Method and system for evaluating point cloud uniformity based on Radial fitting

Abstract

The invention relates to the technical field of point cloud data processing, in particular to a method and system for evaluating point cloud uniformity based on Radial fitting, a universal point cloud uniformity discrimination model is established through the Radial fitting technology, and the uniformity of the point cloud can be accurately quantified. Compared with the traditional method, the method not only has the characteristics of high efficiency and accuracy, but also can adapt to various complicated point cloud data types. Through the method, the point cloud uniformity can be accurately evaluated. Meanwhile, the method provides a reliable means for the basic evaluation of the point cloud data, facilitates the optimization of the manufacturing process of a digital point cloud model acquisition instrument, and accurately evaluates the quality of the model, thereby promoting the wide application and further development of the digital technology in various fields.

Description

Technical Field

[0001] The present invention relates to the technical field of point cloud data processing, and particularly relates to a method and system for evaluating the uniformity of point clouds based on Rational fitting. Background Art

[0002] With the rapid development of the digital age, point cloud data, as an important three-dimensional information carrier, has played a crucial role in multiple fields such as manufacturing, construction, autonomous driving, and robot navigation. Whether it is the acquisition of digital point cloud models in manufacturing, three-dimensional reconstruction in construction, or in cutting-edge technology fields such as autonomous driving and robot navigation, point cloud data plays an indispensable role. However, the quality of point cloud data directly affects the effect and accuracy of its subsequent applications. As one of the key factors for evaluating the quality of point cloud data, the uniformity of point clouds is of great significance in ensuring the accuracy and reliability of digital models. Uniform point cloud data can ensure that the density and accuracy of the model are consistent in all directions, thus avoiding problems such as data loss and error accumulation in subsequent processing.

[0003] Currently, traditional methods for evaluating point cloud uniformity usually rely on manual visual inspection or simple statistical analysis. These methods are not only time-consuming and laborious, but also difficult to accurately quantify the uniformity of point clouds, and there are large subjectivity and limitations. Therefore, there is an urgent need for an efficient and accurate method for evaluating point cloud uniformity to meet the needs of the digital age. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to propose a method and system for evaluating the uniformity of point clouds based on Rational fitting to solve the problem of large subjectivity and limitations existing in existing methods.

[0005] Based on the above purpose, the present invention provides a method for evaluating the uniformity of point clouds based on Rational fitting, including the following steps:

[0006] S1. Use the Monte Carlo method to simulate a two-dimensional plane model, randomly generate point clouds on the model surface, divide the plane into multiple small squares, and generate multiple groups of simulation models;

[0007] S2. Select the square at the center of the model, count the number and positions of all point clouds within the square, repeatedly calculate for P simulation models with n points each, obtain the distance deviation between the mean position of all point clouds and the geometric centroid in each group of models, and calculate its average value. Use the Rational method to fit the number of points n and the distance deviation to obtain a point cloud uniformity discrimination model;

[0008] S3. Expand the point cloud uniformity discrimination model from the small grid range to the large plane area, and calculate the general point cloud uniformity discrimination model through the corresponding relationship between the small grid and the large plane;

[0009] S4. Obtain the two-dimensional plane point cloud data of the target workpiece, perform local division within the two-dimensional plane area, count the number of points and their positions in different domain planes, calculate the average value of the distance deviation of each point from the geometric centroid, substitute it into the general point cloud uniformity discrimination model, and obtain the corresponding number of points n to evaluate the uniformity of the point cloud on different domain planes.

[0010] Preferably, in step S1, the plane is divided into multiple small grids so that the number of points n in each grid is the same and n is not zero.

[0011] Preferably, in step S2, repeat the calculation for P simulation models with n points each, where P ≥ 500000.

[0012] Preferably, after step S2, the method further includes:

[0013] Use R 2 and the adjusted R 2 and the RMSE index to verify the fitting effect.

