Introduction

The continual development of 3D scanning and digital image processing technology has facilitated the exploration of expressing real-world objects as 3D images. The acquisition of 3D data has become faster and more convenient through the emergence of equipment such as 3D scanners, depth cameras, and LIDAR. Because of these properties, 3D point cloud data have been widely used in the fields of augmented reality1,2, autonomous driving3, and road engineering4. Currently, extensive research efforts are being directed toward identifying various types of road damage and predicting skid resistance using the 3D point cloud data of pavements5,6.

The three-dimensional point cloud data of objects often contain noise points, leading to deviations from the real data. These noises are due to factors such as ambient light, measurement equipment accuracy, target background, electronic industrial interference, and matching reconstruction error7. High-precision 3D point cloud data enable various kinds of analyses and applications, such as point cloud segmentation8,9, point cloud classification10,11, target detection12, and other advanced tasks. Taking 3D pavement reconstruction as an example, noise causes a deviation of the discrete point set from the original real distribution through perturbations of the spatial coordinate information of the point cloud. Moreover, the accumulation of substantial deviated spatial information degrades the 3D spatial shape information, preventing an accurate reconstruction of the 3D pavement image. Subsequently, the original point set fails to represent the continuous distribution of the pavement texture accurately, thus influencing the accuracy of the 3D pavement reconstruction. Therefore, improving denoising algorithms for 3D point cloud data is an essential research topic in 3D point cloud research.

The research on image denoising algorithms has been widely conducted using two approaches: spatial domain denoising and transform domain denoising13. The increasing acquisition and application of 3D point cloud data is attracting greater attention on research related to the denoising of 3D point cloud14. Currently, algorithms for denoising 3D point cloud data are mainly divided into two categories: traditional filtering algorithms based on optimization and denoising algorithms based on deep learning. The former are mainly used to estimate the geometric information of 3D point cloud through spatial domain filtering and transform domain filtering. Classical spatial domain filtering algorithms15, such as mean filtering, median filtering, Gaussian filtering, and statistical filtering act directly on the coordinate space of the point cloud to eliminate outliers and noise. Meanwhile, the 3D point cloud denoising approaches based on domain features use the similarity of feature information of neighboring points in the 3D point cloud to update the coordinates of noisy points. For example, the bilateral filtering operator proposed by Tomasi and Manduch for image denoising was extended and applied to denoising 3D point cloud data16,17. Inspired by the application of sparse theory in 2D image denoising, Avron et al.18 introduced the idea of sparsification and transformed the denoising process into a sparse reconstruction task, proposing the use of the L1 paradigm for denoising 3D point cloud data. Han19 extended signal processing-based denoising methods for 2D images to 3D point cloud data. Pauly et al.20 proposed a spectral analysis method based on the Fourier transform to denoise 3D point cloud data. To achieve the denoising of 3D point cloud data, Huang et al.21 proposed a weighted local optimal projection method that generates a uniformly distributed set of points by incorporating the local adapted density weights of each point in the 3D point cloud into the local optimal projection method. Following the application of deep learning in 2D image denoising, a deep learning-based algorithm for denoising 3D point cloud data has also been proposed22,23. Principally, a neural network framework is first designed, and the features of the 3D point cloud are extracted by encoding; the coded features are then decoded, and the 3D point cloud data are denoised while computing the gradient descent of the loss function. Existing deep learning-based denoising algorithms are categorized into two main types: supervised learning and unsupervised learning. Supervised learning algorithms require that the target generation data are known, and examples are PointProNets proposed by Roveri et al.22 and Pointfilter proposed by Zhang et al.23. Real point cloud data are difficult to obtain. To address this problem, Casajus et al.24 proposed total denoising to construct a network framework for unsupervised learning with a loss function. These highlighted approaches are not suitable for the 3D point cloud data of pavements.

