An Adaptive Determination Method for Curved Surface Variational Threshold

Abstract

The present invention belongs to the technical field of point cloud data processing, and particularly relates to an adaptive determination method for surface variation thresholds. This method first calculates the surface variation values of each point cloud in the original sampled point cloud data and sorts them; then, it performs curve fitting on the surface variation values of the sorted point clouds; next, it calculates the curvature radius / slope corresponding to each point cloud on the fitted curve, and selects the surface variation value corresponding to the point cloud whose curvature radius is within a set range near the minimum curvature radius / the absolute value of the slope is 1±x as the surface variation threshold. The surface variation threshold adaptively determined by this method is accurate and reasonable, can distinguish the high and low curvature regions of the original sampled point cloud data, avoids the defects of randomness, lack of basis, and long time consumption caused by the artificial method of selecting the surface variation threshold, and ensures that there are neither too many redundant flat points nor enough feature points reflecting object details in the finally extracted feature points.

Description

Technical Field

[0001] The present invention belongs to the technical field of point cloud data processing, and particularly relates to an adaptive determination method for a surface variation threshold. Background Art

[0002] The continuous improvement of the scanning speed and accuracy of three-dimensional laser scanning devices has promoted the wide application of laser scanning technology in various fields, and these applications have collected a large amount of point cloud data in the target area. The high-density massive point cloud data not only has a lot of redundant information, but also occupies a large amount of memory and reduces the efficiency of subsequent processing steps. Therefore, in practical applications, an appropriate balance will be found between the fineness of the point cloud model expression and the processing efficiency, that is, according to different application requirements, useful information sufficient to express the model features is extracted from the original sampled point cloud, which is the simplification of point cloud data.

[0003] The feature-preserving point cloud simplification method realizes the simplification of point cloud data while retaining the detailed feature information of the point cloud data, and seeks an optimal balance between the simplification rate of the point cloud data and the retention of feature information. This method first selects relevant feature measurement factors such as point cloud curvature, normal direction, normal angle, local feature size, feature parameters, and minimum surface distance to measure the feature saliency of each point, and finally obtains a simplified point cloud retaining detailed information by the strategy of retaining feature points in the point cloud data and deleting a certain number of non-feature points.

[0004] The point cloud curvature information is the intrinsic attribute information of the point cloud, and its size reflects the feature distribution information, which is the most commonly used feature measurement factor. There are many types of point cloud curvatures, and those applied to point cloud simplification include: normal curvature, mean curvature, Gaussian curvature, principal curvature, surface variation, mean curvature of a circle, mixed curvature, etc. As an index describing the local geometric features of a surface, the surface variation is similar to the normal curvature. At the same time, the surface variation has geometric invariance, and its size is independent of the scale of the point cloud model. It is more applicable to use the surface variation to distinguish flat points and non-flat points.

[0005] The threshold of the feature measurement factor is an important basis for distinguishing feature points from non-feature points and is the key to the point cloud simplification algorithm. At present, the surface variation threshold is determined manually and requires multiple trials to complete, which consumes a lot of time. Moreover, the manual determination method lacks a scientific and quantifiable standard, which brings great uncertainty to the subsequent processing of the point cloud, or results in few extracted feature points of the point cloud and cannot fully reflect the detailed features of the object, or extracts more redundant flat points, resulting in a large amount of data in the subsequent point cloud data processing. Summary of the Invention

[0006] The object of the present invention is to provide an adaptive determination method for the surface variation threshold, so as to solve the problems that fewer feature points are extracted by using the artificial method to determine the surface variation threshold, which cannot reflect the detailed features of the object, or more feature points are extracted, resulting in a large amount of subsequent point cloud data processing.

[0007] To solve the above technical problems, the technical solutions provided by the present invention and the corresponding beneficial effects of the technical solutions are as follows:

[0008] The present invention provides an adaptive determination method for the surface variation threshold, including the following steps:

[0009] 1) Obtain the original sampled point cloud data and calculate the surface variation values of each point cloud;

[0010] 2) Sort each point cloud according to the magnitude of the surface variation value of each point cloud;

[0011] 3) Perform curve fitting on the surface variation values of the sorted point clouds to obtain a fitting curve;

[0012] 4) Calculate the curvature radius / slope corresponding to each point cloud on the fitting curve, and select the surface variation value corresponding to the point cloud whose curvature radius is within a set range near the minimum curvature radius / whose absolute value of the slope is 1±x as the surface variation threshold, where x is 0 or a positive number representing much less than 1.