[0014] Preferably, using R 2 and the adjusted R 2 and the RMSE index to verify the fitting effect includes:

[0015] Calculate the sum of squared residuals, that is, the sum of the squares of the differences between the model prediction values and the actual values;

[0016] Calculate the total sum of squares, that is, the sum of the squares of the differences between the actual values and their mean values;

[0017] Use the sum of squared residuals and the total sum of squares to calculate R 2 ;

[0018] Consider the number of variables in the model to calculate the adjusted R 2 ;

[0019] Use the prediction values and actual values of the model to calculate RMSE.

[0020] The present invention also provides a system for evaluating point cloud uniformity based on Rational fitting, including:

[0021] A data simulation module that simulates a two-dimensional plane model using the Monte Carlo method, randomly generates point clouds on the model surface, divides the plane into multiple small grids, and generates multiple groups of simulation models;

[0022] The point cloud uniformity discrimination model generation module is used to select the grid at the center of the model, count the quantity and positions of all point clouds within the grid, repeatedly calculate P simulation models each with n points, obtain the distance deviation between the mean position of all point clouds and the geometric centroid in each group of models, calculate its average value, and use the Rational method to fit the number of points n and the distance deviation to obtain the point cloud uniformity discrimination model;

[0023] The general-purpose point cloud uniformity discrimination model generation module is used to expand the point cloud uniformity discrimination model from the small grid range to the large plane area, and calculate the general-purpose point cloud uniformity discrimination model through the corresponding relationship between the small grid and the large plane;

[0024] The evaluation module is used to obtain the two-dimensional plane point cloud data of the target workpiece, perform local division within the two-dimensional plane area, count the number of points and their positions in different domain planes, calculate the average value of the distance deviation of each point from the geometric centroid, substitute it into the general-purpose point cloud uniformity discrimination model, obtain the corresponding number of points n, and evaluate the uniformity degree of the point cloud on different domain planes.

[0025] Advantages of the present invention:

[0026] 1. Compared with the prior art, the present invention creatively proposes a method for evaluating point cloud uniformity based on Rational fitting, realizing the data simulation of the centroid offset in the two-dimensional plane, the grid division, the generation method of the point cloud uniformity discrimination model, the general-purpose point cloud uniformity discrimination model, and the evaluation method of point cloud uniformity.

[0027] 2. This method not only has the characteristics of high efficiency and accuracy, but also can be applied to processing various complex point cloud data, laying a necessary technical foundation for the development of the digital age.

[0028] 3. Through the application of this method, the optimization of the manufacturing of digital point cloud model acquisition instruments and the accurate evaluation of the quality of the acquired models can be realized, thus promoting the wide application and development of digital technology in various fields. Description of the Drawings

[0029] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings in the following description are only those of the present invention. For those of ordinary skill in the art, other drawings can also be obtained based on these drawings without creative efforts.

[0030] Figure 1 It is the flowchart of the method for evaluating point cloud uniformity based on Rational fitting according to the embodiment of the present invention;

[0031] Figure 2 Schematic diagram of grid division according to an embodiment of the present invention;

[0032] Figure 3 Schematic diagram of grid coordinate representation according to an embodiment of the present invention;

[0033] Figure 4 Schematic diagram of the generation method of a general point cloud uniformity discrimination model according to an embodiment of the present invention;

[0034] Figure 5 Schematic diagram of the correspondence between small grids and large planes according to an embodiment of the present invention. Detailed implementation manners

[0035] To make the objectives, technical solutions, and advantages of the present invention clearer and more understandable, the present invention will be further described in detail below in conjunction with specific embodiments.

[0036] It should be noted that unless otherwise defined, the technical terms or scientific terms used in the present invention should have the ordinary meanings understood by those of ordinary skill in the field to which the present invention belongs. The "first", "second" and similar terms used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. The terms such as "comprising" or "including" mean that the elements or objects appearing before this word cover the elements or objects listed after this word and their equivalents, without excluding other elements or objects. The terms such as "connected" or "coupled" are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. The terms such as "upper", "lower", "left", "right" are only used to represent relative positional relationships, and when the absolute position of the object being described changes, the relative positional relationship may also change accordingly.

[0037] An embodiment of the present invention provides a method for evaluating the uniformity of a point cloud based on Rational fitting, and its specific steps are as Figure 1 shown.