The recent application of 3D scanning technologies on pavements has facilitated research into the application of 3D point cloud denoising algorithms on pavement surfaces. Cao25 designed a scheme for filtering a pavement’s 3D point cloud data based on the noise characteristics of the data; the scheme was used to remove large- and small-scale noise according to different filtering methods. Xiao26 used a local density-based denoising algorithm to deal with the fragmentary noise in 3D point cloud data of concrete surfaces, which solved the problem of the poor adaptation and high procedural complexity of conventional denoising methods. Shi27 filtered out the noise information in the raw data of the pavement by improving the Gaussian and median filtering method, while retaining the edge detail information in the data. Xie28 analyzed the noise characteristics of point cloud images of highway pavements and proposed an improved hybrid filtering approach based on radius filtering and statistical filtering. The radius filtering algorithm is used to filter the point cloud for the isolated points that stray from the main point cloud, and the statistical filtering algorithm is used to filter the outlier points near the main point cloud by calculating the threshold value.

Existing algorithms often use a preset noise type before the model filters out the noise, which produces a noise-bearing model through a perturbation of the input point cloud with Gaussian noise. This artificial noise simulation simplifies the noise environment and keeps it single. The effectiveness of the algorithm is relatively low for mathematically undefined composite noise. Various factors influence the acquisition of 3D point cloud data, and they include lighting conditions, the object’s background, and other complex external environments14. Because of the continuous development of acquisition equipment, a higher precision of 3D point cloud data acquisition results in more complex noise information in the data, leading to increased data processing difficulty. Therefore, constructing point cloud denoising algorithms for complex noise environments is crucial.

In this study, an LS-40 3D scanner was used to obtain high-precision 3D point cloud data of an asphalt pavement, and the 3D images of the pavement were reconstructed from the point cloud data. As the 3D images contain obvious noise, we propose an improved Gaussian filtering approach based on neighborhood smoothing. In this proposed algorithm, the Gaussian kernel center weights are set to 0, and a two-dimensional convolution kernel is convolved with the raw 3D point cloud data of the asphalt pavement to remove the noise. However, small-scale burr noise persists in the raw data; hence, a coefficient of variation (CV) is introduced into the Gaussian filtering method. This approach is used because coefficients of variation can reflect the degree of dispersion in a data distribution, facilitating the identification of the burr noise. Specifically, the raw point cloud data matrix is divided into different sub-matrices (with a size of 3 × 3), and their coefficients of variation are calculated iteratively. If the CV of a sub-matrix is larger than the mean of all sub-matrices, then data of that sub-matrix are considered as noise. Subsequently, the Gaussian kernel is used to filter out the sub-matrix identified as noise data.

3D point cloud data acquisition of asphalt pavement

Acquisition equipment and principles

In this study, raw 3D point cloud data of a pavement surface were collected using a portable 3D scanner LS-40 (Fig. 1). The built-in laser-camera assembly of the LS-40 moves at a certain rate under the battery drive, and the 3D camera captures the 3D point cloud data of the pavement surface in the red line laser scanning area. The horizontal range of the scanning area of the LS-40 is 10 × 11.5 cm. The collected raw data comprise intensity data array and range data array, with each array containing a total of 2448 × 2048 16-bit data points. The horizontal resolution of the data is approximately 0.05 mm, and the vertical resolution is approximately 0.01 mm.

Figure 1
figure 1

LS-40 appearance and its data acquisition principle.

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The LS-40 collects 3D point cloud data through laser triangulation, which is commonly used in non-contact 3D scanning because of its simple structure, high measurement speed, implementation processing capability, and flexibility29. The camera projects a linear laser perpendicularly onto the surface of an object and captures the laser reflection line on each surface point using a high-performance CMOS camera. The 3D information of the scanned object surface is a combination of the data from each laser line, as illustrated in Fig. 1b.

Experimental data collection

To verify the universality of the proposed noise-reduction algorithm of 3D point cloud data across various asphalt pavement structures, we prepared asphalt mixtures (i.e., pavement slab samples) of various structural types through indoor experiments for data collection. Actual operational roads were selected for the 3D point cloud data acquisition to examine the algorithm’s effect in practical engineering. The operational specifications of the LS-40 system were strictly followed to collect the data.