[0013] The beneficial effect of the above technical solution is that the present invention provides an adaptive determination method for the surface variation threshold. This method first sorts the surface variation values of each point cloud in the original sampled point cloud data, performs curve fitting after sorting, and then selects the surface variation value corresponding to the point cloud whose curvature radius is within a set range near the minimum curvature radius on the fitting curve as the surface variation threshold, or selects the surface variation value corresponding to the point cloud whose slope on the fitting curve is infinitely close to 1 as the surface variation threshold. Finally, the extracted surface variation threshold can be used for point cloud simplification, point cloud normal adjustment, etc. Through experiments, the results show that the surface variation threshold adaptively determined by this method is accurate and reasonable, can distinguish the high and low curvature regions of the original sampled point cloud data, avoids the defects of randomness, lack of basis and long time consumption caused by the artificial method of selecting the surface variation threshold, ensures that there are neither too many redundant flat points nor enough feature points reflecting the details of the object in the finally extracted feature points, and improves the efficiency of subsequent point cloud processing.

[0014] Further, if the slope corresponding to each point cloud on the fitting curve is selected for calculation in step 4), the process of performing curve fitting on the surface variation values of the sorted point clouds in step 3) includes: normalizing the surface variation values and / or the point cloud numbers of each point cloud, and performing curve fitting on the surface variation values of the normalized point clouds.

[0015] The beneficial effects of the above technical solution are as follows: Since the amount of data of the original sampled point cloud data is huge and the value of the surface variation is not more than 1 / 3, and the order of magnitude of the two is too different, the surface variation values and / or point cloud numbers of each point cloud are normalized here, and the display scales of the horizontal and vertical coordinates of the fitting curve are adjusted to be the same to ensure the accuracy of the curve fitting using the slope calculation method subsequently.

[0016] Furthermore, the surface variation values of each point cloud are normalized.

[0017] The beneficial effects of the above technical solution are as follows: Only normalizing the surface variation values of each point cloud has a simple processing method and relatively high curve fitting accuracy, and can accurately reflect the actual variation law of the surface variation.

[0018] Furthermore, the normalization process is as follows:

[0019]

[0020] In the formula, σ′(p) is the surface variation value of point cloud p after normalization; σ(p) is the surface variation value of point cloud p before normalization; index is the number of the largest point cloud.

[0021] The beneficial effects of the above technical solution are as follows: This normalization method is simple and easy to implement.

[0022] Furthermore, in step 3), a Gaussian function, a polynomial, a power function, or an exponential function is used for curve fitting.

[0023] Furthermore, two parameters, the root mean square error and the coefficient of determination of the fitting function, are used to select the fitting function used for curve fitting in step 3) from multiple fitting functions.

[0024] The beneficial effects of the above technical solution are as follows: Experimental results show that using two parameters, the root mean square error (RMSE) and the coefficient of determination (R-square), to select the final fitting function ensures that the used fitting function can best reflect the variation law of the surface variation values of each point cloud.

[0025] Furthermore, in step 2), each point cloud is sorted in ascending order or descending order.

[0026] Furthermore, after step 4), it further includes: step 5) According to the determined surface variation threshold, the point clouds with surface variation values greater than or equal to the surface variation threshold are extracted as feature points.

[0027] The beneficial effects of the above technical solution are as follows: The point clouds with surface variation values greater than or equal to the surface variation threshold are extracted as feature points, and the flat points are deleted, improving the effect of subsequent point cloud processing.

[0028] Further, the formula for calculating the surface variation value of each point cloud in step 1) is:

[0029]

[0030] In the formula, σ(p) is the surface variation value of point cloud p; λ0, λ1, and λ2 are the three eigenvalues of matrix C, and λ0 < λ1 < λ2; the k-nearest neighbor point set of point cloud p is P = {p i (x i ,y i ,z i )|i = 1, 2…, k}, then matrix C is the covariance matrix of point cloud p and is:

[0031]

[0032] In the formula, k is the number of nearest neighbor points, is the coordinate average value of k nearest neighbor points. Description of the Drawings

[0033] Figure 1 is the flowchart for extracting feature points of point cloud data using the method for adaptively determining the surface variation threshold of the present invention;

