# Pavement Crack Detection from Mobile Laser Scanning Point Clouds Using a Time Grid

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Methods

#### 2.3. Construction of a Tgrid for MLS Point Clouds

_{k}

_{+1}− θ

_{k}) ≠ 0, k = 1, 2, …, N, the kth point is a piecewise point. Let m represent the number of k detected. The numerical array [1, k

_{1}, k

_{2}, …, k

_{m}, N] then forms (m + 1) non-overlapping intervals, which correspond to (m + 1) scan lines. On each scanning line, the multiples of scan angles, θ, with respect to the angular resolution, ∆θ, is calculated to obtain the j value of each point, j = θ/∆θ.

_{G}be the time series of the scanner ground track, T

_{G}= {T

_{G}

_{1}, T

_{G}

_{2}, T

_{G}

_{3}, …, T

_{Gm}

_{+1}}, and T

_{Gi}

_{+1}− T

_{Gi}= Δt, where Δt is the elapsed time on each scan line. The time range [T

_{Gi}− Δt/2, T

_{Gi}+ Δt/2] divides the laser points to the ith scanning line. The j indexes of points on ith scanning line can be derived as $j=\lfloor \left(T-{T}_{Gi}\right)/\mathsf{\Delta}T+0.5\rfloor $, where ΔT denotes the emission time interval of the laser beams. If ∆T is unknown, it can be estimated using the time difference (T

_{i}

_{+1}− T

_{i}) between the adjacent laser points. Note that (T

_{i}

_{+1}− T

_{i}) may change over time. We use the symbol ⌊ ⌋ to reduce the estimation error (for more detail, please refer to Reference [34]). In the Tgrid, each point (i, j) has a maximum of four side neighbors: (I − 1, j), (i + 1, j), (i, j − 1), and (i, j + 1), and four diagonal neighbors: (i − 1, j − 1), (i + 1, j − 1), (i − 1, j + 1), and (i + 1, j + 1). The spatial position of these neighbors is free. In addition, eight neighbors may not always exist. When there are no laser beam returns and no neighbors, they are shown as empty nodes (as shown in (i − 1, j − 1) in Figure 2b).

_{t}, y

_{t}) before P(X, Y, Z, T, I) to the expressed MLS point clouds as a Tgrid map, G(x

_{t}, y

_{t}, X, Y, Z, T, I), where (x

_{t}, y

_{t}) represents the row and column of a point in the Tgrid map. Similar to a multi-band image, (X, Y, Z, T, I) represent the multi-band characteristics. The cost of building and maintaining such a 2D grid is quite low.

#### 2.4. Detection of Road Surface Points and Crack Candidates

#### 2.4.1. Detection of Road Surface Points

_{t}× Wy

_{t}. The sub-block located by the scanner ground track serves as the initialized searching sub-block, P

_{0}(shown in red in Figure 5b). Next, both the road surface and road boundary areas are searched along x

_{t}and y

_{t}directions through a statistical hypothesis test based on the point altitudes in the sub-block. Then, the possible road points are extracted from the sub-blocks of the road surface and road boundary and finally, identified by finding the largest connected region in the Tgrid.

_{S}, in a road patch conforms to the Gaussian distribution of N (μ, σ) and that μ is unknown. Let the number of points within the sub-block be N

_{b}. A statistical test problem for the population variance with unknown mean is as follows:

^{2}is the standard deviation. The statistical variable and its region of rejection are:

_{1}is accepted (shown in green in Figure 4b) and H

_{0}is denied. This means that no road boundary area is found; otherwise, H

_{0}is accepted (shown in blue in Figure 4b). The associated sub-block is selected for the road boundary area. Figure 4b illustrates the process of detecting this area. The proposed method can be summarized as follows:

- (1)
- Set an initialized searching sub-block, P
_{0}, where trajectory data are located, and calculate the statistical variance, σ_{0}^{2}, of the point altitudes within it. - (2)
- Search forward to find the road boundary area along the direction of x
_{t}, y_{t}, and the opposite x_{t}and opposite y_{t}, until a sub-block (shown in blue) that passes the test is found. Pause searching. - (3)
- Iterate for all trajectory points until all road boundary areas are beside each other.
- (4)
- Filter the non-road points in the road boundary area (shown in blue) and its closed road surface neighbors (the closed sub-block shown in green) using a height threshold, h
_{th}, to the local road plane. - (5)
- Extract the complete road surface by finding the largest connected region in the Tgrid.

