Additive manufacturing quality inspection system and method based on thermal imaging

Abstract

The present invention discloses an additive manufacturing quality inspection system and method based on thermal imaging. The present invention relates to the field of image processing technology, and solves the problems of low detection accuracy and real-time performance in the existing additive manufacturing quality inspection field. The additive manufacturing quality inspection system based on thermal imaging of the present invention includes: a model printing module, a data acquisition module, a data processing module and a data comparison module; the model printing module includes a powder spreading rod, a powder feeding bin, a molding bin, a platform and a scanning galvanometer; the present invention can evaluate the quality of each printing layer in real time and comprehensively, improve the inspection quality and printing efficiency, and realize real-time detection of printing quality in the additive manufacturing process.

Description

Technical Field

[0001] The present invention relates to the field of image processing technology, and in particular to an additive manufacturing quality detection system and method based on thermal imaging. Background Art

[0002] Additive manufacturing is a technology that uses material integration to create complex three-dimensional objects. This technology has been widely used in manufacturing, medical, and construction industries. Although additive manufacturing technology has made significant progress, it still faces challenges in ensuring the printing quality of additive manufacturing. At present, additive manufacturing quality inspection mainly relies on manual inspection, visual inspection, and contact measurement. Although these technologies can achieve additive manufacturing quality inspection, these methods lack real-time performance in the additive manufacturing quality inspection process. Quality control and process adjustment of the printing process are the key to ensuring the quality of additive manufacturing workpieces.

[0003] Thermal imaging, also known as long-wave infrared imaging, is a method of forming an image by detecting infrared radiation emitted by an object. Its working principle is to use the principle that objects above absolute zero will radiate infrared radiation, and these infrared radiations are captured by infrared detectors and converted into electrical signals. After processing, these electrical signals are converted into visual thermal images, in which different colors or grayscales represent different temperature levels.

[0004] Although the analysis of thermal imaging images during the printing process can provide temperature information during the printing process, such as the scanning trajectory of the laser, the melting area of ​​the powder, etc., thermal imagers mainly focus on the detection of temperature anomalies, but lack a comprehensive analysis of the printed layer shape. At the same time, the existing thermal imaging system cannot fully utilize the temperature distribution information of the thermal imaging image to effectively analyze and compare with the additive manufacturing model, ignoring the possibility of in-depth analysis of the printing quality through the combination of thermal imaging images and point cloud data, and cannot directly convert the thermal imaging data into an accurate description of the geometric shape of the printed part, thus affecting the comprehensiveness and accuracy of the detection. Summary of the invention

[0005] The present invention provides an additive manufacturing quality inspection system and method based on thermal imaging to solve the problems of low inspection accuracy and real-time performance in the existing additive manufacturing quality inspection field.

[0006] In a first aspect, the present invention provides an additive manufacturing quality inspection system based on thermal imaging, comprising: a model printing module, a data acquisition module, a data processing module and a data comparison module;

[0007] The model printing module includes a powder spreading rod, a powder feeding bin, a molding bin, a platform and a scanning galvanometer; the powder feeding bin and the molding bin are arranged on both sides below the platform, the powder spreading rod is arranged above the platform, and the scanning galvanometer is located above the platform; the data acquisition module includes a photoelectric switch sensor, a microcontroller and a thermal imaging camera; the photoelectric switch sensor and the thermal imaging camera are arranged above the platform; the data processing module and the data comparison module are respectively used to complete data processing and data comparison on an industrial computer, the photoelectric switch sensor and the thermal imaging camera are connected to the microcontroller, and the microcontroller is connected to the industrial computer;

[0008] The powder delivery bin is used to deliver printing powder to the platform;

[0009] The powder spreading rod is used to evenly spread the printing powder on the platform to form a powder layer;

[0010] The molding chamber is a manufacturing chamber for additively manufactured workpieces. The printing powder in the powder feeding chamber is transported to the molding chamber under the drive of the powder spreading rod. In the molding chamber, the printing powder is melted and bonded together under the heating of the laser beam to form an additively manufactured model.