[0034] Figure 2-1 is the original scatter plot of the surface variation of each point cloud in the bunny dataset;

[0035] Figure 2-2 is the original scatter plot of the surface variation of each point cloud in the block dataset;

[0036] Figure 3-1 is the sorted scatter plot of the surface variation of each point cloud in the bunny dataset;

[0037] Figure 3-2 is the sorted scatter plot of the surface variation of each point cloud in the block dataset;

[0038] Figure 4-1 is the curve fitting result diagram of the bunny dataset;

[0039] Figure 4-2 is the curve fitting result diagram of the block dataset;

[0040] Figure 5-1 is the schematic diagram of the position of the surface variation threshold of the bunny dataset determined by the manual method;

[0041] Figure 5-2Schematic diagram of the surface variation threshold position of the block data set determined by the artificial method;

[0042] Figure 6-1 Schematic diagram of the surface variation threshold position of the bunny data set determined by the minimum curvature radius method;

[0043] Figure 6-2 Schematic diagram of the surface variation threshold position of the block data set determined by the minimum curvature radius method;

[0044] Figure 7-1(a) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.05 is determined by the artificial method for the bunny data set;

[0045] Figure 7-1(b) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.02 is determined by the artificial method for the bunny data set;

[0046] Figure 7-1(c) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.008 is determined by the artificial method for the bunny data set;

[0047] Figure 7-1(d) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.0243 is determined by the minimum curvature radius method for the bunny data set;

[0048] Figure 7-2(a) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.05 is determined by the artificial method for the block data set;

[0049] Figure 7-2(b) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.005 is determined by the artificial method for the block data set;

[0050] Figure 7-2(c) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.008 is determined by the artificial method for the block data set;

[0051] Figure 7-2(d) is the feature point extraction result diagram when the surface variation threshold σ0 = 0.0015 is determined by the minimum curvature radius method for the block data set. Specific implementation manner

[0052] First, the related definitions of surface variation are introduced below.

[0053] The covariance matrix C of the neighborhood points of any point cloud p in the point cloud data can be used to analyze the surface properties of the local area where the point cloud is located. Let the k-nearest neighbor point set of the point cloud p be P = {p i (x i ,y i ,z i) If \(i = 1, 2, \cdots, k\}, then the covariance matrix \(C\) corresponding to the point cloud \(p\) can be expressed as:

[0054]

[0055] Where \(k\) is the number of neighboring points; is the average coordinate value of \(k\) neighboring points.

[0056] Let the three eigenvalues of the covariance matrix \(C\) be \(\lambda_0\), \(\lambda_1\), \(\lambda_2\) respectively, and \(\lambda_0 \lt \lambda_1 \lt \lambda_2\). The three eigenvectors corresponding to the eigenvalues are \(e_0\), \(e_1\), \(e_2\) respectively. Then the eigenvalues \(\lambda_0\), \(\lambda_1\), \(\lambda_2\) can respectively represent the offsets of the point cloud \(p\) along the eigenvectors \(e_0\), \(e_1\), \(e_2\). \(\lambda_0\) characterizes the degree to which the point cloud \(p\) deviates from the tangent plane formed by \(e_2\) and \(e_1\). In differential geometry, curvature is a description of the differential properties of a surface. Similarly, the surface variation can be used as a measure criterion for the local differential properties of a scattered point cloud. The surface variation of the local area of the point cloud \(p\) is defined as:

[0057]

[0058] Since \(\lambda_0\) is the minimum value among the three eigenvalues, according to Equation (2), it can be known that \(0\leq\sigma(p)\leq1 / 3\). When \(\sigma(p)=1 / 3\), at this time, point \(p\) is a feature point, and the nearby area is a high-curvature area; when \(\sigma(p)=0\), at this time, the nearby area of point \(p\) is a plane, and point \(p\) is a flat point. \(\sigma(p)\) represents the gentle undulation situation of the area near point \(p\). The larger \(\sigma(p)\) is, the greater the curvature of the area near point \(p\) is, and the greater the possibility that point \(p\) is a feature point. Therefore, \(\sigma(p)\) can be used to distinguish flat points and feature points. For example, set a threshold \(\sigma_0\). When \(\sigma(p)\lt\sigma_0\), it is a flat point, otherwise it is a feature point.