Preparation of pavement slab samples

Asphalt mixtures of different structural types were used for the experiments. Three types of pavement slab samples, namely, AC-13 asphalt mixture, SMA-13 asphalt mixture, and OGFC-13 asphalt mixture, were prepared (as shown in Fig. 2). The samples had dimensions of 300 mm × 400 mm × 50 mm and a maximum nominal aggregate size of 13.2 mm. All samples were produced using the optimal asphalt content. The gradation details are provided in Table 1. To enrich the sample data and avoid the high discreteness and deviation of a single sample, multiple pavement slab samples were prepared for each type of asphalt mixture, and data were collected from different areas of each sample. For the three asphalt mixtures of AC-13, SMA-13, and OGFC-13, the 3D point cloud data were collected from 30 test points in different areas, respectively.

Figure 2
figure 2

Pavement slab samples.

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Table.1 Asphalt mixture gradation.
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On-site data collection

Warm-mix asphalt pavement construction technology and quality control technology under high altitude and low temperature conditions were considered; these technologies were from a project by Sichuan Yakang Expressway Co., Ltd. To avoid relying on a single source of experimental data, the data were collected from a total of 30 locations in two sections of the Yakang Expressway were, namely, the Tianquan and Luding sections. The mixture type of the on-site data was SMA-13; the data collection activity is shown in Fig. 3.

Figure 3
figure 3

On-site collection of 3D point cloud data.

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Characterization of raw 3D point cloud data

When acquiring and transmitting asphalt pavement texture point cloud data, various types of noise are generated because of multiple factors such as the collection equipment (e.g., sensor material properties, electronic components) and the surface material of the asphalt pavement being measured7. MATLAB was used to visualize the raw 3D point cloud data of the pavement surface collected by the LS-40 equipment as 3D cloud images and cross-section profiles. Three types of noise were observed in the raw 3D point cloud data: point cloud image edge noise, obvious outlier noise, and burr noise, as shown in Fig. 4 (taking the collected point cloud data from AC-13 asphalt mixture as an example).

Figure 4
figure 4

Raw point cloud data image of AC-13 asphalt mixture. (a) (i) represents the 3D cloud image of the pavement texture at test point i; (b) (i) represents the i-th cross-section profile of the pavement texture.

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Figure 4a1 shows the 3D cloud image of the pavement texture at test point 1. Upon observation, it is found that there are obvious outlier noises (manifested as vertical lines) at the edges of the point cloud image, which obscures the structure of the pavement texture. Extracting the matrix data from the noisy region (as indicated by the red arrow in the figure) shows that its values are much greater than the adjacent values. The pavement texture’s cross-sectional profile corresponding to the edge noise is reconstructed, as shown in Fig. 4b1. Figure 4a2 and b2 show the 3D cloud image of the pavement texture at test point 2. The noise manifestation is similar to that in Fig. 4a1 and b1, which are both obvious outlier noises. The difference is that the noise is not located at the edge of the image. This noise may be caused by factors such as the instability of the laser scanner itself, temperature variations during the point cloud image acquisition, or specular reflection from the surface material (such as oil stains) of the asphalt pavement26.

Figure 4a3 shows the 3D point cloud image of the pavement texture at test point 3, which is obviously different from the images in Fig. 4a2,a3. The structure of the pavement texture can be roughly discerned, but numerous burrs are present in the image, indicating a large amount of noise in the data. Similarly, the cross-section profile of the pavement texture cannot be seen at measurement points 1 and 2; however, that at measurement point 3 clearly indicates the presence of significant burr noise in the data (Fig. 4b3).