_{t}× Wy

_{t}) can be determined through the geometric dimension, W

_{D}. Although the distance of the adjacent points is inconsistent in y

_{t}directions, we unified the W

_{yt}for convenience. The mean spacing between the adjacent scanner ground track, ${d}_{s}$ (in x

_{t}direction), and the largest distance between the adjacent road grid points, ${d}_{a}$ (in y

_{t}direction), are used to determine Wx

_{t}and Wy

_{t}. This means that Wx

_{t}=$\lfloor {W}_{D}/{d}_{s}+0.5\rfloor $ and Wy

_{t}= $\lfloor {W}_{D}/{d}_{a}+0.5\rfloor $. Due to the fixed size of the sub-blocks, it is also possible that the road boundary lies in the road sub-block adjacent to the boundary area. Thus, we derive the local road plane by fitting the 3D coordinates of the points in a road boundary area (shown in blue) and its closed road neighbors (the closed sub-block shown in green) using the robust least-squares method. Hence, more road points are participating in the fitting of the local plane. The conformity of the fitting plane to the road surface is thereby ensured. The height of points involved in the fitting operation to the local plane is taken as the evaluation standard of whether this is a non-road point. The height threshold, h

_{th}, can be given according to the roughness of the road surface.

#### 2.4.2. Detection of Crack Candidates

_{R}, that is larger than the common maximum width of the crack. An M estimator of Andrew’s type was applied to derive the robust altitude, Z

_{M}, of the road surface and the standard interquartile interval, Z

_{NIQR}, is used to measure the degree of the pavement roughness. The two conditions are combined as follows:

_{d}expresses the maximum possible depth of the crack, which is designed to eliminate the penetration laser point caused by loose pavement facilities, such as rainwater grates, well covers, etc. Next, gradf(i, j) represents the average gradient value centered on (i, j), which is calculated through the geometric coordinates (X, Y, Z) of eight neighbors using Equation (7). Note that only the existing neighbors are calculated. Following this, v

_{th}defines the minimum gradient change requirement of the crack candidates. Figure 7 depicts the characteristics of the valley points. The extracted valley points were recorded to dataset G

_{V}:

_{P}) is preset to reduce the unfavorable effects of any generous non-crack points. Figure 8 shows the flow of the detection method.

_{B}, using a median filter from the input intensity Tgrid map, G

_{I}, which derives from the grid index (i, j) and its intensity. Next, the background-differential map, G

_{F}, is obtained using a minus operation as follows: G

_{F}= G

_{I}− G

_{B}. In Figure 8b, the proportion limitation of the crack points (C

_{P}) is given and the relevant truncation value, F

_{B}, is calculated on the histogram of G

_{F}. The differential truncation map, G

_{FC}, is generated in Figure 8c by transforming the value of G

_{F}(i,j) that is higher than F

_{B}to F

_{B}. The maximum entropy method is then adopted to determine the segment threshold, T

_{C}, of the possible crack points (recorded in G

_{P}) and non-crack points. Finally, G

_{P}is filtered through the valley effect to remove the nearest non-crack point on both sides of the G

_{P}point along the t

_{x}and t

_{y}directions to compare their altitude. As shown in Figure 8f, two rectangles frame the crack points in the directions of t

_{x}and t

_{y}respectively, with non-crack points intercepted at two ends when centered on a candidate. If the altitude of the candidate is no greater than the largest of the four non-crack neighbors, the candidate is reserved; otherwise, it is filtered out. The remaining crack candidates are saved to the binary map, G

_{C}.