[0059] The method of the present invention aims to explore an automatic determination method for the surface variation threshold on the basis of in-depth analysis of the variation law of the surface variation, in order to solve the problem of threshold uncertainty, so as to accurately extract the feature points of the point cloud data. The overall process is as follows: First, arrange the surface variation scattered point diagram in a certain order, then use the fitting function to fit the surface variation scattered point diagram, and finally use the minimum curvature radius method or the curve slope method to automatically determine a reasonable surface variation threshold, and use the determined surface variation threshold to extract feature points. The following will combine the accompanying drawings and embodiments to elaborate in detail on an adaptive determination method for the surface variation threshold of the present invention.

[0060] Method embodiment:

[0061] In this embodiment, the point clouds in the bunny and block datasets are used as the original point cloud data to explore the method for determining the surface variation threshold, and then the extraction of feature points from the point cloud data is realized. Among them, block represents the type of point cloud with significant feature points such as corner points and edges, and bunny represents the type of point cloud without significant feature points. The specific process is as Figure 1 shown, and the process is as follows:

[0062] Step 1: Solve the surface variation values of each point cloud in the bunny dataset and the block dataset respectively, and obtain the original scatter plots of the surface variations of the bunny dataset and the block dataset.

[0063] To solve the surface variation, the k-nearest neighbors need to be retrieved. To achieve fast indexing of the neighborhood relationship, the k-d tree is used to organize the point cloud data, and then the set of k-nearest neighbors of any point cloud p is retrieved. Combining Equation (1) and Equation (2), the surface variation value σ(p) of the point cloud p is calculated. The original scatter plots of the surface variations of each point in the bunny dataset and the block dataset are respectively as Figure 2-1 and Figure 2-2 shown. From Figure 2-1 and Figure 2-2 , it can be seen that most of the surface variation values are very small, and a small number are greater than 0.02, which corresponds to the actual situation that the feature points in the point cloud data account for a small part of all the point cloud data. These surface variation values are scattered without any pattern, making it difficult to determine a reasonable surface variation threshold to distinguish between flat points and feature points.

[0064] Step 2: According to the magnitude of the surface variation values, sort the points in the bunny and block datasets in ascending order, and redraw the scatter plot to obtain the sorted scatter plot of the surface variation.

[0065] The sorted scatter plots of the surface variations of each point cloud in the bunny dataset and the block dataset are respectively as Figure 3-1 and Figure 3-2 shown. From these two figures, it can be seen that after sorting the original scatter plot of the surface variation, it shows a changing trend of first growing slowly and then increasing steeply. Although the characteristics of the point cloud data of bunny and block are different, the changing rules of their surface variation values are consistent. Therefore, in this embodiment, the same function is selected to perform curve fitting on the surface variation values of different types of point clouds.

[0066] Step 3: Perform curve fitting on the sorted scatter plot of the surface variation to obtain the fitting curve.

[0067] From Figure 3-1 and Figure 3-2As can be seen, the abscissa (point cloud serial number) is often as high as tens of thousands or more, and the ordinate (surface variation value) does not exceed 1 / 3. The scales of the abscissa and ordinate axes differ greatly. When the display scales of the abscissa and ordinate are adjusted to be the same, the scatter plot of the surface variation values is approximately linearly distributed. If curve fitting is directly performed, the actual variation law of the surface variation values will be masked, and the actual variation law of the surface variation cannot be accurately reflected. Therefore, in this embodiment, the surface variation values of each point in the point cloud are enlarged in equal proportion so that the scales of the abscissa and ordinate are in the same order of magnitude and their variation laws are not changed, which is called the normalization of the scales of the abscissa and ordinate. In this embodiment, the surface variation values are selected for normalization processing, and the calculation formula for the enlarged surface variation values is:

[0068]

[0069] In the formula, index is the serial number of the largest point cloud; σ′(p) is the surface variation value of point cloud p after normalization processing; σ(p) is the surface variation value of point cloud p before normalization processing.

[0070] After the normalization of the scales of the abscissa and ordinate, four fitting methods, namely polynomial fitting (9th order), power exponential fitting, exponential function fitting, and Gaussian fitting, are selected for fitting, and two fitting indexes, namely the root mean square error RMSE and the coefficient of determination R-square of each method, are statistically calculated. The calculation formulas are:

[0071]

[0072]

[0073] In the formula, y i is the original value of the surface variation; is the calculated value of the fitting function; n is the number of point clouds; is the average value of the original values.

