Method and system for evaluating uniformity of point cloud based on rational fitting

Abstract

The present application relates to the technical field of point cloud data processing, in particular to a method and system for evaluating the uniformity of point cloud based on Rational fitting, which establishes a general point cloud uniformity discrimination model through Rational fitting technology, and can accurately quantify the uniformity of point cloud. Compared with traditional methods, this method not only has the characteristics of high efficiency and accuracy, but also can adapt to various complex point cloud data types. Through this method, accurate evaluation of the uniformity of point cloud can be realized. At the same time, this method provides a reliable means for the basic evaluation of point cloud data, which helps to optimize the manufacturing process of digital point cloud model acquisition instrument, accurately evaluate the model quality, and thus promote the wide application and further development of digital technology in various fields.

Description

Technical Field

[0001] This invention relates to the field of point cloud data processing technology, and in particular to a method and system for evaluating the uniformity of point clouds based on Rational fitting. Background Technology

[0002] With the rapid development of the digital age, point cloud data, as an important carrier of three-dimensional information, has played a crucial role in various fields such as manufacturing, construction, autonomous driving, and robot navigation. Whether it's acquiring digital point cloud models in manufacturing, 3D reconstruction in construction, or cutting-edge technologies like autonomous driving and robot navigation, point cloud data plays an indispensable role. However, the quality of point cloud data directly affects the effectiveness and accuracy of its subsequent applications. As one of the key factors in evaluating point cloud data quality, the uniformity of the point cloud is of great significance in ensuring the accuracy and reliability of the digital model. Uniform point cloud data ensures consistent density and accuracy in all directions, thereby avoiding problems such as data loss and error accumulation in subsequent processing.

[0003] Currently, traditional point cloud uniformity assessment methods typically rely on manual visual inspection or simple statistical analysis. These methods are not only time-consuming and labor-intensive, but also struggle to accurately quantify the uniformity of point clouds, and are subject to significant subjectivity and limitations. Therefore, there is an urgent need for an efficient and accurate point cloud uniformity assessment method to meet the demands of the digital age. Summary of the Invention

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

[0005] To achieve the above objectives, this invention provides a method for evaluating the uniformity of point clouds based on Rational fitting, comprising the following steps:

[0006] S1. Use the Monte Carlo method to simulate a two-dimensional plane model. Randomly generate point clouds on the surface of the model, divide the plane into multiple small squares, and make the number of points n in each square consistent and n is not zero, and generate multiple sets of simulation models.

[0007] S2. Count the number and location of all point clouds within the grid. Repeat the calculation for the simulation model with P points, each with n points. Calculate the distance from each point in each small grid to the geometric centroid of the small grid in each simulation model, and obtain the average distance deviation. Then, the average distance deviation of all small squares in each simulation model group is calculated. average As the average distance deviation of the model, the average of all results obtained from the same set of points is finally calculated to obtain the average distance deviation corresponding to the number of points in each class. The Rational method was used to compare the number of points n with the average distance deviation. By fitting the model, a point cloud uniformity discrimination model is obtained.

[0008] S3. Extend the point cloud uniformity discrimination model from the small square range to the large plane region. Calculate the general point cloud uniformity discrimination model by the correspondence between the small square and the large plane.

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

[0010] Preferably, in step S2, the simulation model with P points, each with the number of n, is repeatedly calculated, where P ≥ 500000.

[0011] Preferably, after step S2, the method further includes:

[0012] Using R 2 Adjusted R 2 The RMSE metric was used to verify the fit.

[0013] Preferably, R is used. 2 Adjusted R 2 The RMSE metric was used to validate the fit, including:

[0014] Calculate the residual sum of squares, which is the sum of squares of the differences between the model's predicted values ​​and the actual values;

[0015] Calculate the total sum of squares, which is the sum of the squares of the differences between the actual values ​​and their mean.