_{V}∪ G

_{C}is taken as the candidate crack points.

#### 2.5. Generation of the Crack Skeleton and Calculation of Crack-Shape Parameters

#### 2.5.1. Generation of the Crack Skeleton

_{2}. Given that the width and the height of the rectangle are R

_{W}and R

_{H}, they can be determined by the distance between the densest point cloud under the vehicle in the direction of x

_{t}and y

_{t}. We assumed these to be d

_{x}and d

_{y}, respectively. Thus, R

_{W}= 2 × $\lfloor {D}_{2}/{d}_{x}+0.5\rfloor $ + 1, R

_{H}= 2 × $\lfloor {D}_{2}/{d}_{y}+0.5\rfloor $ + 1. The points within the second layer form the structural elements of the morphology algorithm. Note that some empty nodes without geometric coordinates may be expanded during this process. To mark the connected regions of the cracks using the 8-connected neighborhood, the 3D coordinates of the expanded empty nodes are linearly interpolated using the closest existing neighbors at both sides along the t

_{y}direction.

_{x}direction) and height (the number of points in the t

_{y}direction) of the connected regions and recover them to the geometrical space to calculate their geometrical dimensions. If the longest of two sides is larger than the set length threshold, L

_{th}

_{1}, the connected region indicates a curve region. Otherwise, it is marked as noise to be removed. The remaining regions are thinned to extract the continuous crack skeletons.

_{th}

_{1}, between the endpoint and the intersections that were first encountered. Each skeleton only leaves one longest main curve, and the rest are defined as branches, i.e., another skeleton. The skeleton curve is traced by the Freeman chain code and the coordinates of crack points are recorded to a table to calculate the crack-shape parameters.

#### 2.5.2. Calculation of Crack-Shape Parameters

_{LW}of the smallest circumscribed rectangle of the skeleton points and its long axis direction to determine the crack direction. When R

_{LW}exceeds the set threshold, R

_{LWth}, the direction of the crack must be evaluated in sections. Otherwise, the crack is oriented by the angle α between the long axis direction of the minimum circumscribed rectangle and the vehicle path. The crack direction is classified as transverse, vertical, or oblique with the related inclination ranges of the α value [0, π/6], (π/6, π/3), and [π/3, π/2]. In Figure 10, crack 2# and crack 3# are classified as transverse and vertical due to the qualified R

_{LW}and the scope of the values of α. Crack 1# has an R

_{LW}exceeding the specified threshold and is further separated into two sections, the piecewise points of which are given at the farthest point from the straight-line connecting head and tail. The R

_{LW}ratio of the smallest external rectangle of the cracks is recalculated and split again until R

_{LW}≤ R

_{LWth}, and the angle α between the long axis direction and the path line is taken to identify the trends of the segmented cracks.

_{i}corresponds to the width of the ith point of the left edge. Next, j = 1, 2, 3, …, N

_{R}, where N

_{R}denotes the number of points on the right edge. However, limited by the geometric resolution of the MLS data, the extracted cracks contain many single-point-thickness points, particularly the transverse cracks along the scan line:

_{S}, is given to fit the edge points within the search range to a virtual edge line. The maximum distances w

_{iL}and w

_{iR}from the edge points to the line on both sides are calculated, and w

_{i}= max (w

_{iL}, w

_{iR}) is taken as the related width of the point. The procedures of the crack width calculations are as follows:

- In the Tgrid, the Freeman chain code is used to track the edge of the crack connection area. The closed edge curve is disconnected from the endpoint of the skeleton to split the edge into the left and right borders (Figure 11a).
- The edge points shared by the left and right borders are searched and marked as single-point-thickness edge points. In the above method, w
_{i}= max (w_{iL}, w_{iR}) is adopted to calculate the related crack width (Figure 11b), while other edge points use Equation (8). - Output the average width of all edge points to measure the severity of the cracks. The maximum width of the crack and its corresponding location, P
_{m}(i, j, X, Y, Z, T, I), serve as the supplementary information.

