*1.1. The Need for Low-Cost Automated Pavement Distress Application*

Road networks are key drivers towards the economic viability of a country. They provide movement for users, goods and services as well as providing access to social benefits for commuters [1]. Pavements represent a vital part of the road network, and it is imperative that they are kept in a suitable condition to avoid accidents and provide efficient access to road users. Road agencies are tasked with this responsibility and have to make critical decisions to develop road maintenance and rehabilitation strategies. However, globally it has been noted that there has been a growing reduction in budgetary allocations for these purposes [2,3].

To achieve suitable maintenance strategies, a pavement management system is commonly applied by road agencies. The pavement management system (PMS) is seen as the most common and effective system for crafting maintenance strategies and it can be characterized as one that optimizes road management to achieve the most effective use of financial resources given the needs of the road system [4]. The PMS integrates a wide range of functions to give practitioners a decision support system for effective planning for the large investments required for pavements [5]. However, a PMS is reliant on high-quality road condition data. The acquisition of these data can, in turn, be very expensive, exhaustive, and time-intensive [6]. Given the already strained road agency budgets, this leads to many authorities not being able to implement an effective PMS as in many instances road condition surveys are manually carried out [7]. As a result of this, there has been a significant amount of research carried out to obtain new but accurate and low-cost methods of acquiring road condition data, specifically data on pavement distresses that are present within a network [8,9].

### *1.2. Background of Pavement Distress Detection Techniques*

The most studied areas of techniques of detecting and analyzing pavement distresses are techniques involving laser-based systems and those involving imagery from cameras. There are several commercially available equipment that utilize laser technologies equipped to vehicles for the purpose of understanding road conditions. The laser crack measurement system (LCMS) [10] is the basis of many of these systems and relies on the use of high-performance lasers attached to a vehicle that measures the profile of the road, roughness and slope at a high resolution of 1 mm whilst producing 3D profiles of the pavement. There have also been the development of mobile laser-based systems and those employing light detection and ranging systems [11,12].

The systems based on lasers are generally thought to be the most accurate techniques for detection but they are also generally more expensive and this reduces the possibility of road agencies being able to utilize them [13]. There are also systems that incorporate both imagery and lasers to produce additional information on the road conditions [14,15].

Given the costs of the laser systems, the option of utilizing only imagery provides an attractive alternative as costs of camera systems are typically significantly cheaper. Camera-based systems usually include capturing images of the pavement surface followed by subsequent interpretation and analysis based on anomalies detected within the images. The interpretation can be done with the use of algorithms that process the images [16–18]. There is a wide array of image-based technologies that have been studied for the purpose of detection, classification and analysis of pavement distresses [19]. One particular low-cost image-based method is stereoscopic surveying including the use of photogrammetry and structure-from-motion. These techniques aim to recreate 3D models of the object being analyzed and recent work on this in the field of pavement distress detection has shown the accuracy of utilizing this method [20]. This field of research provides additional opportunities for the analysis of pavement distresses as accurately generated 3D models can provide critical metric information on the distress that can yield effective intervention strategies.

### *1.3. Using 3D Imagery to Detect and Analyze Pavement Distresses*

Structure-from-motion (SfM) is a photogrammetric modelling technique utilized to replicate 3D models of objects. It is a low-cost method that employs the use of algorithms to reconstruct the object using simple 2D imagery [21]. Within the technique, overlapping images are typically taken around the object at different angles. Specific algorithms for image alignment and bundle adjustment are then applied to establish the object's position in three-dimensional space [22]. Figure 1 showcases an example of a dataset obtained across a distressed asphaltic pavement section.