[0074] The smaller the RMSE, the better the function fitting and the smaller the error. The closer the R-square is to 1, the more relevant the fitting function is to the scatter plot and the more it can describe the variation law of the scatter plot. The statistical results of the function fitting indexes are shown in Table 1.

[0075] Table 1 Statistical results of function fitting indexes

[0076]

[0077] As can be seen from Table 1, when Gaussian function fitting is used, the RMSE is the smallest and the R-square is the closest to 1, that is, when Gaussian function fitting is used, the RMSE is the smallest and the R-square is the closest to 1. Therefore, using Gaussian function fitting can best reflect the variation law of the surface variation scatter plot. Therefore, in this embodiment, Gaussian function is selected to perform curve fitting on the surface variation points. The form of the Gaussian function is:

[0078]

[0079] Wherein, a1, b1, c1, a2, b2, c2 are parameters to be determined; x is the input of the Gaussian function, referring to the serial number of the point cloud; f(x) is the output of the Gaussian function, referring to the surface variation value.

[0080] The function fitting results are as Figure 4-1 and Figure 4-2 shown. It can be seen from these two figures that the fitted function curve fits well with the original surface variation scatter plot, verifying the correctness of using the Gaussian function to fit the curve.

[0081] Step Four, calculate the curvature radius of each point cloud on the fitted curve, and select the surface variation value corresponding to the point cloud with the smallest curvature radius (here it should be the original surface variation value of this point cloud) as the surface variation threshold.

[0082] As Figures 7-1(a) to 7-1(c) , and Figures 7-2(a) to 7-2(c) shown (these figures will be introduced in detail in the following experimental verification part), after multiple experiments by the manual method, the surface variation thresholds that can better distinguish the flat points and feature points in the bunny dataset and the block dataset are selected as 0.02 and 0.005 respectively. To adaptively determine the surface variation threshold, first magnify the relatively appropriate threshold selected by the manual method according to Equation (3) and mark it on the fitted curve, as shown in Figure 5-1 and Figure 5-2 shown respectively.

[0083] The positions of the circles in the figure are the positions of the appropriate surface variation thresholds determined manually on the fitted function. It can be observed that these threshold points are located near the point with the smallest curvature radius or the slope equal to 1 of the curve, and the surface variation threshold can be automatically found according to these two indicators. Further analysis shows that the curve slope is an absolute indicator, which is closely related to the magnification factor of the surface variation value when the horizontal and vertical coordinate scales are normalized. Different magnification factors will result in different slopes for the same serial number point. After adopting the horizontal and vertical coordinate scale normalization method of this embodiment, the curve slope method can be used. If not normalized, the curve slope method will fail. However, the smallest curvature radius is a relative indicator and is not sensitive to the vertical coordinate scale transformation. Therefore, this embodiment selects the minimum curvature radius method. The calculation formula for the curvature radius of the curve is:

[0084]

[0085] According to the above formula, the curvature radius corresponding to each point cloud is calculated, and the surface variation value corresponding to the point with the smallest curvature radius (after reducing the magnification factor) is the surface variation threshold determined by the method of the present invention. Among them, the threshold for bunny is 0.0243, and the threshold for block is 0.0015, asFigure 6-1 the dot closer to the right side Figure 6-2 and the dot closer to the left side as shown. From Figure 6-1 and Figure 6-2 it can be seen that the surface variation threshold automatically determined by the minimum curvature radius method and the thresholds repeatedly selected by the manual method are approximately equal numerically, indicating the correctness and feasibility of the method for adaptively determining the surface variation threshold of the present invention. The automatically determined threshold can better distinguish flat points and feature points. At the same time, the difference in the serial numbers of the manual threshold and the adaptive threshold is very small, indicating that the number of feature points determined by the two thresholds is basically the same.

[0086] Step Five: Using the determined surface variation threshold, the point clouds in the original sampled point cloud data that are greater than or equal to the surface variation threshold are used as feature points for feature point extraction. Thus, the extraction of feature points from the point cloud data can be completed.