_{k}, Y

_{k}) and (X

_{k}

_{+1}, Y

_{k}

_{+1}) express the plane coordinates of two adjacent crack skeleton points, assuming there are N

_{L}skeleton points in the crack.

## 3. Results and Discussion

_{D}, α, and h

_{th}in Section 2.4.1 represent the geometric dimension of the initialized searching sub-block P

_{0}, the significance level or the confidence of the statistical test problem, and the roughness of the road surface, respectively. The parameters h

_{d}and v

_{th}express the maximum possible depth and the minimum gradient change requirement of the valley point. The parameter C

_{P}in Section 2.4.2 presets the proportion of the crack points in the number of all point clouds. The parameter D

_{2}is the preset searching radius of the second layer of the structural elements in the morphological closing algorithm. The parameter L

_{th}

_{1}denotes the minimum length threshold of the connected region of crack points. The parameter R

_{lwth}in Section 2.5.2 is the threshold of the length/width ratio to determine the crack direction. The parameter R

_{s}illustrates a search radius to define a virtual edge line when dealing with the single-point-thickness edge point.

_{P}is the true positive, i.e., the correctly detected crack curves, while F

_{P}expresses the false positive, i.e., the number of cracks detected incorrectly. F

_{N}denotes false negative, i.e., the number of crack curves not detected.

_{W}and C

_{L}:

_{W}and E

_{W}represent the average width of the actual crack and extracted crack respectively, and T

_{L}and E

_{L}are the total length of the actual crack and extracted crack. Figure 14 shows the histogram of the width and length compliance of 60 extracted cracks at 0.05 intervals, in piles of three types of cracks.

_{W}and C

_{L}, the estimated width of the longitudinal crack was the closest to the actual width, followed by that of the oblique crack. In addition, the width compliance of the transverse curves was the lowest at only 0.812. This may be attributable to the fact that most of the transverse cracks are single-point-width cracks. With only one laser point on the width direction of the crack curve, it is difficult to obtain high-precision calculation results. The width accuracy of the oblique cracks was second, which may owe to its scattered distribution across multiple scan lines, bringing challenges to its identification and width measurement. The longitudinal crack points gather in the t

_{x}direction with high geometric resolution. With multiple points in the crack width direction, the longitudinal crack achieved the highest accuracy of the width measurement, i.e., up to 91.05%. It is worth noting that spot checks were also made on the widest section and related position of the extracted cracks. However, no satisfactory results were obtained. Considering the positioning error rate of the MLS system, a position error within ±5 cm is regarded as an accurate detection. Nonetheless, the correct detection rate of the widest section was less than 60%. It may be inferred that the geometric resolution requiring improvement is still the bottleneck of the crack detection from the MLS data.

_{P}with T

_{C}was also tested. Figure 16a shows the changing trends of the value of T

_{C}with C

_{P}; where C

_{P}increases, T

_{C}increases. When C

_{P}reaches 6%, T

_{C}approaches saturation. We did not test for cases greater than 10%, as crack points rarely account for more than 10% of the surface points on large roadways.

_{P}(not exceeding 10%). It is also evident that when C

_{P}exceeds 4% (Figure 16b), the extracted crack curve is almost complete. As C

_{P}continues to increase, the noise increases. It is preferable to infer that the real proportion of cracks of the test data was approximately 4%. The results show that presetting the crack ratio is effective for eliminating interference.