[0016] Calculate R using the sum of squared residuals and the sum of squares. 2 ;

[0017] Calculate the adjusted R based on the number of variables in the model. 2 ;

[0018] The RMSE is calculated using the model's predicted values ​​and the actual values.

[0019] The present invention also provides a system for evaluating the uniformity of point clouds based on Rational fitting, comprising:

[0020] The data simulation module uses the Monte Carlo method to simulate a two-dimensional plane model. It randomly generates point clouds on the surface of the model, divides the plane into multiple small squares, and generates multiple sets of simulation models.

[0021] The point cloud uniformity discrimination model generation module is used to count the number and position of all points in the grid. It repeatedly calculates the distance from each point in each small grid to the geometric centroid of that small grid in each simulation model, and then calculates the average distance deviation. Then, the average distance deviation of all small squares in each simulation model group is calculated. average As the average distance deviation of the model, the average of all results obtained from the same set of points is finally calculated to obtain the average distance deviation corresponding to the number of points in each class. The Rational method was used to compare the number of points n with the average distance deviation. By fitting the data, a point cloud uniformity discrimination model is obtained, where n refers to the number of points in each small square.

[0022] The general point cloud uniformity discrimination model generation module is used to extend the point cloud uniformity discrimination model from a small square range to a large planar region. By calculating the correspondence between the small squares and the large planar region, the general point cloud uniformity discrimination model is obtained.

[0023] The evaluation module is used to acquire two-dimensional planar point cloud data of the target workpiece, perform local division within the two-dimensional planar region, count the number of points and their positions in different areas of the plane, calculate the distance deviation between all points and the geometric centroid, calculate the average value, substitute it into a general point cloud uniformity discrimination model, obtain the corresponding number of points n, and evaluate the uniformity of the point cloud on different areas of the plane.

[0024] The beneficial effects of this invention are:

[0025] 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 and grid division of two-dimensional plane centroid offset, point cloud uniformity discrimination model, generation method of general point cloud uniformity discrimination model and point cloud uniformity evaluation method.

[0026] 2. This method is not only efficient and accurate, but also applicable to processing various complex point cloud data, laying the necessary technical foundation for the development of the digital age.

[0027] 3. By applying this method, the manufacturing of instruments for acquiring digital point cloud models can be optimized, and the quality of the acquired models can be accurately evaluated, thereby promoting the widespread application and development of digital technology in various fields. Attached Figure Description

[0028] To more clearly illustrate the technical solutions in this invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only for this invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0029] Figure 1 This is a flowchart of a method for evaluating point cloud uniformity based on Rational fitting according to an embodiment of the present invention.

[0030] Figure 2 This is a schematic diagram of grid division according to an embodiment of the present invention;

[0031] Figure 3 This is a grid coordinate representation diagram of an embodiment of the present invention;

[0032] Figure 4 This is a schematic diagram illustrating the generation method of the general point cloud uniformity discrimination model according to an embodiment of the present invention;

[0033] Figure 5 This is a diagram showing the correspondence between the small squares and the large plane in an embodiment of the present invention. Detailed Implementation

[0034] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0035] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0036] This invention provides a method for evaluating point cloud uniformity based on Rational fitting, the specific steps of which are as follows: Figure 1 As shown.

[0037] In terms of steps, this method consists of four parts: data simulation and grid division of two-dimensional planar centroid offset, point cloud uniformity discrimination model, generation method of general point cloud uniformity discrimination model, and point cloud uniformity evaluation method.

[0038] Simulation and grid division of 2D planar centroid offset data: Due to the inherent randomness in the acquisition of actual measurement points, the point cloud distribution is not entirely uniform. Therefore, the Monte Carlo method is used to simulate the 2D planar model, randomly generating point clouds on the model surface. Considering that the simulation is of a small industrial part's point cloud, the point cloud arrangement is relatively dense within a small size. The plane is divided into multiple small squares, requiring that the number of points n in each square be approximately the same and not zero. The number of points within each square is used as the model establishment index, generating multiple sets of simulation models for subsequent analysis.