[0011] The scanning galvanometer is located above the molding chamber and is used to emit laser light. The laser light scans the powder layer in the molding chamber according to the path of the slice data, so that the printing powder is partially melted and solidified to form an additive manufacturing model.

[0012] The photoelectric switch sensor is used to send a signal to the microcontroller after detecting that a layer is printed;

[0013] The industrial computer is used to send a shooting instruction to the thermal imaging camera after receiving the signal, so as to shoot a thermal imaging image of the layer of the additive manufacturing model; perform binarization processing and edge extraction processing on the thermal imaging image through a data processing module, discretize the contour of the thermal imaging image, and generate point cloud data of the thermal imaging image; compare the point cloud data of the slice layer image of additive manufacturing and the thermal imaging image through a data comparison module, calculate the distance between discrete points in the two sets of point cloud data, and judge that the distance is less than or equal to a preset threshold; if the distance is less than or equal to the preset threshold, it is judged that the printing quality is qualified; if the distance is greater than the preset threshold, it is judged that the printing quality is unqualified.

[0014] In a second aspect, the present invention provides an additive manufacturing quality inspection method based on thermal imaging, comprising:

[0015] Acquire a thermal imaging image of the additive manufacturing model, wherein after the scanning galvanometer prints a layer of printing powder, the photoelectric switch sensor sends a signal to the microcontroller; after receiving the signal, the industrial computer sends a shooting instruction to the thermal imaging camera to shoot a thermal imaging image of the layer of the additive manufacturing model;

[0016] Performing binarization and edge extraction processing on the thermal imaging image, discretizing the contour of the thermal imaging image, and generating point cloud data of the thermal imaging image;

[0017] Compare the point cloud data of the additively manufactured slice layer image and the thermal imaging image, calculate the distance between discrete points in the two sets of point cloud data, and determine whether the distance is less than or equal to a preset threshold; if the distance is less than or equal to the preset threshold, determine that the printing quality is qualified; if the distance is greater than the preset threshold, determine that the printing quality is unqualified.

[0018] Furthermore, the binarization process includes:

[0019] The pixel threshold is compared with all pixel values ​​of the thermal imaging image. When the pixel value of a certain point is greater than the pixel threshold, the pixel value of the point is set to white; when the pixel value of a certain point is less than the pixel threshold, the pixel value of the point is set to black; the value range of the pixel threshold is 0 to 255.

[0020] Furthermore, the edge extraction process includes:

[0021] The brightness value change rate is regarded as the gradient value, and two 3x3 convolution kernels are used to perform convolution kernel operations on the binary thermal imaging image. The operation methods include:

[0022] Use a 3x3 convolution kernel in the horizontal direction , 3x3 convolution kernel in the vertical direction Traverse the corresponding area in the image;

[0023] The horizontal direction G is obtained by calculating the weighted sum between pixels. x , vertical direction G y The convolution calculation result of ;

[0024] Calculate the gradient value G using the gradient calculation formula:

[0025] ;

[0026] Points whose gradient value G change rate is greater than a preset change rate threshold are extracted as edge contours of the thermal imaging image, and the contours of the thermal imaging image are discretized to generate point cloud data of the thermal imaging image.

[0027] Furthermore, the point cloud data of the additively manufactured slice layer image and the thermal imaging image are compared to obtain the distance between the discrete points in the two sets of point cloud data, including:

[0028] Export the STL file of the additive manufacturing model. The structure of the exported STL model is composed of several triangular facets. When there is a section P with an intersection within the range of any triangular facet, it is considered that the section P is located in a layer of the STL additive manufacturing, and the intersection of the section P and the STL model is recorded as the coordinate (i, j), and all values ​​of (i, j) are recorded as the point cloud data of the slice layer.