SfM techniques have generally been utilized in other fields such as architecture and archaeology for the preservation of artefacts and historical figures [23]. There have also been studies on asphalt pavements wherein the techniques were used for replicating road surfaces and their distresses [16,17] and other studies have considered using drones to carry out the process [24,25]. Previous works concluded that there was a lack of available industry tools to utilize the techniques [26]. However, new developments in processing power and algorithms have made it possible for application to pavement engineering [20]. Recent studies have shown the accuracy of models by comparing results to those from laser technologies [27]. This verification of accuracy is in line with typical photogrammetry accuracy development cases for buildings and other structures [28,29]. With the comparisons made to lasers, it was established that professional cameras are capable of carrying out the process. However, these cameras can still be quite expensive and establishing a pipeline using professional cameras still requires the procurement of the devices followed by subsequent training on their use by road agency staff. To this end, if a pipeline could be established using mobile phones then the process can be considered more operational and the potential for its use is accelerated. Therefore, whilst other studies have focused on using the techniques with drones and expensive cameras, this study aims to demonstrate the accuracy of using the techniques with mobile phones to generate 3D pavement distress models to help bridge this research gap and provide quantitative results on the accuracy of developing this mobile pipeline. Furthermore, whilst other studies have focused on simple metric analysis, using metric parameters typically recovered from distresses such as distress dimensions of length and width, the second goal of the study is to establish methods to critically evaluate the distress using segmentation and enhancement strategies. This provides therefore, a sectional analysis methodological point of view. By doing this, distresses can be easily isolated and at this point then the common metric evaluation can be done. To do these analyses, case studies utilizing different strategies and distresses are considered for specific distress types. *Infrastructures* **2020**, *5*, x FOR PEER REVIEW 3 of 25 then the process can be considered more operational and the potential for its use is accelerated. Therefore, whilst other studies have focused on using the techniques with drones and expensive cameras, this study aims to demonstrate the accuracy of using the techniques with mobile phones to generate 3D pavement distress models to help bridge this research gap and provide quantitative results on the accuracy of developing this mobile pipeline. Furthermore, whilst other studies have focused on simple metric analysis, using metric parameters typically recovered from distresses such as distress dimensions of length and width, the second goal of the study is to establish methods to critically evaluate the distress using segmentation and enhancement strategies. This provides therefore, a sectional analysis methodological point of view. By doing this, distresses can be easily isolated and at this point then the common metric evaluation can be done. To do these analyses, case studies utilizing different strategies and distresses are considered for specific distress types.

**Figure 1.** Example of dataset during a SfM survey of a distressed pavement section. **Figure 1.** Example of dataset during a SfM survey of a distressed pavement section.

### *1.4. The Use of Image Segmentation in Pavement Condition Evaluations 1.4. The Use of Image Segmentation in Pavement Condition Evaluations*

Whilst it is useful to recreate the pavement distress with 3D imagery, it is also useful to identify features on these models. Image segmentation is considered for this. It is the process of dividing an image into smaller related segments for the purpose of analyzing and isolating particular features. With regards to pavements, the purpose of image segmentation would be to isolate pavement distresses in order to quickly pinpoint the location of the distress and also for analyzing the type of distress. There have been several attempts over the years to carry this task out utilizing different datasets. Studies have tried to extract useful features from drone image data [25], LIDAR point cloud data [30], Google street view image data [31], 3D laser profilers [32,33], 3D laser images [34] and normal 2D images [35]. There have also been attempts to utilize convolutional neural networks for the purpose of segmenting pavement images using annotated masks on the images [36]. Whilst it is useful to recreate the pavement distress with 3D imagery, it is also useful to identify features on these models. Image segmentation is considered for this. It is the process of dividing an image into smaller related segments for the purpose of analyzing and isolating particular features. With regards to pavements, the purpose of image segmentation would be to isolate pavement distresses in order to quickly pinpoint the location of the distress and also for analyzing the type of distress. There have been several attempts over the years to carry this task out utilizing different datasets. Studies have tried to extract useful features from drone image data [25], LIDAR point cloud data [30], Google street view image data [31], 3D laser profilers [32,33], 3D laser images [34] and normal 2D images [35]. There have also been attempts to utilize convolutional neural networks for the purpose of segmenting pavement images using annotated masks on the images [36].

There are challenges to the acquisition of these types of data sets and then also with regards to the processing power required to analyze them. To this end, this study focuses on the use of a lowcost image acquisition pipeline using mobile phones. Mobile imagery data has an advantage over drone data in that higher resolutions can be yielded given that distance to the object is smaller and also surveys can be made in areas where drone use is forbidden. When coupled with the SfM techniques, mobile imagery can be utilized to create point clouds of a distress and these point clouds There are challenges to the acquisition of these types of data sets and then also with regards to the processing power required to analyze them. To this end, this study focuses on the use of a low-cost image acquisition pipeline using mobile phones. Mobile imagery data has an advantage over drone data in that higher resolutions can be yielded given that distance to the object is smaller and also surveys can be made in areas where drone use is forbidden. When coupled with the SfM techniques, mobile imagery can be utilized to create point clouds of a distress and these point clouds

can be segmented without excessive processing power. Point clouds have previously been classified to produce depth maps and smaller more useful models within the original model in other fields of study [37]. Generally, the process can function as depicted in Figure 2. *Infrastructures* **2020**, *5*, x FOR PEER REVIEW 4 of 25

**Figure 2.** Pipeline for image segmentation. **Figure 2.** Pipeline for image segmentation.

Given these factors, this study aims to generate depth maps and extract and isolate critical elements and sections from 3D models generated by imagery from mobile phones. Given these factors, this study aims to generate depth maps and extract and isolate critical elements and sections from 3D models generated by imagery from mobile phones.