3D point cloud filtering method

Median filtering

Median filtering30 is a nonlinear filter. Its working principle is as follows: first, sort the pixels in the image area surrounded by the image filter, and then replace the central pixel value with the median pixel value determined by the statistical sorting results. After median filtering, the calculated median is assigned to \(g(x,y)\):

$$g(x,y) = med(f(x,y)) \, (x,y) \in M,$$
(1)

where the function \(med( \cdot )\) represents the median operation, x represents the horizontal coordinate of a data point, y represents the vertical coordinate of a data point, and M is the set of all pixel points within the \({\text{K}} \times {\text{K}}\) window neighborhood of the current pixel point \((x,y)\).

Mean filtering

Mean filtering is a typical linear filtering algorithm. Its basic principle is to calculate the average pixel value of all pixels within a square region centered on the current pixel, where the number of rows is equal to the number of columns, and then replace the center pixel value with this average value31. Yang Enhui et al.32 used mean value filtering with a parameter of a 3 × 3 window size to filter raw 3D pavement surface data, as shown in Fig. 5.

Figure 5
figure 5

Schematic diagram of mean filtering.

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The calculation formula for pixel values after mean filtering is \({\text{G}}(x,y)\):

$$\begin{aligned} {\text{G}}(x,y) & = (f(x,y - 1) + f(x,y) + f(x,y + 1) + f(x - 1,y - 1) + f(x - 1,y) \hfill \\ & \quad + f(x - 1,y + 1) + f(x + 1,y - 1) + f(x + 1,y) + f(x + 1,y + 1)) \hfill \\ \end{aligned}$$
(2)

In the formula, x and y represent the horizontal and vertical coordinates of a data point, respectively.

Gaussian filtering

Gaussian filtering is a linear low-pass filter, whose essence is weighted average filtering with weighted values. The magnitude of the weight is related to the distance from the element in the filter to the filtering center. The weight of the convolution kernel center is the largest, and it decreases towards the periphery. Gaussian filters are very effective in suppressing normally distributed noise. It achieves a smoother effect and better edge preservation than those of mean filtering, attracting much attention from researchers33.

In Gaussian filtering, a 2D Gaussian convolution kernel based on the 2D Gaussian function (3) is first generated.

$$G(x,y) = \frac{1}{{2\pi \sigma^{2} }}e^{{ - }{(x^{2} + y^{2} )/2\sigma^{2} }}$$
(3)

where \((x,y)\) is the coordinate of the point, and σ is the standard deviation.

Then, the raw point cloud data of the pavement surface are convolved with the Gaussian convolution kernel to filter the noise.

$$I^{\prime}(x,y) = I(x,y) \otimes G\quad$$
(4)

where \(I(x,y)\) represents the raw point cloud data, and \(I^{\prime}(x,y)\) represents the convolution result with the 2D Gaussian convolution.

Proposed algorithm

Raw 3D point cloud data consist of noise and non-noise parts. When performing a smoothing process on the raw point cloud data, only the part containing noise need to be processed; otherwise, the non-noise part may be altered. Therefore, the noise reduction approach of the proposed method is as follow: first, identify and locate the noise part in the raw point cloud data, and then perform noise reduction processing on the identified noise data.

Meanwhile, according to the noise causes and characteristics of pavement surface point cloud data discussed in "Characterization of raw 3D point cloud data" section, the noise in the 3D pavement point cloud data includes large-scale, obvious outlier noise and small-scale burr noise. Therefore, we design a filtering algorithm suitable for pavement surface 3D point cloud data. Our method uses different filtering methods for different noise types to achieve point cloud data denoising. The technical roadmap is shown in Fig. 6.

Figure 6
figure 6

Technical roadmap.

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This proposed method is novel for the following reasons:

First, an improved Gaussian filtering method based on neighborhood smoothing is proposed to address the characteristics of prominent outlier noise in the raw point cloud data. Compared to traditional Gaussian filtering methods, this method sets the central weight of the Gaussian kernel to zero and uses a novel two-dimensional convolution kernel. The kernel is then convolved with the original 3D point cloud data of the road surface to filter out the significant outliers in the data.

Second, to address the characteristics of small-scale spike noise in the original data, the proposed method combines the CV and Gaussian filtering. The CV, which reflects the dispersion in the data distribution, is used to identify spike noise in the raw point cloud data, after which a Gaussian filtering method is applied to remove the spike noise.