_{x}and t

_{y}direction can be compressed to 0.1–1 cm), detecting cracks from MLS data would have more potential and research value. In addition, the proposed structure makes point cloud processing easier and can introduce mature image processing methods into point cloud processing. More efforts are expected to be devoted to the detection of other on-road facilities, such as curbs, road markings, and manholes, from MLS data using the Tgrid method. Furthermore, the potential of Tgrid for improving the current deep learning point cloud frameworks is promising.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

- Koch, C.; Georgieva, K.; Kasireddy, V.; Akinci, B.; Fieguth, P. A review on computer vision based defect detection and condition assessment of concrete and asphalt civil infrastructure. Adv. Eng. Inform.
**2015**, 29, 196–210. [Google Scholar] [CrossRef][Green Version] - Weng, X.; Huang, Y.; Wang, W. Segment-based pavement crack quantification. Autom. Constr.
**2019**, 105, 102819. [Google Scholar] [CrossRef] - Hoang, N.D.; Nguyen, Q.L.; Tran, V.D. Automatic recognition of asphalt pavement cracks using metaheuristic optimized edge detection algorithms and convolution neural network. Autom. Constr.
**2018**, 94, 203–213. [Google Scholar] - Yousaf, M.H.; Azhar, K.; Murtaza, F.; Hussain, F. Visual analysis of asphalt pavement for detection and localization of potholes. Adv. Eng. Inform.
**2018**, 38, 527–537. [Google Scholar] [CrossRef] - Kim, J.; Lee, H.D. Development of New Automated Crack Measurement Algorithm to Analyze Laser Images of Pavement Surface. Diss. Theses Gradworks
**2009**, 112, 1231–1236. [Google Scholar] - Jahanshahi, M.R.; Jazizadeh, F.; Masri, S.F.; Becerik-Gerber, B. Unsupervised Approach for Autonomous Pavement-Defect Detection and Quantification Using an Inexpensive Depth Sensor. J. Comput. Civ. Eng.
**2013**, 27, 743–754. [Google Scholar] [CrossRef] - Du, Y.; Zhang, X.; Li, F.; Sun, L. Detection of Crack Growth in Asphalt Pavement Through Use of Infrared Imaging. Transp. Res. Rec. J. Transp. Res. Board
**2017**, 2645, 24–31. [Google Scholar] [CrossRef] - Radopoulou, S.C.; Brilakis, I. Automated Detection of Multiple Pavement Defects. J. Comput. Civ. Eng.
**2017**, 31, 04016057. [Google Scholar] [CrossRef][Green Version] - Dorafshan, S.; Thomas, R.J.; Maguire, M. Comparison of deep convolutional neural networks and edge detectors for image-based crack detection in concrete. Constr. Build. Mater.
**2018**, 186, 1031–1045. [Google Scholar] [CrossRef] - Fan, Z.; Li, C.; Chen, Y.; di Mascio, P.; Chen, X.; Zhu, G.; Loprencipe, G. Ensemble of Deep Convolutional Neural Networks for Automatic Pavement Crack Detection and Measurement. Coatings
**2020**, 10, 152. [Google Scholar] [CrossRef][Green Version] - Jeong, J.-H.; Jo, H.; Ditzler, G. Convolutional neural networks for pavement roughness assessment using calibration-free vehicle dynamics. Comput. Aided Civ. Infrastruct. Eng.