### **2. Materials and Methods 2. Materials and Methods**

### *2.1. Structure-from-Motion Setup and Workflow 2.1. Structure-from-Motion Setup and Workflow*

is given by Equation (1) below.

typically used phone device by any user.

Whilst utilizing structure-from-motion techniques, the most critical parameter to be considered is the ground sampling distance (GSD). This is the typical parameter from which models are interpreted. It is a representation of the distance between two consecutive pixel centers, with respect to actual ground measurements. The GSD is considered as a representation of the smallest details that can be accurately observed on an image [38]. The smaller the value of the GSD, the greater the details that are measurable. This shows the importance of this value as it will dictate the resolution of the replicated models and thus the possible level of observable features. For the GSD, it has been demonstrated that the smallest visible details are two to three times the value of the GSD [39]. Generally, cracks and common distress are smaller than 0.01 m (10 mm) and with resolutions of 3mm these distresses can be accurately identified [40]. Therefore, the technique must be able to produce a resolution less than this. For typical 2D imagery used for detection, a 3 mm resolution is utilized [9]. Given that a detection of 3 mm which would be appropriate for pavement distresses, the GSD should be no greater than 1 mm. As a lower resolution would be better, a value of approximately 0.5 mm was sought after within this study. The GSD is related to specific parameters of the camera used and Whilst utilizing structure-from-motion techniques, the most critical parameter to be considered is the ground sampling distance (GSD). This is the typical parameter from which models are interpreted. It is a representation of the distance between two consecutive pixel centers, with respect to actual ground measurements. The GSD is considered as a representation of the smallest details that can be accurately observed on an image [38]. The smaller the value of the GSD, the greater the details that are measurable. This shows the importance of this value as it will dictate the resolution of the replicated models and thus the possible level of observable features. For the GSD, it has been demonstrated that the smallest visible details are two to three times the value of the GSD [39]. Generally, cracks and common distress are smaller than 0.01 m (10 mm) and with resolutions of 3mm these distresses can be accurately identified [40]. Therefore, the technique must be able to produce a resolution less than this. For typical 2D imagery used for detection, a 3 mm resolution is utilized [9]. Given that a detection of 3 mm which would be appropriate for pavement distresses, the GSD should be no greater than 1 mm. As a lower resolution would be better, a value of approximately 0.5 mm was sought after within this study. The GSD is related to specific parameters of the camera used and is given by Equation (1) below.

$$\text{GSD} = \frac{D \times p\text{x}\_{\text{size}}}{f} \tag{1}$$

where *D* = object distance, ƒ = focal length, and *pxsize* = pixel size (as defined by the ratio of the camera's sensor height to the image height). The focal length and pixel size are attributes from the camera and the other parameters can be manipulated to produce an appropriate GSD. For the purpose of this study, a GSD of 0.5 mm was aimed for so the object distance was manipulated to ensure this value was obtained for the survey. Three devices were utilized for the surveys. A professional camera was used and two different common market mobile phones were used to test the accuracy of the technique using mobile phones. The camera was used as a control in the experiment. The specifications for these devices are given in Table 1. Mobile phones were utilized within the study to obtain imagery because they are typically already in the possession by the average person in today's society and it has been shown that the image quality obtained from these devices are now commonly comparable to even entry-level DSLR cameras [41]. Moreover, the phones used were not the recent most expensive versions of the flagship phones. Both phones used in the study (Huawei P20 Pro and Samsung Galaxy s9) have already been superseded by newer models and it is expected that newer models of both devices will be released shortly. This was done deliberately to show that the process does not require the most recent model releases and it further shows that as time progresses the then 'older' models will still be able to accurately carry out the process without heavy costs of new models. It is expected that the specifications of cameras on mobile phones will keep increasing as demonstrated by market trends and therefore even the average phone used by anyone will have the where *D* = object distance, ƒ = focal length, and *pxsize* = pixel size (as defined by the ratio of the camera's sensor height to the image height). The focal length and pixel size are attributes from the camera and the other parameters can be manipulated to produce an appropriate GSD. For the purpose of this study, a GSD of 0.5 mm was aimed for so the object distance was manipulated to ensure this value was obtained for the survey. Three devices were utilized for the surveys. A professional camera was used and two different common market mobile phones were used to test the accuracy of the technique using mobile phones. The camera was used as a control in the experiment. The specifications for these devices are given in Table 1. Mobile phones were utilized within the study to obtain imagery because they are typically already in the possession by the average person in today's society and it has been shown that the image quality obtained from these devices are now commonly comparable to even entry-level DSLR cameras [41]. Moreover, the phones used were not the recent most expensive versions of the flagship phones. Both phones used in the study (Huawei P20 Pro and Samsung Galaxy s9) have already been superseded by newer models and it is expected that newer models of both devices will be released shortly. This was done deliberately to show that the process does not require the most recent model releases and it further shows that as time progresses the then 'older' models will still be able to accurately carry out the process without heavy costs of new models. It is expected that the specifications of cameras on mobile phones will keep increasing as demonstrated by market trends

