Method for calculating rut depth by using persistent coherence

Abstract

The invention discloses a method for calculating rut depth by using long-lasting coherence, and relates to the technical field of road defect detection. The method is meticulous in logic, good in data processing effect and capable of accurately obtaining the rut depth. According to the technical scheme, the method comprises the following steps of 1, obtaining a pavement three-dimensional picture through laser scanning, and slicing the pavement three-dimensional picture in the width direction; step 2, for each slice, finding out a topological structure by using persistent coherence; step 3, selecting a disappearance position of the required 0-dimensional coherence, and setting a standard for eliminating originating noise; 4, after the noise is eliminated in the step 3, a virtual line is drawn between the zero-dimensional homology disappearing positions arranged in the step 2, and the maximum height between the virtual line and the slices in the step 1 is calculated; and establishing a rule for drawing a straight line based on definitions of a straight line method and an envelope method, and calculating the maximum height of a slice between the virtual line and the step 1. According to the invention, the obtained data can be more accurate.

Description

Technical Field

[0001] This invention relates to the field of road defect detection technology. Background Technology

[0002] Ruts are longitudinal grooves that gradually form on asphalt pavements under repeated tire pressure (especially in hot weather) due to the flow and compaction deformation of the asphalt mixture. They typically appear on wheel tracks in busy traffic lanes. Rut depth refers to the maximum vertical height difference between the bottom of these ruts and the original pavement unaffected by ruts. It is a key indicator for evaluating the structural performance and service quality of road surfaces. Excessive rut depth not only affects the aesthetics of the road but also leads to a series of serious problems: First, there is a risk to driving safety; in rainy weather, water can easily accumulate in the ruts, causing vehicles to hydroplane at high speeds, which reduces handling stability and increases braking distance.

[0003] Secondly, it reduces comfort: vehicles traveling on rutted roads will experience severe bumps, affecting the comfort of driving and riding.

[0004] Third, it accelerates road damage: poor drainage in ruts allows water to seep into and erode the road base, further weakening the road structure and potentially causing other defects such as potholes and loosening.

[0005] Therefore, how to accurately obtain rut depth to characterize the structural performance and service quality of road surfaces has become a technical problem that those skilled in the art are committed to solving.

[0006] Specifically, rut depth is the depth of the depression at the wheel track. The key to obtaining rut depth lies in how to define this "reference surface of the depression". There are two commonly used traditional methods for calculating rut depth, and the fundamental difference between the two methods lies in the different ways of defining the reference surface.

[0007] The first method is the straight-line datum method. This is a relatively traditional and intuitive method used in early manual surveying and some simple systems. The core idea is to define the reference surface of the rut as a simple straight line. This straight line typically connects the raised portions on both sides of the wheel track. The calculation steps are as follows: Step 1: Determine the baseline straight line: On the obtained road cross-section curve, manually or automatically determine two points. These two points are usually located at the highest points of the ridges on both sides of the rut groove (point A and point B).

[0008] Step 2: Connect the baseline: Connect the two points with a straight line. This straight line is the baseline for calculating the rut depth.

[0009] Step 3: Measure the maximum vertical distance: Measure the vertical distance from this reference line to the lowest point of the rut groove. This distance is the rut depth.

[0010] The second method is the envelope method. This is a more advanced calculation method that better reflects engineering realities and is currently the standard method widely used in automated testing equipment (such as laser profilometers). This method assumes that ruts are formed by the lateral flow of material, and the reference surface for the depression should not be a simple straight line, but rather a virtual line that simulates the original smooth road surface before rutting deformation. This virtual line is the "envelope." The calculation steps are as follows: Step 1: Obtain the road cross-section curve: First, a complete road cross-section elevation curve perpendicular to the driving direction is obtained using a high-precision sensor. This curve is uneven.

[0011] Step 2: Generate the moving baseline envelope: The computer simulates a "virtual ruler" of fixed length, which rolls from one end of the road surface curve, closely following the highest point of the curve, towards the other end. As this "ruler" rolls, a smooth curve is formed on its outer side, always tangent to the highest point of the road surface; this curve is the envelope. It effectively "ignores" the grooves formed by ruts.