Through these novel aspects, the proposed method effectively removes outlier and spike noises from the raw point cloud data while preserving the overall shape and structure of the road surface in the data.

Obvious outliers denoising

Based on the characteristics of the outliers in the raw data, a threshold filtering method is designed to remove the outlier noise. First, our definition of obvious outliers is data points with values higher than three times the mean of the point cloud data. Iterate through all the point cloud data, determine whether each point is an obvious outlier, and identify the coordinate positions of these outliers. Some outliers are concentrated in certain areas of the point cloud data; as such, we propose to replace these outlier data with the mean value of the overall dataset. Meanwhile, to ensure that the point cloud data closely resemble the true data values after removing obvious outliers, we design a convolution kernel for smoothing obvious noise points based on the smoothing approach within adjacent neighborhoods.

A 2D Gaussian kernel is generated using a 2D Gaussian function, considering the large outliers in the point cloud data. To eliminate the influence of these outliers, the Gaussian kernel center weight is set to 0, creating the designed convolution kernel. The convolution kernel is then normalized to eliminate errors caused by grayscale value deviations. Finally, the convolution kernel is used to smoothen and denoise the central outliers, as shown in Figs. 7 and 8 (using a 3 × 3 convolution kernel as an example). The obvious outliers located at the edges of the point cloud data (e.g., Fig. 4a1) have insufficient points in their domains for the filtering process; thus, the mean value of the raw point cloud data is used for the peripheral padding. Experiments were conducted using different convolution kernels, and a 9 × 9 convolution kernel was selected.

Figure 7
figure 7

Convolution kernel solution process.

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Figure 8
figure 8

Denoising process for obvious outliers.

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The calculation formula \(I^{\prime}(x,y)\) for the point cloud data after filtering out the obvious noise points is expressed below:

$$I^{\prime}(x,y) = \left\{ \begin{gathered} I(x,y) \otimes J\quad \quad if\;I(x,y) \ge T \hfill \\ I(x,y)\quad \quad others \hfill \\ \end{gathered} \right.\quad \quad$$
(5)

In the formula,\((x,y)\) represents the coordinates, which are integers in image processing; \(I^{\prime}(x,y)\) represents the point cloud data after eliminating obvious outlier noise; \(I(x,y)\) represents the raw 3D point cloud data; \(J\) represents the designed convolution kernel; \(T\) represents the threshold for judging obvious noise points, which is set as three times the mean value of the point cloud data.

Small-scale burr noise filtering

Characteristics of burr noise data

As described in "Characterization of raw 3D point cloud data" section, the raw 3D point cloud data of the pavement surface still contain numerous small-scale burr noises. Figure 9a shows the 3D point cloud image of the pavement surface including burr noise, and the local box in Fig. 9a is zoomed-in to obtain Fig. 9b. Upon careful observation, it can be found that the burr noise data (indicated by the red frame in the figure) is obviously different from the surrounding non-noise data, and there is a large difference in their sizes.

Figure 9
figure 9

Raw 3D point cloud image of pavement surface.

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Coefficient of variation

The CV is a normalized measure of the dispersion of a probability distribution, defined as the ratio of the standard deviation to the mean (Eq. 6). The CV can help us to better understand the data distribution, the larger its value, the greater the dispersion degree of the data distribution. In addition, the CV can be used to assess the stability and reliability of the data. If the CV of a dataset is small, the data distribution is relatively stable, and the differences between the data points are not excessive. On the contrary, if the CV of a certain dataset is relatively large, the data distribution is relatively unstable, and the difference between the data points is large, which may affect the reliability and accuracy of the data.

$$CV = \frac{S}{A},\;\;\;A = \frac{1}{n}\sum\limits_{i = 1,j = 1}^{n} {r_{ij} } ,\;\;\;S = \sqrt {\frac{1}{n}\sum\limits_{i = 1,j = 1}^{n} {(r_{ij} - A)^{2} } }$$
(6)

In the formula, \(CV\) represents the coefficient of variation of the data; \(A\) represents the mean;\(S\) represents the standard deviation; and \(r_{ij}\) represents the standardized data in row i and column j.