and therefore even the average phone used by anyone will have the capacity to carry out the process. Additionally, by using mobile devices as opposed to cameras, there is no need for the purchase of other devices and the process would then therefore possible with the typically used phone device by any user.


**Table 1.** Specifications of devices used for SfM surveys. *Infrastructures* **2020**, *5*, x FOR PEER REVIEW 5 of 25

For the surveys, three different sections were chosen for the case study. The section chosen had distresses comprising longitudinal and transverse cracking, alligator cracking, block cracking and depressions. The predominant distress type covered within the sections is cracking. Sections with a lot of cracking were considered as cracking is the most frequently occurring distress in the geographical region of study [42]. For the actual surveys a typical SfM pipeline was utilized and this is shown in Figure 3. Images of the pavement sections used in the surveys are shown in Figures 4–6. For the surveys, three different sections were chosen for the case study. The section chosen had distresses comprising longitudinal and transverse cracking, alligator cracking, block cracking and depressions. The predominant distress type covered within the sections is cracking. Sections with a lot of cracking were considered as cracking is the most frequently occurring distress in the geographical region of study [42]. For the actual surveys a typical SfM pipeline was utilized and this

Focal length used [mm] 24 3.95 4.3

**Figure 3.** Typical SfM pipeline for generating pavement distress models. **Figure 3.** Typical SfM pipeline for generating pavement distress models.

During the survey of the pavements, images were taken in sequence and with the use of coded markers on the pavement which allowed for scaling of the models. The images were also captured with an estimated overlap of 80% and slightly varying angles around the pavement distresses. Each distressed section was surveyed by each device and this was done consecutively to replicate the same environmental conditions to ensure the results were thus comparable. During the survey of the pavements, images were taken in sequence and with the use of coded markers on the pavement which allowed for scaling of the models. The images were also captured with an estimated overlap of 80% and slightly varying angles around the pavement distresses. Each distressed section was surveyed by each device and this was done consecutively to replicate the same environmental conditions to ensure the results were thus comparable.

The survey was carried out with users operating the devices by hand. The Images were taken from varying inclined angles in a rotational manner around the distressed section. This was done to capture details at the crevices of the distresses that are hard to be seen if the image is taken directly vertical above the object. This methodological choice of using inclined imagery is typical in photogrammetry to allow for the registration of the small minor details on the object being analyzed. By carrying out the survey at angles, the minor details along these crevices are easier to collect and the 3D model generated can be more accurate. The survey was carried out with users operating the devices by hand. The Images were taken from varying inclined angles in a rotational manner around the distressed section. This was done to capture details at the crevices of the distresses that are hard to be seen if the image is taken directly vertical above the object. This methodological choice of using inclined imagery is typical in photogrammetry to allow for the registration of the small minor details on the object being analyzed. By carrying out the survey at angles, the minor details along these crevices are easier to collect and the 3D model generated can be more accurate.

type of 3D survey will yield results that are not possible as with common manual surveys as a full 3D metric evaluation is possible with the SfM approach as evidenced by other studies [20]. The speed of the survey could nevertheless be improved and future studies will consider other data acquisition strategies such as mounting the mobile device. Once this was completed the images were transferred

For each section, the survey took approximately ten minutes per device. It should be noted here that whilst this length of time can be considered as more than that of a manual survey of a particular

presented in Section 2.2.