[0012] Step 3: Calculate the maximum vertical distance: Within the entire measurement range, find the maximum vertical distance between the envelope and the original road surface curve. This maximum vertical distance is the rut depth.

[0013] Currently, in order to manage and maintain roads, it is necessary to regularly check the depth of ruts, but the two commonly used traditional methods mentioned above obviously have many significant drawbacks.

[0014] First, it is highly subjective and lacks precision: the human eye cannot accurately determine the lowest point of a rut and the highest point of the road surface, causing the measurement results to heavily rely on personal experience, and different inspectors may arrive at completely different conclusions. This is far from sufficient for engineering assessments that require millimeter-level precision.

[0015] Secondly, it is inefficient and disruptive to traffic: manual inspection requires closing some lanes, and inspectors work near traffic flow, which is not only slow and affects road capacity, but also poses a huge threat to the safety of the inspectors themselves.

[0016] Third, it lacks comprehensiveness and relies on isolated examples: Due to time and manpower limitations, manual inspection can only be a "sampling survey," selecting only a few cross-sections along a long road section for measurement. This easily leads to the omission of severely rutted areas, failing to reflect the true and comprehensive condition of the entire road.

[0017] Fourth, the data is difficult to quantify and manage: the results of manual inspections are usually based on paper records, making it difficult to form a systematic and digital database. This is not conducive to long-term pavement performance trend analysis, the development of scientific maintenance plans, and the optimization of maintenance fund allocation.

[0018] Fifth, there is a lack of historical data for comparison: Without accurate digital records, it is difficult to effectively compare the rutting development of the same road section at different times, making it difficult to assess the effectiveness of maintenance measures or predict the future deterioration of the road surface.

[0019] In addition, those skilled in the art have found that the three-dimensional data obtained from road surface laser scanning can be represented by a two-dimensional array, with each value representing the height of the scanned road surface. This technique also presents some difficulties when used to calculate rut depth, including: difficulty in determining the location of artificial straight lines when using the straight line method or envelope method; and even if the location is determined, it is difficult to determine the points where artificial straight lines connect.

[0020] In summary, existing technologies have not yet been able to propose a technical means to accurately obtain rut depth in order to characterize the structural performance and service quality of road surfaces. Summary of the Invention

[0021] To address the above problems, this invention proposes a method for calculating rut depth using a persistent homology. This method is logically sound, performs well in data processing, and can accurately obtain rut depth.

[0022] The technical solution of the present invention includes the following steps: Step 1: Use laser scanning to acquire a 3D image of the road surface, slice it along the width direction (all the following steps are performed only on each slice), rescale the image, and reduce the image size by a factor of 4 by slicing; Step 2: For each slice, find the topological structure using persistent homology; use one-dimensional image slices for calculation, considering only 0-dimensional homology (refer to a book on algebraic topology). The application of 0-dimensional homology in one dimension is that the birth and vanishing points are both one-dimensional points (e.g., ...). Figure 2 The blue markers indicate different vanishing points; since the rut depth has a dimension greater than the width threshold, this threshold is set as the standard for the birth and death positions of the component; then, the vanishing positions of locally 0-dimensional homology are arranged from left to right (e.g., Figure 2 The vanishing points, marked in blue, can be arranged from left to right because they are one-dimensional points. Step 3: Select the desired 0-dimensional cohomology vanishing position and set the criteria for excluding noise-induced points. Because the lifetime of points caused by noise is relatively short, in order to eliminate the 0-dimensional cohomology vanishing position caused by noise, a depth threshold is set at the above 0-dimensional cohomology vanishing position, that is, the depth difference between the birth and death positions of 0-dimensional cohomology. Step 4: After eliminating noise in Step 3, determine the disappearance positions of the 0-dimensional homology in the arrangement from Step 2 (see...). Figure 2Draw a virtual line between the virtual line and the slice between step 1, and calculate the maximum height between the virtual line and the slice between step 1; establish rules for drawing straight lines based on the definitions of the straight line method and the envelope method, and calculate the maximum height between the virtual line and the slice between step 1. When using the straight line method, the vanishing positions of 0-dimensional homology are arranged from left to right. Then, a virtual line is found between two points. Then, only the points where the maximum height of the slice between the virtual line and step 1 is greater than the threshold are taken. Finally, the maximum height of the slice between the virtual line and step 1 is calculated. When using the envelope method, find the highest point, and then iterate continuously to find the vanishing positions of the 0-dimensional homology with the minimum slope on both the left and right sides. Connecting these points forms the pseudo-line for calculating the depth of the virtual ruts. Finally, calculate the maximum height of the slice between the virtual line and step 1.