Noise data identification filtering

The 3D point cloud data of a pavement is stored in a matrix form, and we use the CV to identify burr noise in the raw point cloud data according to the difference between the burr noise data and non-noise data. Primarily, the raw point cloud data matrix is divided into multiple sub-matrices (taking a 3 × 3 size as an example, as shown in Fig. 10), the CV of the sub-matrices is calculated iteratively, and the mean CV is obtained. If the CV of the sub-matrix is greater than the mean value, the sub-matrix data are identified as noise data.

Figure 10
figure 10

Schematic diagram of sub-matrix division of raw point cloud data.

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Next, a Gaussian kernel is used to filter the submatrix identified as noise data. Points near the sub-matrix boundaries do not have enough points in their domains for the filtering process. Therefore, the upper, lower, left, and right boundary expansion operations are required before filtering, and the width of each boundary expansion is the size of the filtering radius, as shown in Fig. 11. If the sub-matrix is at the center of the raw point cloud data, the raw data expansion around the sub-matrix is used; if the sub-matrix is at the peripheral position of the raw point cloud data, the raw data mean value expansion is used. For different research objects, different sub-matrices are used for experiments according to the actual noise situation.

Figure 11
figure 11

Gaussian kernel convolutional filtering process.

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Evaluation content and indicators

Evaluation content

The performance of the proposed algorithm was compared to that of traditional median filtering, mean filtering, and Gaussian filtering on raw pavement texture point cloud data. To verify the universality of the proposed algorithm on various asphalt pavement structures, these filtering processes were conducted on three types of asphalt mixtures: AC-13, SMA-13, and OGFC-13, as well as on asphalt pavements collected in the field.

Evaluation indicators

Obtaining noise-free 3D point cloud image data of pavement surfaces is impossible because of various reasons. Therefore, to better evaluate the processing effect of the proposed 3D data filtering algorithm, Information Entropy34 are used as objective efficiency and performance metrics of the different filtering methods. The pavement surface contains a rich micro-texture structure, which can be reflected by the information entropy: the larger the entropy value, the richer the data information. Excessive filtering during the noise filtering process of the point cloud data will lead to the relative smoothness of the 3D surface, and the micro-texture will be filtered out. Therefore, the information entropy is needed to protect the micro-texture during the noise filtering and is calculated as shown below:

$$C = - \sum\limits_{i}^{n} {pv_{i} \log_{2} pv_{i} }$$
(7)

In the formula, \(C\) represents the entropy value of the overall point cloud; \(pv_{i}\) represents the density of the probability distribution of the data in region i.

Texture parameters are calculated based on 3D data, and quantitative analysis is performed on these parameters to evaluate the filtering effect of the proposed algorithm in this paper.

Results and discussion

This chapter evaluates the 3D point cloud image denoising results through the subjective visual quality and objective evaluation indexes, and the research objects include the raw 3D point cloud images of three types of asphalt mixtures, namely, AC-13, SMA-13, and OGFC-13, as well as the on-site asphalt pavement.

Subjective visual quality assessment

Comparison of filtering effects

The SMA-13 pavement slab sample and on-site asphalt pavements are used to evaluate the noise reduction effects of the proposed algorithms, Gaussian filtering, median filtering, and mean filtering. The subjective visual quality of the 3D point cloud images and 2D cross-section profile are considered.

