter method relies on 3D-to-2D projection and subsequent crack extraction via edge detection and shape fitting, which can be limited by image resolution and projection angles, possibly affecting the accuracy of crack feature extraction. In contrast, our method avoids complex data transformation, directly extracting features from the raw point cloud, thus reducing error loss and accumulation. The enhanced automation in our method minimizes manual intervention, increasing the efficiency of crack detection. To enhance the clarity and comparative ease of the presented results, Figure 10 presents a bar chart that visually contrasts the different methods.

Additionally, the qualitative assessment is employed to evaluate the accuracy of crack detection. Initially, a total of 166,493 crack points were successfully identified in this paper. During crack detection, some noise points were erroneously classified as crack components due to various interference factors. An outlier removal algorithm was employed, successfully eliminating 45,682 noise points. To assess the comprehensiveness of crack identification, a comparison was conducted between the identified cracks and the actual crack count. The recall rate, defined as the ratio of correctly identified cracks to the total number of cracks, was calculated. The method identified a total of 110 cracks, with 62 accurately classified as such. An additional 15 cracks were not accounted for in Table 1 due to their small size. The achieved recall rate of 85% demonstrates the high efficiency and reliability of our method for real-world applications.

5. Discussion

From the perspective of this paper, the detection and feature extraction of wall crack diseases based on point cloud data is for the case where there is no point cloud inside the cracks. Due to the missing point clouds, it is not feasible to directly identify crack diseases on the wall based on point cloud features such as normal vectors, curvature, and density. Moreover, K-means and region growing algorithms cannot directly classify and extract the cracks. The method used in this paper is to fill the cracks in the point clouds of the wall so that the inside of the cracks has information and then identify and extract them through clustering methods. The feasibility and accuracy of this method are also verified through experiments. In this paper, cracks are defined as linear areas characterized by the longitudinal absence of point clouds. Despite the effective extraction of cracks, there are many connecting gaps at the boundaries of the bricks on the city wall, which have a certain impact on crack identification. The surface structure of the wall is not particularly complex to a certain extent and each segmented module tends to be planar. The curved surface undergoing reconstruction is actually approximately planar. Therefore, whether the method of curved surface reconstruction has minimal effect on more complex three-dimensional models needs further verification.

In data processing, it is important to remove ground points and segment the point clouds of the wall into modules. The purpose of removing ground points is to clean the point clouds and eliminate irrelevant information to the cracks, such as ground and vegetation, thus reducing data noise and improving the recognizability of cracks. Additionally, removing ground points reduces the size of the dataset, thus improving the efficiency of subsequent processing. Segmenting the point clouds of the wall into multiple modules with planar characteristics allows independent processing of each module, reducing computational complexity and facilitating subsequent processing. Furthermore, the structure of segmented point clouds aids in the better analysis and detection of cracks on the wall, making it easier to capture crack features in each module and improve the accuracy and repeatability of experimental results.

According to the results of crack extraction, the information inside the cracks on the wall was successfully restored and 62 cracks were identified. The cracks were divided into three levels based on their area: less than 0.01 m², between 0.01 m² and 0.05 m², and greater than 0.05 m². Accordingly, there were 54 cracks in the first level, 5 cracks in the second level, and 3 cracks in the third level. Furthermore, the length, width, and area of each crack were calculated and compared with the actual crack dimensions. The analysis shows that the error between the results of this study and the measurement results is within the millimeter range. The results of the experiment confirm the scientificity and feasibility of this study. It should be noted that the surface reconstruction of the wall data tends to be more planar. In reality, the wall is not a perfectly planar surface. This study conducted experiments under the assumption of disregarding this condition. Future research will focus on more accurate curved surface reconstruction methods to further improve measurement accuracy. The qualitative assessment of the method revealed a recall rate of 85% but underperforms in detecting cracks in complex heritage structures. For the improvement in this method, especially in improving the outlier removal algorithm to reduce the number of false positives, the integration of additional qualitative metrics is pertinent, such as the precision of crack length and width measurements, which will further enhance our method’s evaluative capabilities.

6. Conclusions

The paper aims to effectively and accurately identify and analyze the characteristics of wall cracks without internal point cloud information. To achieve this method, a local curved surface reconstruction method combined with super-voxel segmentation is adopted and crack identification and feature analysis are performed through Euclidean clustering. The main contribution of this paper lies in crack identification and feature analysis.

(1)

CSF filtering is applied to the original wall point cloud data to remove ground points and obtain wall point clouds. By employing super-voxel segmentation, the wall surface is segmented into eight modules exhibiting planar characteristics, aiding in the use of RANSAC plane fitting to remove disturbances like vegetation;

(2)

Based on the principle of the convex hull algorithm, surface reconstruction is performed for each module to restore point cloud information within the cracks. Euclidean clustering is used to extract crack points;

(3)

In the feature analysis of cracks, geometric features such as the length, width, and area of the cracks are studied. Experimental results show that the method can accurately identify crack diseases on the surface of the wall and determine basic information such as the location, number, and orientation of cracks on the wall. After comparing and analyzing the extracted results with the actual crack size, the error is at the millimeter level;

(4)

The qualitative measurements further validate the efficacy of the method. With a recall rate of 85% and the successful identification of 166,493 crack points, the method exhibits superior adaptability and robustness. It avoids the data transformation required by point cloud-to-image techniques, thereby minimizing information loss and cumulative error. The high level of automation in the method reduces manual intervention, significantly improving the efficiency of crack detection.

In addition, cracks are classified and statistically analyzed based on their area sizes. Crack information and characteristics provide an important basis for the structural safety assessment in ancient buildings. Future research directions include further studying effective strategies for dealing with missing data and introducing deep learning techniques.