[0038] In terms of steps, this method consists of four parts: data simulation and grid division of two-dimensional plane centroid offset, point cloud uniformity discrimination model, generation method of a general point cloud uniformity discrimination model, and evaluation method of point cloud uniformity:

[0039] Data simulation of the centroid offset in the two-dimensional plane and grid division: Since the acquisition of actual measurement points has a certain randomness and the point cloud distribution is not completely uniform, the Monte Carlo method is used to simulate the two-dimensional plane model, and point clouds are randomly generated on the model surface. Considering that the point clouds of small industrial parts are simulated, the point clouds are arranged densely within a small size. By dividing the plane into multiple small grids, it is required that the number of points n in each grid is basically the same and n is not zero. Using the number of points in the grid as an index for model establishment, multiple groups of simulation models are generated for subsequent analysis.

[0040] Point cloud uniformity discrimination model: Select the grid at the center of the model, and count the quantity and positions of all point clouds in the grid. Repeat the calculation for P (P≥500000) simulation models with n points each, calculate the distance deviation between the mean value of all point cloud positions and the geometric centroid in each group of models, and calculate its average value. Use the Rational method to fit the number of points n and the distance deviation, and use R 2 , the adjusted R 2 and the RMSE index to verify the fitting effect. R 2 represents the coefficient of squared residuals, and RMSE is the root mean square error.

[0041] Generation method of the general point cloud uniformity discrimination model: For the locally uniform model, the point cloud uniformity discrimination model can be extended from the small grid range to the large plane area to improve the generality of the model. By studying the corresponding relationship between the small grid and the large plane and deriving its mathematical expression, the general point cloud uniformity discrimination model is obtained.

[0042] Evaluation method of point cloud uniformity: Conduct local division in the plane area with unknown uniformity, count the number of points and their positions in different domain planes, and calculate the average value of the distance deviation of each point from the geometric centroid. Substitute this value into the general point cloud uniformity discrimination model to obtain the corresponding number of points n, that is, the uniformity of this plane is equivalent to n points randomly distributed within the area of the small grid. Through this method, the uniformity of point clouds on different domain planes can be intuitively evaluated.

[0043] Example 1:

[0044] 1. Data simulation of the centroid offset in the two-dimensional plane and grid division, including the following steps:

[0045] 1) Design and use the Monte Carlo method to simulate the two-dimensional plane model, set the model size range X0×Y0, and randomly generate point clouds on the model surface. The coordinates of a certain point in the random point cloud can be expressed as (X I , Y I ):

[0046]

[0047] Where:

[0048] rand() - A random function that returns a uniformly distributed random real number in the range from 0 to 1.

[0049] I - Represents the number of generated points, where I = 1, 2, …, N.

[0050] 2) Based on the 2D planar point cloud model generated in step 1), perform planar division design. Divide the plane into small squares with an area of x0×y0 to facilitate the counting of points within the squares and the subsequent reading of the position data of the point cloud, and to improve the calculation efficiency. Refer to Figure 2 as shown.

[0051] 3) Observe the small - side - length squares obtained in step 2). It is required that the number of points in each grid is as uniform as possible and non - zero. Otherwise, the side - length of the square should be re - selected for division. Each square area has a random distribution of points, and has the following relationship with the total number of points N:

[0052]

[0053] 4) Based on the processing steps 1) to 3), generate a series of point cloud models, including the number of points in the squares ranging from 1 to 10000. Group the models with the same number of points as the same group. At least 500000 groups with the same number of points are generated for experiments to reduce randomness and improve the credibility of subsequent model fitting.

[0054] 2. Point cloud uniformity discrimination model, including the following steps:

[0055] 1) Conduct data research on the small squares divided in the 2D planar point cloud model, and count the number and position coordinates of all the point clouds within the squares. Place the small square on the xoy axis, with x0 on the x - axis and y0 on the y - axis. The point coordinates within the square are represented as (x i , y i ), refer to Figure 3 as shown.