Figure 12 illustrates the subjective filtering effect of the different methods on the 3D point cloud image for the SMA-13 pavement slab sample. Figure 12a shows the raw 3D point cloud image of the sample, which cannot clearly show the texture construction information because of the obvious outlier noise data. Therefore, the raw point cloud data need to be filtered. Figure 12b shows the 3D point cloud image after noise reduction using the proposed algorithm. The texture structure information can be clearly seen, indicating effective noise removal while preserving the micro-texture structure information. Figure 12c shows the 3D point cloud image after noise reduction using Gaussian filtering, where some obvious outliers are not effectively processed. Figure 12d shows the 3D point cloud image after noise reduction using median filtering. Incomplete outlier processing, the destruction of texture structure, and edge noise can be observed in the image. Figure 12e shows the 3D point cloud image after noise reduction using mean filtering. Incomplete outlier processing, edge blunting, and excessive filtering, which affect micro-texture structure information, can be observed in the image.

Figure 12
figure 12

Filtering effect of 3D point cloud images for pavement slab sample (SMA-13).

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Figure 13 illustrates the filtering effect of the cross-section profile of the SMA-13 pavement slab sample. Figure 13a shows the raw cross-section profile of the SMA-13 pavement slab sample, clearly revealing the presence of burr noise and other data anomalies. Figure 13b shows the cross-section profile after noise reduction using the proposed algorithm: the noise data are well filtered out, and by local magnification, we observe that the micro-texture structure is preserved. Figure 13c shows the cross-section profile after noise reduction using Gaussian filtering. While the noise data are effectively removed, local magnification reveals that the filtering process is too smooth, resulting in the loss of the micro-texture details. Figure 13d,e shows the cross-section profile after noise reduction using median filtering and mean filtering, respectively. Both figures exhibit issues such as edge noise within the red oval frame and partial filtering of micro-texture structures.

Figure 13
figure 13

Filtering effect on the cross-section profile for pavement slab sample (SMA-13).

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Figure 14 illustrates the subjective filtering effect of different methods on the 3D point cloud image of asphalt pavement in the field. Figure 14a shows the raw 3D point cloud image of the pavement surface, clearly revealing the presence of numerous burr noises. From Fig. 14, we observe that both the proposed algorithm and Gaussian filter have a better filtering effect for small-scale burr noise. However, median filtering and mean filtering both exhibit edge blunting issues.

Figure 14
figure 14

Filtering effect of 3D point cloud image of asphalt pavement in the field.

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Figure 15 illustrates the filtering effect of the cross-section profile of the asphalt pavement in the field. Figure 15a shows the raw section profile of a certain asphalt pavement’s cross-section on-site, which clearly indicates the presence of burr noise and other information in the data. Figure 15b shows the section profile after noise reduction using the proposed algorithm. The noise data are well filtered out, and through local magnification, we observe that the micro-texture structure is preserved. Figure 15c shows the denoised cross-section profile for Gaussian filtering. The noise data are also well filtered out; however, through local magnification, we observe that the filtering is too smooth, resulting in the loss of the micro-texture structure. Figure 15d,e show the denoised cross-section profile for median filter and mean filter, respectively. Both figures exhibit issues such as edge noise within the red oval frame and partial filtering out of micro-texture structures.

Figure 15
figure 15

Filtering effect on the cross-section profile for asphalt pavement in the field.

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In summary, in both indoor experiments and direct on-site testing, by observing the visual quality of both 3D images and 2D section profiles, we conclude that the proposed algorithm cannot only filter out noise but also ensure that the information of the micro-texture structure is unaffected. Thus, the proposed algorithm is significantly more effective than Gaussian filtering, median filtering, and mean filtering.

Filtering stability

Figure 16 illustrates the filtering effect of the proposed algorithm on three types of asphalt mixtures: AC-13, SMA-13, and OGFC-13, as well as on asphalt collected from a pavement in the field. A close observation of Fig. 16 shows that the algorithm has a stable filtering effect for different test objects and different test positions of the same test object.

Figure 16
figure 16

Filtering effect on different test objects for the proposed algorithm.

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Objective indicator evaluation

Subjective visual quality is only suitable for qualitatively evaluating the filtering effect of different algorithms. Therefore, we used C-values to quantitatively evaluate the noise reduction effect of different methods on the raw 3D point cloud image.