[0023] The potential advantage of this invention over other methods is that existing methods, when calculating rut depth, require identifying the rut edges, which are the starting and ending points of the virtual rut depth line. However, the potential difficulty lies in how to programmatically find these points (because these points are not local maxima or minima). The innovation of this invention lies in the observation that the rut edges are precisely the vanishing points of 0-dimensional homology, because the vanishing points are exactly the boundaries of the depressions (ruts).

[0024] Furthermore, considering that traditional methods for finding extreme points (such as differentiation) are very sensitive to noise and will find many meaningless small fluctuations, this invention proposes a persistent cohomology method. Persistent cohomology assigns a "lifetime" to each extreme point through a scale change process, thereby helping us to distinguish which are significant, macroscopic extreme points and which are small fluctuations that may be caused by noise. Ultimately, this makes the acquired data more accurate. Attached Figure Description

[0025] Figure 1 This is an example of the 3D road surface map obtained in step 1, where each point on the 2D plane has a height value. The black lines represent slices along the width direction. Figure 1 The black line will appear as Figure 2 The orange line; Figure 2 This is a diagram illustrating the calculation process in steps 2-4. The orange line represents a slice of the road, the blue markings indicate the edges of the depressions, which are also the vanishing points of 0-dimensional homology. The black line connects the blue markings, and the rut depth is the maximum difference between the black and orange lines. Detailed Implementation

[0026] To clearly illustrate the technical features of this patent, the following detailed description is provided through specific embodiments and in conjunction with the accompanying drawings.

[0027] This case employs persistent homology to address the shortcomings of existing technologies. The core idea of ​​this method is to treat a one-dimensional signal as a winding path and utilize the "filtering" process of persistent homology to precisely quantify the "significance" or "persistence" of each extreme point. The following is a brief summary of persistent homology: Each pixel on the image slice is considered to have its x-coordinate as its position and its grayscale intensity value as its "altitude". In this way, a one-dimensional intensity signal becomes an undulating mountain line with peaks (local maxima) and valleys (local minima).

[0028] Continuous cohomology assigns a "lifecycle" to each extremum through a scaling process, helping us distinguish between significant, macroscopic extrema and minor fluctuations that may be caused by noise. In contrast, traditional methods for finding extrema (such as differentiation) are very sensitive to noise and will find many meaningless, tiny fluctuations.

[0029] The specific methodology is similar to a water level model. We use sub-set filtering, which means "filling in water" starting from the lowest point of the image (minimum intensity).

[0030] For finding local minima: The 0-dimensional features (connected components) of continuous homology directly correspond to local minima.

[0031] Birth: When the water level (scale parameter) rises to a local minimum, a new "puddle" (connected component) is born. Each local minimum is the birth point of a 0-dimensional feature.

[0032] Extinction: As the water level continues to rise and two separate puddles are about to merge, according to the "elder rule" rule, the puddle that forms later will disappear. The location where this merger occurs is the height of the saddle point connecting the two puddles (in this case, the local maximum between two minimums in a one-dimensional signal).

[0033] Persistence calculation: The persistence of a local minimum is the difference between its extinction height and its birth height.

[0034] Interpretation of Results (Finding the Minimum): Elongated shape: Represents a deep valley. Its persistence is high because it would require a significant rise in water level to submerge it. This is a significant and important local minimum.

[0035] Short bars: Represent a shallow depression. Their persistence is very low; they may simply be a tiny dip in the signal or noise. We can ignore these short bars when filtering noise.

[0036] For finding local maxima: To find local maxima, we need to use a dual perspective: superset filtering. Imagine starting from the highest point of the mountain (maximum intensity) as "glacial melting" or "flooding".

[0037] Birth: When the water level starts to drop from the highest point and touches a local maximum point, this "peak" is born as an independent connected component (from the perspective of a super-layer set).