[0056] 2) Calculate the geometric centroid coordinates of the small square, which can be expressed as:

[0057]

[0058] where:

[0059] x0 - The length of the small square. For small workpieces, it is generally less than 1 mm;

[0060] y0 - The width of the small square. For small workpieces, it is generally less than 1 mm.

[0061] 3) Based on 1) and 2), calculate the distance from each point within the square to the geometric centroid of the small square, and obtain the average distance deviation. The calculation formula is as follows:

[0062]

[0063] Consider setting the model size range as X0×Y0, which is divided into small squares. Therefore, the calculation formula for the average distance deviation of the model is:

[0064]

[0065] Where:

[0066] K——The number of small squares,

[0067] Take the average of all results obtained from the same-point arrays, and finally obtain the average value corresponding to the number of points in each category.

[0068]

[0069] Where:

[0070] P——The number of models randomly generated under the condition of the same number of points.

[0071] 4) Based on the values obtained in 3), use the Rational method to fit the number of points n and the average distance deviation to obtain a point cloud uniformity discrimination model.

[0072] The representation form of the Rational fitting function is as follows:

[0073]

[0074] Where:

[0075] a0, a1,..., a α 、b0, b1,..., b β ——Coefficients to be determined.

[0076] 5) Based on the fitting formula obtained in 4), use R 2 、Adjusted R 2 and the RMSE index to verify the fitting effect.

[0077] First, calculate the sum of squared residuals (SSE), which is the sum of the squares of the differences between the model prediction values and the actual values; then calculate the total sum of squares (SST), which represents the sum of the squares of the differences between the actual values and their mean.

[0078]

[0079] Then, use SSE and SST to calculate R 2 ; Consider the number of variables in the model to calculate Adjusted R 2; Calculate the RMSE using the predicted value and the actual value of the model.

[0080]

[0081] Where:

[0082] n —— The number of observed values;

[0083] p —— The number of independent variables in the model.

[0084] 3. Generation of a general point cloud uniformity discrimination model, including the following steps:

[0085] 1) Roughly judge the uniformity of the plane and perform module division processing. For the local uniformity model, consider expanding the point cloud uniformity discrimination model from the small grid A 11 range to the large plane A area to improve the generality of the model and save computing resources. Refer to Figure 4 as shown.

[0086] 2) Observe the influence of the area size of the uniformity model on the average deviation, study the corresponding relationship between the small grid and the large plane, and combine the graph with the mathematical expression. Refer to Figure 5 as shown, and derive the general point cloud uniformity discrimination model.

[0087] To improve the generality of the model, study the point cloud generation error model of grids with different side lengths. When the side length of the grid is η mm, a 1 mm × 1 mm plane will be divided into multiple η mm × η mm small grids, and the number k s of small grids is:

[0088]

[0089] The original number of points n is relatively high and evenly distributed. The number of points N that each small grid should theoretically contain is:

[0090]

[0091] Therefore, if the local density of the model is uniform, the selection of the area range does not affect the uniformity determination of the model. The point cloud generation error model that can be used to evaluate the point cloud uniformity can be expressed as:

[0092] F(N) = f(n).

[0093] 4. Evaluation method for point cloud uniformity, including the following steps:

[0094] 1) There is a plane with unknown uniformity, such as the 2D plane of the point cloud data of a digital measuring tool. Consider performing uniformity analysis on it. Roughly observe the uniformity of the plane and perform a rough domain division, dividing it into plane A, plane B, plane C, etc.

[0095] 2) Based on the domain division in 1), count the number of points and their positions in different domain planes, and calculate the average value of the distance deviation |ΔT A |, |ΔT B |, |ΔT C |, etc., between each point in the same domain and the geometric centroid.

[0096] 3) Based on the average value of the distance deviation in each domain obtained in 2), substitute these values into the general point cloud uniformity discrimination model respectively to obtain the corresponding number of points n. That is, the uniformity of the plane is equivalent to n points randomly distributed within the area of the small grid x0×y0. Taking the uniformity discrimination of plane A as an example, the following derivation relationship is obtained:

[0097]

[0098] 4) Based on the equivalent number of points in different domains calculated in 3), judge the plane uniformity by comparing the number of points, and compare and evaluate its uniformity degree. That is, only by comparing the numerical values of n A , n B , n C , the uniformity of the plane can be evaluated and compared.