[0029] The point cloud data of the thermal imaging image and slice layer image of the additive manufacturing model are regarded as two discrete irregular point sets P = {p1, p2, ..., p m} and Q={q1,q2,...,q n}, where p1, p2, ..., p m Indicates that there are m points in the point set P, and the subscripts 1 to m are the sequence numbers of the points; q1, q2, ..., q n Indicates that there are n points in the point set Q, and the subscripts 1 to n are the sequence numbers of the points; for each point p in the point set P i , calculate its distance to all points in the point set Q, and take the minimum value d among all distances i Q ;

[0030] ;

[0031] In the formula ;

[0032] In the formula, p i represents a point in the point set P; q j represents a point in the point set Q;

[0033] x i ,y i 、z i Respectively represent point p i The xyz coordinates, x j ,y j 、z j Respectively represent point q j The xyz coordinates of

[0034] Similarly, for each point q in the point set Q j , calculate its distance to all points in the point set P, and take the minimum value d j P ;

[0035] ;

[0036] In the formula ;

[0037] Define the average value Ave(P,Q) of the minimum distance between two sets of points;

[0038] ;

[0039] The value of Ave(P,Q) determines the similarity between two point clouds P and Q. The smaller the value of Ave(P,Q), the more similar the point clouds are.

[0040] The present invention has the following beneficial effects: The present invention provides an additive manufacturing quality detection system and method based on thermal imaging, which realizes automated high-precision detection by integrating a photoelectric switch sensor, a thermal imaging camera and an additive manufacturing machine into a unified detection system. The system can not only acquire thermal imaging images in real time, but also generate point cloud data of thermal imaging images through binarization processing and edge detection algorithms, and accurately compare these data with the point cloud data of the slice layer image of the additive manufacturing model. The uniqueness of this system is that by combining thermal imaging technology with geometric analysis of point cloud data, it can evaluate the quality of each printed layer in real time and comprehensively, significantly improving the detection quality and printing efficiency, and realizing real-time detection of printing quality in the additive manufacturing process. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] In order to more clearly illustrate the technical solution of the present invention, the drawings required for use in the embodiments are briefly introduced below. Obviously, for ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0042] Figure 1 Schematic diagram of the additive manufacturing quality inspection system based on thermal imaging;

[0043] Figure 2 A binary image of the thermal imaging image of the additive manufacturing model;

[0044] Figure 3 A schematic diagram of the process of traversing the corresponding area in the image using a horizontal 3x3 convolution kernel;

[0045] Figure 4 A schematic diagram of the process of traversing the corresponding area in the image using a 3x3 convolution kernel in the vertical direction;

[0046] Figure 5 Schematic diagram of the process of obtaining slice layer point cloud data for additive manufacturing models;

[0047] Figure 6 An example of point cloud data obtained from slice layer images of an additive manufacturing model.

[0048] Illustration: 1-photoelectric switch sensor; 2-powder spreading rod; 3-powder feeding bin; 4-molding bin; 5-platform; 6-industrial computer; 7-microcontroller; 8-scanning galvanometer; 9-thermal imaging camera. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described in conjunction with the specific embodiments of the present invention and the corresponding drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. The technical solutions provided by the embodiments of the present invention are described in detail below in conjunction with the drawings.

[0050] See also Figures 1 to 6 An embodiment of the present invention provides an additive manufacturing quality inspection system based on thermal imaging, including: a model printing module, a data acquisition module, a data processing module and a data comparison module.

[0051] The model printing module includes a powder spreading rod 2, a powder feeding bin 3, a molding bin 4, a platform 5 and a scanning galvanometer 8; the powder feeding bin 3 and the molding bin 4 are arranged on both sides below the platform 5, the powder spreading rod 2 is arranged above the platform 5, and the scanning galvanometer 8 is located above the platform 5. The data acquisition module includes a photoelectric switch sensor 1, a microcontroller 7 and a thermal imaging camera 9; the photoelectric switch sensor 1 and the thermal imaging camera 9 are arranged above the platform 5. The data processing module and the data comparison module are respectively used to complete data processing and data comparison on the industrial computer 6, the photoelectric switch sensor 1 and the thermal imaging camera 9 are connected to the microcontroller 7, and the microcontroller 7 is connected to the industrial computer 6.