[0039] Point cloud uniformity discrimination model: This model is used to count the number and location of all points within a grid. It iteratively calculates the distance from each point within each small grid to the geometric centroid of that grid in each simulation model, and then calculates the average distance deviation. Then, the average distance deviation of all small squares in each simulation model group is calculated. average As the average distance deviation of the model, the average of all results obtained from the same set of points is finally calculated to obtain the average distance deviation corresponding to the number of points in each class. The Rational method was used to compare the number of points n with the average distance deviation. To perform the fitting, use R. 2 Adjusted R 2 The RMSE metric was used to verify the fit. 2 denoted as the squared residual coefficient, RMSE is the root mean square error, where n refers to the number of points in each small square.

[0040] A method for generating a general point cloud uniformity discrimination model: For locally uniform models, the point cloud uniformity discrimination model can be extended from small square areas to large planar regions to improve the model's versatility. By studying the correspondence between small squares and large planes and deriving its mathematical expression, a general point cloud uniformity discrimination model is obtained.

[0041] A method for evaluating point cloud uniformity involves dividing the plane region into local sub-regions, counting the number of points and their positions within each sub-region, calculating the distance deviation between all points and the geometric centroid, and then averaging these deviations. This average value is then substituted into a general point cloud uniformity discrimination model to determine the corresponding number of points, n. This means the uniformity of the plane is equivalent to n points randomly distributed within a small grid area. This method provides a direct way to evaluate the uniformity of point clouds across different sub-regions.

[0042] Example 1:

[0043] 1. Data simulation and grid division of two-dimensional planar centroid offset, including the following steps:

[0044] 1) Design and use the Monte Carlo method to simulate a two-dimensional planar model, and set the model size range. A point cloud is randomly generated on the model surface. The coordinates of a point in the random point cloud can be represented as... :

[0045] ;

[0046] in:

[0047] — A random function that returns a uniformly distributed random real number in the interval between 0 and 1;

[0048] —Indicates the number of points generated. .

[0049] 2) Based on the two-dimensional planar point cloud model generated in step 1), perform planar partitioning design. Divide the plane into... The small square grid facilitates the counting of points within the square and the subsequent reading of point cloud position data, thus accelerating computational efficiency. (See also...) Figure 2 As shown.

[0050] 3) Observe the small-sided squares obtained in step 2). The number of dots in each square should be as evenly distributed as possible, and the number should not be zero. Otherwise, the squares should be re-divided using different side lengths. The area of ​​each square is randomly distributed. The number of points and the total number of points N have the following relationship:

[0051] ;

[0052] 4) Based on the processing steps 1) to 3), generate a series of point cloud models, including grids with 1 to 10,000 points. Models with the same number of points are grouped together. At least 500,000 groups with the same number of points are generated for testing to reduce randomness and improve the reliability of subsequent model fitting.

[0053] 2. Point cloud uniformity discrimination model, including the following steps:

[0054] 1) Conduct data analysis on the small squares obtained from the two-dimensional planar point cloud model, and count the number and position coordinates of all points within each square. Place the small squares... axis, lie in On the axis, lie in On the axis, the coordinates of the points in the grid are... This indicates that you should refer to [the relevant document / reference]. Figure 3 As shown.

[0055] 2) Calculate the geometric centroid coordinates of the small squares. The coordinates can be expressed as:

[0056] ;

[0057] in:

[0058] —The length of the small squares is for small workpieces and is generally less than 1 mm;

[0059] —Small grid width, for small workpieces, generally less than 1 mm.

[0060] 3) Based on 1) and 2), calculate the distance from all points within the grid to the geometric centroid of the smaller grid, and obtain the average distance deviation. The calculation formula is as follows:

[0061] ;

[0062] Consider setting the model size range Divided into The model consists of several small squares, therefore the average distance deviation is calculated as follows:

[0063] ;

[0064] in:

[0065] —Number of small squares .