[0099] Those of ordinary skill in the art should understand that the discussion of any above embodiment is only exemplary, and is not intended to imply that the scope of the present invention is limited to these examples; under the concept of the present invention, the technical features in the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations in different aspects of the present invention as described above, which are not provided in detail for the sake of brevity. Any omission, modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A method for evaluating the uniformity of point clouds based on Rational fitting, characterized in that, The method includes the following steps: S1. Simulate a two-dimensional plane model using the Monte Carlo method, randomly generate point clouds on the model surface, divide the plane into multiple small squares, and generate multiple groups of simulation models; S2. Select the square at the center of the model, count the number and positions of all point clouds within the square, repeatedly calculate for P simulation models each with n points, obtain the distance deviation between the mean value of all point cloud positions and the geometric centroid in each group of models, calculate its average value, and use the Rational method to fit the number of points n and the distance deviation to obtain a point cloud uniformity discrimination model; S3. Expand the point cloud uniformity discrimination model from the small square range to the large plane area, and calculate a general point cloud uniformity discrimination model through the corresponding relationship between the small squares and the large plane; S4. Obtain the two-dimensional plane point cloud data of the target workpiece, perform local division within the two-dimensional plane area, count the number and positions of points in different domain planes, calculate the average value of the distance deviation of each point from the geometric centroid, substitute it into the general point cloud uniformity discrimination model, obtain the corresponding number of points n, and evaluate the uniformity degree of the point clouds on different domain planes.

2. The method for evaluating the uniformity of point cloud based on Rational fitting according to claim 1, wherein In step S1, the plane is divided into multiple small squares such that the number of points n in each square is the same and n is not zero.

3. The method for evaluating the uniformity of point cloud based on Rational fitting according to claim 1, wherein In step S2, the P simulation models each with n points are repeatedly calculated, where P≥500000.

4. The method for evaluating the uniformity of a point cloud based on Rational fitting according to claim 1, wherein After step S2, the method further includes: Using R 2 , the adjusted R 2 and the RMSE index are used to verify the fitting effect.

5. The method for evaluating the uniformity of point cloud based on Rational fitting according to claim 4, characterized in that The use of R 2 , the adjusted R 2 and the RMSE index to verify the fitting effect includes: Calculating the sum of squared residuals, that is, the sum of the squares of the differences between the model prediction values and the actual values; Calculating the total sum of squares, that is, the sum of the squares of the differences between the actual values and their mean values; Calculate R using the sum of squared residuals and the total sum of squares 2 ; Calculate the adjusted R considering the number of variables in the model 2 ; Using the prediction values and actual values of the model to calculate the RMSE.

6. A system for evaluating the uniformity of point clouds based on Rational fitting, characterized in that, Including: A data simulation module that simulates a two-dimensional plane model using the Monte Carlo method, randomly generates point clouds on the model surface, divides the plane into multiple small squares, and generates multiple groups of simulation models; A point cloud uniformity discrimination model generation module for selecting the square at the center of the model, counting the number and positions of all point clouds within the square, repeatedly calculating for P simulation models each with n points, obtaining the distance deviation between the mean value of all point cloud positions and the geometric centroid in each group of models, calculating its average value, and using the Rational method to fit the number of points n and the distance deviation to obtain a point cloud uniformity discrimination model; A general point cloud uniformity discrimination model generation module for expanding the point cloud uniformity discrimination model from the small square range to the large plane area and calculating a general point cloud uniformity discrimination model through the corresponding relationship between the small squares and the large plane; An evaluation module for obtaining the two-dimensional plane point cloud data of the target workpiece, performing local division within the two-dimensional plane area, counting the number and positions of points in different domain planes, calculating the average value of the distance deviation of each point from the geometric centroid, substituting it into the general point cloud uniformity discrimination model, obtaining the corresponding number of points n, and evaluating the uniformity degree of the point clouds on different domain planes.

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