[0087] To verify the effect of the method of the present invention, experimental verification is carried out below. In the hardware environment of Win7 system Intel(R) Core(TM) i7-4790M CPU 3.60GHz, programming experiments are carried out in combination with software such as Matlab 2014a, VS2013, and PCL and third-party libraries. The manual threshold determination method and the minimum curvature radius method are respectively used to determine the surface variation threshold, and the feature points are extracted and retained based on this. The extraction results are as Figures 7-1(a) to 7-1(d) shown in Figures 7-2(a) to 7-2(d), Figures 7-1(a) to 7-1(c) Figure 7-1(d) is the feature point extraction result diagram when the surface variation threshold σ0 determined by the manual method for the bunny data set is 0.05, 0.02, and 0.008 respectively, and Figure 7-1(d) is the feature point extraction result diagram when the surface variation threshold σ0 determined by the minimum curvature radius method for the bunny data set is 0.0243. Figures 7-2(a) to 7-2(c) Figure 7-2(d) is the feature point extraction result diagram when the surface variation threshold σ0 determined by the manual method for the block data set is 0.05, 0.005, and 0.008 respectively, and Figure 7-2(d) is the feature point extraction result diagram when the surface variation threshold σ0 determined by the minimum curvature radius method for the block data set is 0.0015.

[0088] From Figures 7-1(a) to 7-1(c) and Figures 7-2(a) to 7-2(c)It can be seen that selecting an appropriate surface variation threshold manually requires multiple experiments. When the threshold is selected to be small, the remaining feature point cloud is sparse and cannot fully reflect the detailed features of the object. When the threshold is selected to be large, many flat points are also retained as feature points, resulting in data redundancy. After multiple experiments, a relatively appropriate surface variation threshold can better extract the feature points in the point cloud data. The feature points extracted based on the threshold determined by the minimum curvature radius method retain the feature information of the object and have no redundant flat points. Compared with the relatively appropriate threshold determined manually, the two have comparable effects. However, the threshold is adaptively determined, with a quantifiable basis and a significant improvement in efficiency.

[0089] In summary, regarding the problem that the curvature threshold involved in the point cloud data reduction algorithm based on curvature is difficult to determine, the present invention proposes a method for extracting feature points based on an adaptively determined surface variation threshold. Based on an in-depth analysis of the law of surface variation values, this method automatically finds the surface variation threshold point using the minimum curvature radius method, avoiding the limitations and uncertainties of manually selecting the threshold multiple times and being able to accurately extract feature points.

[0090] In this embodiment, in the face of the problem that the scales of the horizontal and vertical coordinates in the obtained original scatter plot of surface variation differ greatly, the surface variation values of the vertical coordinate are normalized. The specific normalization formula is shown in Equation (3) to ensure that the scales of the horizontal and vertical coordinates are in the same order of magnitude without changing their variation law. As other implementation manners, the point cloud serial numbers of the horizontal coordinate can also be normalized, or both the point cloud serial numbers of the horizontal coordinate and the surface variation values of the vertical coordinate can be normalized to achieve the purpose of ensuring that the scales of the horizontal and vertical coordinates are in the same order of magnitude without changing their variation law.

[0091] In step four of this embodiment, the minimum curvature radius method is used to select the surface variation threshold from it. It should be noted that if the minimum curvature radius method is used, the normalization process in step three is not necessary. Curve fitting can be performed after normalization, and then the minimum curvature radius method can be used to select the surface variation threshold from it; or normalization can be not performed, and curve fitting can be directly performed using the original surface variation scatter values of each point cloud before normalization, and then the minimum curvature radius method can be used to select the surface variation threshold from it.

[0092] In step four of this embodiment, the surface variation value corresponding to the point cloud with the smallest curvature radius is directly selected as the surface variation threshold. As other implementation manners, instead of directly selecting the point cloud with the smallest curvature radius, the surface variation value corresponding to the point cloud whose curvature radius is infinitely close to the minimum curvature radius can be selected as the surface variation threshold. For example, the minimum curvature radius is ρ min , the surface variation threshold corresponding to the point cloud with a curvature radius of ρ min + 0.01 can be selected as the surface variation threshold.

[0093] In this embodiment, the Gaussian function is used for curve fitting. The experimental results show that this method has a better fitting effect for the bunny dataset and the block dataset. As other embodiments, for other original sampled point cloud data, other curve fitting methods in the prior art can be used, such as polynomial fitting, power function fitting, or exponential function fitting mentioned in this embodiment. For different original sampled point cloud data, the fitting method with the best fitting effect is selected for curve fitting.