**2020**. [Google Scholar] [CrossRef] - Ju, H.; Li, W.; Tighe, S.; Xu, Z.; Zhai, J. CrackU-net: A novel deep convolutional neural network for pixelwise pavement crack detection. Struct. Control. Heal. Monit.
**2020**, e2551. [Google Scholar] [CrossRef] - Kalfarisi, R.; Wu, Z.Y.; Soh, K. Crack Detection and Segmentation Using Deep Learning with 3D Reality Mesh Model for Quantitative Assessment and Integrated Visualization. J. Comput. Civ. Eng.
**2020**, 34, 04020010. [Google Scholar] [CrossRef] - Mei, Q.; Gul, M.; Azim, M.R. Densely connected deep neural network considering connectivity of pixels for automatic crack detection. Autom. Constr.
**2020**, 110, 103018. [Google Scholar] [CrossRef] - Yang, F.; Zhang, L.; Yu, S.; Prokhorov, D.; Mei, X.; Ling, H. Feature Pyramid and Hierarchical Boosting Network for Pavement Crack Detection. IEEE Trans. Intell. Transp. Syst.
**2020**, 21, 1525–1535. [Google Scholar] [CrossRef][Green Version] - Hadjidemetriou, G.M.; Christodoulou, S.E. Vision-and Entropy-Based Detection of Distressed Areas for Integrated Pavement Condition Assessment. J. Comput. Civ. Eng.
**2019**, 33, 04019020. [Google Scholar] [CrossRef] - Cha, Y.-J.; Choi, W.; Suh, G.; Mahmoudkhani, S.; Büyükztürk, O. Autonomous Structural Visual Inspection Using Region-Based Deep Learning for Detecting Multiple Damage Types. Comput. Aided Civ. Infrastruct. Eng.
**2017**. [Google Scholar] [CrossRef] - Gopalakrishnan, K.; Khaitan, S.K.; Choudhary, A.; Agrawal, A. Deep Convolutional Neural Networks with transfer learning for computer vision-based data-driven pavement distress detection. Constr. Build. Mater.
**2017**, 157, 322–330. [Google Scholar] [CrossRef] - Cha, Y.J.; Choi, W.; Buyukozturk, O. Deep Learning-Based Crack Damage Detection Using Convolutional Neural Networks. Comput. Civ. Infrastruct. Eng.
**2017**, 32, 361–378. [Google Scholar] [CrossRef] - Zhang, D.; Zou, Q.; Lin, H.; Xu, X.; He, L.; Gui, R.; Li, Q. Automatic pavement defect detection using 3D laser profiling technology. Autom. Constr.
**2018**, 96, 350–365. [Google Scholar] [CrossRef] - Tsai, Y.-C.; Wu, Y.-C.; Price, G. A Cost-Effective and Objective Full-Depth Patching Identification Method using 3D Sensing Technology with Automated Crack Detection and Classification. Transp. Res. Rec. J. Transp. Res. Board
**2018**, 2672, 50–58. [Google Scholar] [CrossRef] - Pavement crack image acquisition methods and crack extraction algorithms: A review. J. Traffic Transp. Eng.
**2019**, 6, 535–556. - Gui, R.; Xu, X.; Zhang, D.; Pu, F. Object-Based Crack Detection and Attribute Extraction From Laser-Scanning 3D Profile Data. IEEE Access
**2019**, 7, 172728–172743. [Google Scholar] [CrossRef] - Xu, Z.-G.; Chen, Y.-L.; Li, J.-L.; Zhao, X.-M.; Pan, Y.; Wang, Z.-R.; Wei, N.; Song, H.-X. Research progress on automatic image processing technology for pavement distress. J. Traffic Transp. Eng.
**2019**, 19, 172–190. [Google Scholar] - Li, L.; Wang, K.C.P. Bounding Box-Based Technique for Pavement Crack Classification and Measurement Using 1 mm 3D Laser Data. J. Comput. Civ. Eng.