[0052] When the thermal imaging camera 9 does not affect the normal operation of the additive manufacturing machine, the thermal imaging camera 9 is installed directly above or in the vicinity of the additive manufacturing machine to ensure that the thermal imaging camera can completely cover the printing area of ​​the additive manufacturing machine. When the normal operation of the additive manufacturing machine and the thermal imaging camera 9 is not affected, the photoelectric switch sensor 1 is installed to ensure that the photoelectric switch sensor 1 can trigger the thermal imaging camera 9 to take a photo after the additive manufacturing model prints a layer. The thermal imaging camera 9 and the photoelectric switch sensor 1 are connected to the industrial computer 6 through the same microcontroller 7.

[0053] When the additive manufacturing machine starts working, the powder feeding bin 3 delivers the printing powder to the platform 5; the powder spreading rod 2 evenly spreads the printing powder on the platform 5 to form a powder layer; when printing starts, the molding bin 4 is the manufacturing chamber of the additive manufacturing workpiece, and the printing powder in the powder feeding bin 3 is transported to the molding bin 4 under the drive of the powder spreading rod 2. In the molding bin 4, the printing powder is melted and bonded together under the heating of the laser beam to form an additive manufacturing model; the scanning galvanometer 8 is located above the molding bin 4 and is used to emit laser. The laser scans the powder layer in the molding bin 4 according to the path of the slice data, so that the printing powder is partially melted and solidified to form an additive manufacturing model; the photoelectric switch sensor 1 sends a signal to the microcontroller 7 after detecting that a layer is printed; after receiving the signal, the industrial computer 6 sends a shooting instruction to the thermal imaging camera 9 to shoot a thermal imaging image of the layer of the additive manufacturing model.

[0054] The industrial computer 6 performs binarization and edge extraction processing on the thermal imaging image through the data processing module, discretizes the contour of the thermal imaging image, and generates point cloud data of the thermal imaging image; compares the slice layer image of additive manufacturing and the point cloud data of the thermal imaging image through the data comparison module, calculates the distance between the discrete points in the two sets of point cloud data, and determines whether the distance is less than or equal to a preset threshold; if the distance is less than or equal to the preset threshold, it is determined that the printing quality is qualified; if the distance is greater than the preset threshold, it is determined that the printing quality is unqualified.

[0055] Specifically, the data processing module is used to perform binarization processing on the thermal imaging image according to the following method:

[0056] The pixel threshold is compared with all pixel values ​​of the thermal imaging image. When the pixel value of a certain point is greater than the pixel threshold, the pixel value of the point is set to white; when the pixel value of a certain point is less than the pixel threshold, the pixel value of the point is set to black; the value range of the pixel threshold is 0 to 255.

[0057] The thermal imaging image acquired by the thermal imaging camera 9 and the industrial computer 6 of the present invention is a grayscale image of single-channel data, in which each grayscale pixel value represents a temperature value. For a binary image, each pixel point can be represented by the pixel coordinates of the point. Therefore, the data of the grayscale image can represent grayscale coordinates and pixel values. Set a suitable pixel threshold, and the value range of the pixel threshold parameter can be set to 0 to 255, preferably 20. The pixel threshold is compared with all the pixel values ​​of the thermal imaging image. When the pixel value of a certain point is greater than the threshold, the pixel of the point is set to white; when the pixel value of a certain point is less than the threshold, the pixel value is set to black. The specific results are as follows. Figure 2 shown.

[0058] The obtained black and white pixels are analyzed, because in the binary image, the edge contour is characterized by a large rate of change in brightness. Therefore, in the process of extracting the binary contour, the rate of change in brightness can be used as the gradient value, and two 3x3 convolution kernels can be used to perform convolution kernel operations on the binary thermal imaging image.