[0094] In step two of this embodiment, the surface variation scattered point sorting diagram is obtained by sorting in ascending order. As other embodiments, the surface variation scattered point sorting diagram can also be obtained by sorting in descending order. The subsequent processing steps are the same as those of sorting in ascending order, that is, the surface variation value corresponding to the point cloud with the smallest radius of curvature is selected as the surface variation threshold, but the obtained fitting curves will be different.

[0095] In step four of this embodiment, the minimum radius of curvature method insensitive to the vertical coordinate scale transformation is used to select the surface variation threshold therefrom. As other embodiments, the curve slope method can be used to select the surface variation threshold. Different from the minimum radius of curvature method, normalization must be performed in step three. The surface variation scattered values of each point cloud after normalization are used for curve fitting, and then the slopes of each point cloud on the fitting curve are calculated. The surface variation value corresponding to the point cloud with a slope of 1 is selected as the surface variation threshold (at this time, the surface variation scattered point sorting diagram in step two is sorted in ascending order). Of course, if the surface variation scattered point sorting diagram in step two is sorted in descending order, the surface variation value corresponding to the point cloud with a slope of -1 should be selected as the surface variation threshold. Moreover, the "1" and "-1" here can also be correspondingly selected as values infinitely close to "1" and "-1", such as "0.99" and "-0.99" respectively.

Claims

1. An adaptive determination method for a variational threshold of a curved surface, characterized in that It includes the following steps: 1) Obtain the original sampled point cloud data and calculate the surface variation values of each point cloud; 2) Sort each point cloud according to the magnitude of the surface variation value of each point cloud; 3) Use different fitting functions to perform curve fitting on the surface variation values of the sorted point clouds, statistically calculate the function fitting indicators of each fitting function, and select the fitting curve that can best reflect the variation law of the surface variation value according to the function fitting indicators; 4) Calculate the curvature radius / slope corresponding to each point cloud on the fitting curve, and select the surface variation value corresponding to the point cloud whose curvature radius is within a set range near the minimum curvature radius / the absolute value of the slope is 1±x as the surface variation threshold, where x is 0 or a positive number representing much less than 1.

2. The adaptive determination method of the surface variation threshold according to claim 1, wherein If the slope corresponding to each point cloud on the fitting curve is selected and calculated in step 4), then the process of performing curve fitting on the surface variation values of the sorted point clouds described in step 3) includes: normalizing the surface variation values of each point cloud and / or the point cloud numbers, and performing curve fitting on the surface variation values of the normalized point clouds.

3. The adaptive determination method of the surface variation threshold according to claim 2, characterized in that, Normalize the surface variation values of each point cloud.

4. The adaptive determination method of the surface variation threshold according to claim 3, characterized in that, The normalization process is: In the formula, σ′(p) is the surface variation value of point cloud p after normalization; σ(p) is the surface variation value of point cloud p before normalization; index is the number of the largest point cloud.

5. The adaptive determination method of the curved surface variational threshold according to any one of claims 1 to 4, characterized in that In step 3), a Gaussian function, a polynomial, a power function, or an exponential function is used for curve fitting.

6. The adaptive determination method of the surface variation threshold according to any one of claims 1 to 4, characterized in that The function fitting indicators include two parameters, namely the root mean square error and the coefficient of determination of the fitting function.

7. The adaptive determination method of the surface variation threshold according to claim 1, characterized in that In step 2), each point cloud is sorted in ascending order or descending order.

8. The adaptive determination method of the surface variational threshold according to claim 1, wherein After step 4), it further includes: step 5) Extract the point clouds whose surface variation values are greater than or equal to the surface variation threshold as feature points according to the determined surface variation threshold.

9. The adaptive determination method of the curved surface variational threshold according to claim 1, wherein The formula for calculating the surface variation value of each point cloud in step 1) is: Where, σ(p) is the surface variation value of the point cloud p; λ0, λ1, and λ2 are the three eigenvalues of the matrix C, and λ0 < λ1 < λ2; the k-nearest neighbor point set of the point cloud p is P = {p i (x i ,y i ,z i )|i = 1, 2…, k}, then the matrix C is the covariance matrix of the point cloud p and is: where k is the number of nearest neighbors, is the average coordinate of the k nearest neighbors.

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