to the SfM software, Agisoft PhotoScan where the SfM pipeline demonstrated in Figure 3 was

*Infrastructures* **2020**, *5*, x FOR PEER REVIEW 6 of 25

to the SfM software, Agisoft PhotoScan where the SfM pipeline demonstrated in Figure 3 was

against a model generated using imagery from a professional camera. This methodology to do this is

phones needed to be established and this was done comparing models from imagery mobile devices

Following the completion of the 3D model generation, the point clouds of each model were transferred to CloudCompare in order to establish the accuracy of the models derived from the mobile imagery and to segment the models to analyze the distresses occurring in each section. Before the segmentation strategies can be employed the accuracies of utilizing the techniques using mobile

Following the completion of the 3D model generation, the point clouds of each model were transferred to CloudCompare in order to establish the accuracy of the models derived from the mobile imagery and to segment the models to analyze the distresses occurring in each section. Before

employed in order to replicate 3D models of each pavement section.

employed in order to replicate 3D models of each pavement section.

**Figure 4.** Distressed section 1. **Figure 4.** Distressed section 1. **Figure 4.** Distressed section 1.

**Figure 5.** Distressed section 2. **Figure 5.** Distressed section 2. *Infrastructures* **2020**, *5*, x FOR PEER REVIEW 7 of 25

**Figure 6.** Distressed section 3. **Figure 6.** Distressed section 3.

*2.2. Assessment of the Accuracy of Models Generated from Mobile Phone Imagery*  For a metric evaluation of the differences between models generated by the mobile phones and For each section, the survey took approximately ten minutes per device. It should be noted here that whilst this length of time can be considered as more than that of a manual survey of a particular

and used to determine the accuracies of structure-from-motion models [43]. The distribution is

where *β* is the shape parameter, also referred to as the slope of the Weibull plot, *η* is the scale parameter, also referred to as the characteristic life parameter and *γ* is the location parameter, also referred to as the guaranteed lifetime (typically this value is set to zero). The shape parameter indicates the point at which the variable is likely to fail in its distribution. A value less than 1 indicates that this failure will likely occur in the item's early life. A value of 1 indicates the rate of failure is

With respect to the scale parameter, this value is indicative of 63.2 percentile of the distribution which means that 63.2 percent of the distribution will have failed before obtaining this value. The application of the Weibull analysis was carried out within the CloudCompare software. The critical Weibull distribution shape and scale parameters were ascertained to have an understanding of the

Once the accuracy of the models was established, the next step was to focus on segmenting the 3D models. The first strategy analyzed to do this was the random sampling consensus (RANSAC) segmentation algorithm. The RANSAC was utilized to extract shapes from a derived model. This was done by assigning sets of points that can define a particular geometric feature type and then

The algorithm functions by taking a given point-cloud P = {p1, ..., pN} with associated normals {n1, ..., nN} giving an output of a set of primitive shapes Ψ = {Ψ1, ..., Ψn} with corresponding disjoint sets of points PΨ<sup>1</sup> ⊂ P, ..., PΨ<sup>n</sup> ⊂ P and a set of remaining points R = P\{PΨ1, ..., PΨn}. For every iteration of the algorithm, the primitive with the highest score is sought after. The algorithm iteration will conclude as soon as the defined minimal shape size is achieved for the point cloud. The definition of this minimal shape size can be controlled and for this study, this value was based on the size of the point cloud being analyzed. This process can be visualized in the pseudocode for Algorithm 1 shown

extracting shapes that fit this feature type based on the number of points in the category [44].

> ; , > 0 (2)

ఉିଵ ∙ ିቀ ௧ିఊ <sup>ఎ</sup> <sup>ቁ</sup> ഁ

defined by the probability density function given in Equation (2) below.

constant and a value greater than 1 indicates that the rate is increasing.

reliability and accuracy of the models generated by the mobile images.

below as created by [44]:

*2.3. Application of Random Sampling Consensus (RANSAC) Segmentation Algorithm* 

 ∙ ൬− <sup>൰</sup>

ሺሻ <sup>=</sup>

distress section, this type of survey has the potential to yield results that are not subjective as is often the case with manual surveys. This is as a result of most used pavement condition indices have input parameters that rely on a subjective interpretation of the condition by the surveyor. Additionally, this type of 3D survey will yield results that are not possible as with common manual surveys as a full 3D metric evaluation is possible with the SfM approach as evidenced by other studies [20]. The speed of the survey could nevertheless be improved and future studies will consider other data acquisition strategies such as mounting the mobile device. Once this was completed the images were transferred to the SfM software, Agisoft PhotoScan where the SfM pipeline demonstrated in Figure 3 was employed in order to replicate 3D models of each pavement section.