[0038] Extinction: When the water level drops enough to expose the "valley" between two peaks, thus connecting the two peaks, the connecting component of the later-formed peaks will disappear.

[0039] Persistence calculation: The persistence of a local maximum is its birth height (its own height) minus its death height (the height of the local minimum connected to it).

[0040] Interpretation of Results (Finding the Maximum): Elongated shape: Represents a towering mountain peak. Its continuity is high because it rises significantly above the surrounding valleys. This is a significant and important local maximum.

[0041] Short bar: Represents a tiny bump. Its persistence is very low, and it may just be a tiny fluctuation or noise in the signal.

[0042] Based on the above persistent cohomology, a novel method for calculating rut depth is proposed, including the following steps: Step 1: Slice the image longitudinally and rescale it. The original image size is approximately 4 meters, and the pixel size is approximately 1 millimeter. This pixel scale is much finer than the depth of tire tracks, so it is unnecessary to use this pixel ratio for calculations. To reduce computational complexity, the slices will be reduced by a factor of 4.

[0043] Step 2: For each slice, find the topology using persistent homology; since only one-dimensional image slices are used for calculation in this case, we only consider H0 (0-dimensional homology). Because rut depth has a size greater than the width threshold, this threshold is set as the standard for the birth and death locations of components. Then, local maxima and local minima are organized from left to right.

[0044] Step 3: Select the desired 0-dimensional homology vanishing location and local minimum standard, and set the standard to exclude noise-induced local maxima or minima. In order to eliminate noise-induced local maxima or minima, we set a depth threshold at the selected points above, because noise-induced points have a relatively short lifespan.

[0045] Step 4: Draw a virtual line between the vanishing positions of the 0-dimensional homology and calculate the maximum height between the line and the road segment. Both the straight line method and the envelope method draw virtual straight lines between different local maxima. Therefore, we establish rules for drawing straight lines based on the definitions of the straight line method and the envelope method, and calculate the maximum height between the line and the road segment.

[0046] There are many specific ways to implement this invention. The above description is only a preferred embodiment of this invention. It should be noted that for those skilled in the art, several improvements can be made without departing from the principle of this invention, and these improvements should also be considered within the scope of protection of this invention.

Claims

1. A method for calculating rut depth using a persistent homology, characterized in that, Includes the following steps: Step 1: Use laser scanning to acquire a 3D image of the road surface, slice it along the width direction, rescale the image, and reduce the image size by slicing; Step 2: For each slice, use persistent homology to find the topology; use one-dimensional image slices for calculation, only consider 0-dimensional homology, the application of 0-dimensional homology in one dimension, birth and vanishing points are both one-dimensional points; since the rut depth has a size greater than the width threshold, this threshold is set as the standard for the birth and death positions of components; then, arrange the vanishing positions of local 0-dimensional homology from left to right. Step 3: Select the desired vanishing position of 0-dimensional cohomology and set the criteria for excluding noise; set a depth threshold at the vanishing position of the above 0-dimensional cohomology, that is, the depth difference between the birth and death positions of 0-dimensional cohomology. Step 4: After eliminating noise in Step 3, draw a virtual line between the disappearance positions of the 0-dimensional coherence in Step 2, and calculate the maximum height between the virtual line and the slice in Step 1; establish rules for drawing the line based on the definitions of the straight line method and the envelope method, and calculate the maximum height between the virtual line and the slice in Step 1.

2. The method for calculating rut depth using a sustained coherent harmonic as described in claim 1, characterized in that, When using the straight line method, the vanishing positions of 0-dimensional homology are arranged from left to right. Then, a virtual line is found between two points. Only the points where the maximum height of the slice between the virtual line and step 1 is greater than the threshold are selected. Finally, the maximum height of the slice between the virtual line and step 1 is calculated.

3. The method for calculating rut depth using a sustained coherent harmonic as described in claim 1, characterized in that, When using the envelope method, find the highest point, and then iterate continuously to find the vanishing positions of the 0-dimensional homology with the minimum slope on both the left and right sides. Connecting these points forms the pseudo-line for calculating the depth of the virtual ruts. Finally, calculate the maximum height of the slice between the virtual line and step 1.

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