[0066] The average value of all results obtained from the same point array is calculated to obtain the average value corresponding to the number of points in each class.

[0067] ;

[0068] in:

[0069] — The number of models randomly generated under the same point count conditions.

[0070] 4) Based on the values ​​obtained in 3), the Rational method is used to fit the number of points n and the average distance deviation to obtain the point cloud uniformity discrimination model.

[0071] The Rational fitting function is represented as follows:

[0072] ;

[0073] in:

[0074] , — Coefficients to be determined.

[0075] 5) Based on the fitted equation obtained in 4), use R... 2 Adjusted R 2 The RMSE metric was used to verify the fit.

[0076] First, calculate the residual sum of squares (SSE), which is the sum of squares of the differences between the model's predicted values ​​and the actual values; then calculate the total sum of squares (SST), which represents the sum of squares of the differences between the actual values ​​and their mean.

[0077] ;

[0078] Then, using SSE and SST, R is calculated. 2 ;Calculate Adjusted R-squared by considering the number of variables in the model. 2 The RMSE is calculated using the model's predicted and actual values.

[0079] ;

[0080] in:

[0081] —The number of observations;

[0082] — The number of independent variables in the model.

[0083] 3. Generation of a general point cloud uniformity discrimination model, including the following steps:

[0084] 1) Roughly assess the uniformity of the plane and perform module partitioning. For the local uniformity model, consider dividing the point cloud uniformity discrimination model into small squares. The range is extended to a large plane. Regions are used to improve the model's generality and save computational resources. See also Figure 4 As shown.

[0085] 2) Observe the influence of the area size of the uniform model on the average deviation, study the correspondence between small squares and large planes, and combine graphs with mathematical expressions, referring to... Figure 5 As shown, a general point cloud uniformity discrimination model is derived.

[0086] To improve the model's versatility, a point cloud generation error model for grids with different side lengths is studied. When the grid side length is... At that time, one The plane will be divided into multiple Small squares, number of small squares for:

[0087] ;

[0088] Original points The points are relatively high and evenly distributed; theoretically, each small square should contain a certain number of points. for:

[0089] ;

[0090] Therefore, if the local density of the model is uniform, the selection of the region area does not affect the uniformity determination of the model. A point cloud generation error model that can be used to evaluate point cloud uniformity can be expressed as:

[0091] .

[0092] 4. The method for evaluating the uniformity of point clouds includes the following steps:

[0093] 1) Given a plane with unknown homogeneity, such as a two-dimensional plane representing point cloud data of a digital measuring instrument, consider performing a homogeneity analysis. Roughly observe the homogeneity of the plane and divide it into approximate regions, such as plane A, plane B, and plane C.

[0094] 2) Based on the domain division in 1), count the number of points and their positions in the plane of different domains, and calculate the average distance deviation between each point in the same domain and the geometric centroid. , , wait.

[0095] 3) Based on the average distance deviation obtained in 2), the values ​​are substituted into the general point cloud uniformity discrimination model to obtain the corresponding number of points n. That is, the uniformity of the plane is equivalent to n points randomly distributed in small squares. Within an area. Taking the uniformity criterion of plane A as an example, the following derivation relationship is obtained:

[0096]

[0097] 4) Based on the equivalent point counts in different domains calculated in 3), the plane uniformity is judged by comparing the point counts, and the degree of uniformity is compared and evaluated. That is, it only requires... , , The magnitude of the value can be used to evaluate and compare the uniformity of the plane.