Following the completion of the 3D model generation, the point clouds of each model were transferred to CloudCompare in order to establish the accuracy of the models derived from the mobile imagery and to segment the models to analyze the distresses occurring in each section. Before the segmentation strategies can be employed the accuracies of utilizing the techniques using mobile phones needed to be established and this was done comparing models from imagery mobile devices against a model generated using imagery from a professional camera. This methodology to do this is presented in Section 2.2.

### *2.2. Assessment of the Accuracy of Models Generated from Mobile Phone Imagery*

For a metric evaluation of the differences between models generated by the mobile phones and those generated by a professional camera, a statistical evaluation of the measured geometric differences between the models was done utilizing the Weibull distribution. The Weibull distribution is a continuous probability distribution and it was applied as it is typically used in reliability analyses and used to determine the accuracies of structure-from-motion models [43]. The distribution is defined by the probability density function given in Equation (2) below.

$$f(t) = \frac{\beta}{\eta} \cdot \left(\frac{t-\gamma}{\eta}\right)^{\beta-1} \cdot e^{-\left(\frac{t-\gamma}{\eta}\right)^{\beta}} \qquad t > \gamma; \beta, \eta > 0 \tag{2}$$

where β is the shape parameter, also referred to as the slope of the Weibull plot, η is the scale parameter, also referred to as the characteristic life parameter and γ is the location parameter, also referred to as the guaranteed lifetime (typically this value is set to zero). The shape parameter indicates the point at which the variable is likely to fail in its distribution. A value less than 1 indicates that this failure will likely occur in the item's early life. A value of 1 indicates the rate of failure is constant and a value greater than 1 indicates that the rate is increasing.

With respect to the scale parameter, this value is indicative of 63.2 percentile of the distribution which means that 63.2 percent of the distribution will have failed before obtaining this value. The application of the Weibull analysis was carried out within the CloudCompare software. The critical Weibull distribution shape and scale parameters were ascertained to have an understanding of the reliability and accuracy of the models generated by the mobile images.

### *2.3. Application of Random Sampling Consensus (RANSAC) Segmentation Algorithm*

Once the accuracy of the models was established, the next step was to focus on segmenting the 3D models. The first strategy analyzed to do this was the random sampling consensus (RANSAC) segmentation algorithm. The RANSAC was utilized to extract shapes from a derived model. This was done by assigning sets of points that can define a particular geometric feature type and then extracting shapes that fit this feature type based on the number of points in the category [44].

The algorithm functions by taking a given point-cloud P = {p1, ..., pN} with associated normals {n1, ..., nN} giving an output of a set of primitive shapes Ψ = {Ψ1, ..., Ψn} with corresponding disjoint sets of points PΨ<sup>1</sup> ⊂ P, ..., PΨ<sup>n</sup> ⊂ P and a set of remaining points R = P\{PΨ1, ..., PΨn}. For every iteration of the algorithm, the primitive with the highest score is sought after. The algorithm iteration will conclude as soon as the defined minimal shape size is achieved for the point cloud. The definition of this minimal shape size can be controlled and for this study, this value was based on the size of the point cloud being analyzed. This process can be visualized in the pseudocode for Algorithm 1 shown below as created by [44]:

### **Algorithm 1** Extracting shapes in point Cloud P

Ψ ← Ø {extracted shapes} C ← Ø {shape candidates} **repeat** C ← C ∪ new Candidates() m ← best Candidate (C) **if** P(|m|, |C|> pt **then** P ← P \P<sup>m</sup> {remove points} Ψ ← Ψ ∪ m C ← C \ C<sup>m</sup> {remove invalid candidates} **end if until** P(τ, |C|> pt **return** Ψ

The implementation of this algorithm was done within CloudCompare, utilizing the H-RANSAC plugin. This process is able to isolate several different shapes from the model in question including planes, spheres, cylinders, cones, and tori. For the purpose of this study, the focus was on the planes so as to generate a profile for the pavement to deduce the distressed areas. The purpose, therefore, would be to identify an appropriate plane to be used as a baseline for creating a road profile and to generate depth maps of the section which are able to be metrically referenced. Once the maps are created the particular points of interest on the model can be established and isolated.