**2016**, 30, 04016011. [Google Scholar] [CrossRef] - Tsai, Y.C.J.; Li, F. Critical Assessment of Detecting Asphalt Pavement Cracks under Different Lighting and Low Intensity Contrast Conditions Using Emerging 3D Laser Technology. J. Transp. Eng.
**2012**, 138, 649–656. [Google Scholar] [CrossRef] - Woo, S.; Yeo, H. Optimization of Pavement Inspection Schedule with Traffic Demand Prediction. Procedia Soc. Behav. Sci.
**2016**, 218, 95–103. [Google Scholar] [CrossRef][Green Version] - Chen, K.; Cheng, M.; Zhou, M.; Chen, X.; Chen, Y.; Jonathan, L.; Nie, H. Automated Object Extraction from MLS Data: A Survey. In Proceedings of the 2015 10th International Conference on Intelligent Systems and Knowledge Engineering, Taipei, Taiwan, 24–27 November 2015; pp. 331–334. [Google Scholar]
- Zhang, Z.; Cheng, M.; Chen, X.; Zhou, M.; Chen, Y.; Li, J.; Nie, H. Turning Mobile Laser Scanning Points Into 2d/3d On-Road Object Models: Current Status. In Proceedings of the 2015 IEEE International Geoscience and Remote Sensing Symposium, Milan, Italy, 26–31 July 2015; pp. 3524–3527. [Google Scholar]
- Guan, H.; Li, J.; Yu, Y.; Chapman, M.; Wang, H.; Wang, C.; Zhai, R. Iterative Tensor Voting for Pavement Crack Extraction Using Mobile Laser Scanning Data. IEEE Trans. Geosci. Remote Sens.
**2015**, 53, 1527–1537. [Google Scholar] [CrossRef] - Guan, H.; Li, J.; Yu, Y.; Chapman, M.; Wang, C. Automated Road Information Extraction From Mobile Laser Scanning Data. IEEE Trans. Intell. Transp. Syst.
**2015**, 16, 194–205. [Google Scholar] [CrossRef] - Chen, X.; Li, J. A Feasibility Study On Use Of Generic Mobile Laser Scanning System for Detecting Asphalt Pavement Cracks. In Proceedings of the XXIII Isprs Congress, Prague, Czech Republic, 12–19 July 2016; pp. 545–549. [Google Scholar]
- Yongtao, Y.; Li, J.; Haiyan, G.; Cheng, W. 3D crack skeleton extraction from mobile LiDAR point clouds. In Proceedings of the 2014 IEEE Geoscience and Remote Sensing Symposium, Québec City, QC, Canada, 13–18 July 2014. [Google Scholar]
- Zhong, M.; Sui, L.; Wang, Z.; Yang, X.; Zhang, C.; Chen, N. Recovering Missing Trajectory Data for Mobile Laser Scanning Systems. Remote Sens.
**2020**, 12, 899. [Google Scholar] [CrossRef][Green Version] - Wang, H.; Cai, Z.; Luo, H.; Cheng, W.; Li, J. Automatic road extraction from mobile laser scanning data. In Proceedings of the International Conference on Computer Vision in Remote Sensing, Xiamen, China, 16–18 December 2012. [Google Scholar]
- Wei, C.; Lichun, S.; Zhengchao, X.; Yu, L. Improved Zhang-Suen thinning algorithm in binary line drawing applications. In Proceedings of the 2012 International Conference on Systems and Informatics (ICSAI 2012), Yantai, China, 19–21 May 2012; pp. 1947–1950. [Google Scholar] [CrossRef]
- Yun, H.B.; Mokhtari, S.; Wu, L.L. Crack Recognition and Segmentation Using Morphological Image-Processing Techniques for Flexible Pavements. Transp. Res. Rec. J. Transp. Res. Board
**2015**, 2523, 115–124. [Google Scholar] [CrossRef]