[0098] Those skilled in the art should understand that the discussion of any of the above embodiments is merely exemplary and is not intended to imply that the scope of the invention is limited to these examples; within the framework of the invention, the technical features of the above embodiments or different embodiments can also be combined, the steps can be implemented in any order, and there are many other variations of the different aspects of the invention as described above, which are not provided in detail for the sake of brevity. Any omissions, modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of protection of the 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. Use the Monte Carlo method to simulate a two-dimensional plane model. Randomly generate point clouds on the surface of the model, divide the plane into multiple small squares, and make the number of points n in each square consistent and n is not zero, and generate multiple sets of simulation models. S2. Count the number and location of all point clouds within the grid. Repeat the calculation for the simulation model with P points, each with n points. Calculate the distance from each point in each small grid to the geometric centroid of the small grid in each simulation model, and obtain the average distance deviation. Then, the average distance deviation of all small squares in each simulation model group is calculated. average As the average distance deviation of the model, the average of all results obtained from the same set of points is finally calculated to obtain the average distance deviation corresponding to the number of points in each class. The Rational method was used to compare the number of points n with the average distance deviation. By fitting the model, a point cloud uniformity discrimination model is obtained. S3. Extend the point cloud uniformity discrimination model from the small square range to the large plane region. Calculate the general point cloud uniformity discrimination model by the correspondence between the small square and the large plane. S4. Obtain the two-dimensional planar point cloud data of the target workpiece, perform local division within the two-dimensional planar region, count the number of points and their positions in different areas of the plane, calculate the distance deviation between all points and the geometric centroid, calculate the average value, substitute it into the general point cloud uniformity discrimination model, obtain the corresponding number of points n, and evaluate the uniformity of the point cloud on different areas of the plane.

2. The method for evaluating point cloud uniformity based on Rational fitting according to claim 1, characterized in that, In step S2, at least 500,000 sets of the same point array should be selected for calculation.

3. The method for evaluating point cloud uniformity based on Rational fitting according to claim 1, characterized in that, After step S2, the method further includes: Using R 2 Adjusted R 2 The RMSE metric was used to verify the fit.

4. The method for evaluating point cloud uniformity based on Rational fitting according to claim 3, characterized in that, The use of R 2 Adjusted R 2 The RMSE metric was used to validate the fit, including: Calculate the residual sum of squares, which is the sum of squares of the differences between the model's predicted values ​​and the actual values; Calculate the total sum of squares, which is the sum of the squares of the differences between the actual values ​​and their mean. Calculate R using the sum of squared residuals and the sum of squares. 2 ; Calculate the adjusted R based on the number of variables in the model. 2 ; The RMSE is calculated using the model's predicted values ​​and the actual values.

5. A system for evaluating the uniformity of point clouds based on Rational fitting, characterized in that, include: The data simulation module uses the Monte Carlo method to simulate a two-dimensional plane model. It randomly generates point clouds on the surface of the model, divides the plane into multiple small squares, and generates multiple sets of simulation models. The point cloud uniformity discrimination model generation module is used to count the number and position of all points in the grid. It repeatedly calculates the distance from each point in each small square to the geometric centroid of the small square in each simulation model, and calculates the average distance deviation. Then, the average distance deviation of all small squares in each simulation model group is calculated. average As the average distance deviation of the model, the average of all results obtained from the same set of points is finally calculated to obtain the average distance deviation corresponding to the number of points in each class. The Rational method was used to compare the number of points n with the average distance deviation. By fitting the data, a point cloud uniformity discrimination model is obtained, where n refers to the number of points in each small square. The general point cloud uniformity discrimination model generation module is used to extend the point cloud uniformity discrimination model from a small square range to a large planar region. By calculating the correspondence between the small squares and the large planar region, the general point cloud uniformity discrimination model is obtained. The evaluation module is used to acquire two-dimensional planar point cloud data of the target workpiece, perform local division within the two-dimensional planar region, count the number of points and their positions in different areas of the plane, calculate the distance deviation between all points and the geometric centroid, calculate the average value, substitute it into a general point cloud uniformity discrimination model, obtain the corresponding number of points n, and evaluate the uniformity of the point cloud on different areas of the plane.

Images