For different test objects, the C-values obtained using the proposed algorithm is consistently the highest. Taking the comparison of C-value results of AC-13 asphalt mixture as an example (Fig. 17), the C-value for the proposed algorithm is 2042.28, while the C-values of Gaussian filtering, median filtering, and mean filtering are 1860.2, 1727.72, and 1784.48, respectively. A higher C-value indicates richer detail information and greater retention of 3D microscopic texture data. Therefore, in terms of the C-value, we conclude that the proposed algorithm outperforms median filtering, mean filtering, and Gaussian filtering.

Figure 17
figure 17

Comparison of C-value evaluation index results.

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In summary, the results obtained by considering the objective metric C are consistent with the subjective visual quality evaluation. That is, the proposed algorithm better filters out noise information from 3D point cloud data while preserving the micro-texture information of the pavement surface.

The C-value reflects the preservation of detailed 3D microscopic texture information. To further evaluate the filtering effect, texture parameters are calculated to do quantitative analyses for a comparison. The texture parameter index MTD obtained through sand patch testing, and can also be calculated using the seed filling algorithm based on 3D data35. Therefore, the MTD index is applied to quantitatively analyze and compare the filtering effect of the proposed algorithm.

Fifteen measurements were performed on on-site pavement for sand patch testing and LS-40 scanning, individually. The MTD obtained using sand patch testing (named as MTD-Sand) was compared against the MTD from the 3D data based on the proposed algorithm (named as MTD-3D), the MTD from the 3D data based on Gaussian filtering (named as MTD-3Dg)、the MTD from the 3D data based on Median filtering (named as MTD-3Dm)、the MTD from the 3D data based on Mean filtering (named as MTD-3Dj), respectively. It is worth mentioning that among the results of calculating MTD using different methods in Fig. 18, the MTD from the 3D data based on the proposed algorithm is close to the MTD obtained using sand patch testing, while the other three methods resulted in significantly smaller than the MTD obtained using sand patch testing. The results show that the proposed algorithm has a better filtering effect.

Figure 18
figure 18

Comparison of MTD results.

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Further, the Standard deviation (Std) and the interval difference (Id) that is the difference between the maximum and minimum values were selected to test the filtering stability based on MTD-3D results. The Std and Id calculation results are 0.1 and 0.36, respectively, indicating the proposed algorithm has good filtering stability.

$$\delta_{{{\text{Std}}}} { = }\sqrt {\frac{1}{n}\sum\nolimits_{i = 1}^{n} {(x_{i} - \overline{x})^{2} } }$$
(8)

In the formula: \(\delta_{{{\text{Std}}}}\) is the Std value; \(x_{i}\) is the i-th measurement result at the same test location; \(\overline{x}\) is the mean value at the same test location, n is the number of samples.

Conclusion

  1. 1.

    This study focused on the noise characteristics of high-precision 3D point cloud data collected from pavement surface textures using 3D laser measurement technology. First, an improved Gaussian filter is employed to remove obvious outlier noises. Then, the CV is used to extract small-scale burr noise data, which are subsequently filtered out using the Gaussian filtering method. Ultimately, the noise in the 3D point cloud data of the road surface texture is precisely filtered out.

  2. 2.

    A subjective visual quality evaluation showed that the proposed algorithm filters out noise and preserves the micro-texture information, significantly outperforming Gaussian filtering, median filtering, and mean filtering. Additionally, for different test objects and test positions, the algorithm demonstrated stable filtering effects.

  3. 3.

    In terms of objective evaluation indicators, the proposed algorithm achieved better C-values than those of Gaussian filtering, median filtering, and mean filtering. This indicates less distortion in the 3D point cloud data of road surface textures and greater retention of road surface microscopic texture and structural information. And the MTD from the 3D data based on the proposed algorithm is close to the MTD obtained using sand patch testing, indicating that the proposed algorithm has a better filtering effect and stability.

  4. 4.

    The results of this study indicate that the proposed algorithm effectively filters out noise from high-precision 3D point cloud data of pavement surface textures, facilitating accurate evaluation and analysis of pavement surface textures.