**Figure 1.**The test data. (

**a**) The overall view of test data, and (

**b**) the divergent point intensity in two lanes.

**Figure 2.**The connectivity provided by the arrangement of mobile laser scanning (MLS) point clouds. (

**a**) The arrangement of MLS point clouds collected by a two-dimensional (2D) scanner with equal incremental angle. (

**b**) Create a Time grid (Tgrid) for MLS point cloud by using the scanning line and scan angle information.

**Figure 4.**Construction of a Tgrid for MLS data through (

**a**) the scan angle (θ), and (

**b**) the acquisition time (T).

**Figure 5.**Detection of road surface and boundary area in Tgrid. (

**a**) The cross-section of a road segment, and (

**b**) the searching process of a road boundary area.

**Figure 7.**Characteristics of valley points. (

**a**) Height feature, and (

**b**) gradient effect near crack candidates.

**Figure 8.**The flow of detection of the low-intensity points with height no higher than the road surface. (

**a**) The background-differential map (G

_{F}), (

**b**) the relevant truncation value (F

_{B}) by the given proportion of cracks’ point (T

_{P}), (

**c**) the differential truncation map (G

_{FC}), (

**d**) the segment threshold, T

_{C}, of the possible cracks, (

**e**) the binary map of possible crack candidates (G

_{P}), and (

**f**) the filter about valley effect.

**Figure 11.**Edge points classification to calculate crack width, (

**a**) in Tgrid, and (

**b**) in geometrical space.

**Figure 12.**The extracted point cloud of the road surface and time grid map rendered with intensity. (

**a**) The extracted point cloud of the road surface, and (

**b**) the intensity-based Tgrid map of the road surface.

**Figure 13.**The extracted crack candidates in the Tgrid map and the results of crack craves. (

**a**) The extracted crack candidates (in red) on the intensity-based Tgrid map of the road surface, (

**b**) the remaining crack candidates after Morphological filtering, and (

**c**) overlay of crack craves (in magenta) and road surface point cloud.

**Figure 14.**The histogram of length and width compliance of cracks in 60 samples. (

**a**) Compliance of the crack width, and (

**b**) compliance of the crack length.

**Figure 15.**The detected crack candidates by using different methods. (

**a**) Original point cloud, (

**b**) the detected crack candidates by using the proposed method, (

**c**) by using the maximum entropy sum method, and (

**d**) by using Otsu’s thresholding method.

**Figure 16.**The sensitivity test of the C

_{P}with T

_{C}. (

**a**) The change of the value of T

_{C}with C

_{P}, and (

**b**) crack candidates corresponding to the selected C

_{P}.

Parameters | Values | Parameters | Values | Parameters | Values |
---|---|---|---|---|---|

W_{D} (m) | 0.50 | v_{th} (°) | 10 | R_{lwth} | 3 |

α | 0.05 | C_{P} (%) | 5 | R_{s} (m) | 0.20 |

h_{th} (m) | 0.03 | D_{2} (m) | 0.04 | ||

h_{d} (m) | 0.20 | L_{th}_{1} (m) | 0.25 |

Crack Type | Actual Quantity | Precision(P) | Recall (R) | F1-Measure |
---|---|---|---|---|

Transverse crack | 98 | 95.15% | 98.00% | 96.55% |

Longitudinal crack | 47 | 97.91% | 78.43% | 87.09% |

Oblique crack | 42 | 84.62% | 78.57% | 81.48% |

Crack Type | Number of Samples | Mean (C_{W}) | Variance (V_{W}) | Mean (C_{L}) | Variance (V_{L}) |
---|---|---|---|---|---|

Transverse crack | 20 | 0.812 | 0.149 | 0.921 | 0.066 |

Longitudinal crack | 20 | 0.910 | 0.071 | 0.935 | 0.089 |

Oblique crack | 20 | 0.874 | 0.131 | 0.897 | 0.076 |

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## Share and Cite

**MDPI and ACS Style**

Zhong, M.; Sui, L.; Wang, Z.; Hu, D.
Pavement Crack Detection from Mobile Laser Scanning Point Clouds Using a Time Grid. *Sensors* **2020**, *20*, 4198.
https://doi.org/10.3390/s20154198

**AMA Style**

Zhong M, Sui L, Wang Z, Hu D.
Pavement Crack Detection from Mobile Laser Scanning Point Clouds Using a Time Grid. *Sensors*. 2020; 20(15):4198.
https://doi.org/10.3390/s20154198

**Chicago/Turabian Style**

Zhong, Mianqing, Lichun Sui, Zhihua Wang, and Dongming Hu.
2020. "Pavement Crack Detection from Mobile Laser Scanning Point Clouds Using a Time Grid" *Sensors* 20, no. 15: 4198.
https://doi.org/10.3390/s20154198