[0059] Specifically, the data processing module is used to perform edge extraction processing on the thermal imaging image according to the following method:

[0060] The brightness value change rate is regarded as the gradient value, and two 3x3 convolution kernels are used to perform convolution kernel operations on the binary thermal imaging image. The operation methods include:

[0061] Use a 3x3 convolution kernel in the horizontal direction , 3x3 convolution kernel in the vertical direction Traverse the corresponding regions in the image; for example, for the image , the horizontal and vertical convolution kernels traverse the corresponding areas in the image as follows Figure 3 and Figure 4 As shown in the figure, the bold black box in the convolution diagram represents the movement process of the convolution kernel during the traversal process. K Indicates the pixel values ​​corresponding to the horizontal and vertical coordinates in the image, for example: K 13 Represents the pixel value of the 3rd column in the 1st row. The horizontal direction G is obtained by calculating the weighted sum between pixels. x , vertical direction G y The convolution calculation result of ;

[0062] Calculate the gradient value G using the gradient calculation formula:

[0063] ;

[0064] The larger the gradient value G is, the more obvious the edge is. Therefore, points whose gradient value G change rate is greater than a preset change rate threshold are extracted as edge contours of the thermal imaging image. The contours of the thermal imaging image are discretized to generate point cloud data of the thermal imaging image.

[0065] Specifically, the data comparison module is used to compare the point cloud data of the slice layer image of additive manufacturing and the thermal imaging image according to the following method to calculate the distance between the discrete points in the two sets of point cloud data:

[0066] The STL file of the additive manufacturing model is exported through the industrial computer 6. The structure of the exported STL model is composed of a number of triangular facets; Figure 5 and Figure 6As shown, when there is a section P with an intersection point E in the atmosphere of any triangular face, the section P is considered to be located in a layer of STL additive manufacturing, and the intersection point E of the section P and the STL model is recorded as the coordinate (i, j), and all values ​​of (i, j) are recorded as the point cloud data of the slice layer;

[0067] The point cloud data of the thermal imaging image and slice layer image of the additive manufacturing model are regarded as two discrete irregular point sets P = {p1, p2, ..., p m} and Q={q1,q2,...,q n}, where p1, p2, ..., p m Indicates that there are m points in the point set P, and the subscripts 1 to m are the sequence numbers of the points; q1, q2, ..., q n Indicates that there are n points in the point set Q, and the subscripts 1 to n are the sequence numbers of the points; for each point p in the point set P i , calculate its distance to all points in the point set Q, and take the minimum value d among all distances i Q ;

[0068] ;

[0069] In the formula ;

[0070] In the formula, p i represents a point in the point set P; q j represents a point in the point set Q;

[0071] x i ,y i 、z i Respectively represent point p i The xyz coordinates, x j ,y j 、z j Respectively represent point q j The xyz coordinates of

[0072] Similarly, for each point q in the point set Q j , calculate its distance to all points in the point set P, and take the minimum value d j P ;

[0073] ;

[0074] In the formula ;

[0075] Define the average value Ave(P,Q) of the minimum distance between two sets of points;

[0076] ;

[0077] The value of Ave(P,Q) determines the similarity between two point clouds P and Q. The smaller the value of Ave(P,Q), the more similar the point clouds are.

[0078] Based on the above-mentioned additive manufacturing quality inspection system based on thermal imaging, an embodiment of the present invention further provides an additive manufacturing quality inspection method based on thermal imaging, including:

[0079] Acquire a thermal imaging image of the additive manufacturing model, wherein after the scanning galvanometer prints a layer of printing powder, the photoelectric switch sensor sends a signal to the microcontroller; after receiving the signal, the industrial computer sends a shooting instruction to the thermal imaging camera to shoot a thermal imaging image of the layer of the additive manufacturing model;

[0080] Perform binarization and edge extraction on the thermal imaging image, discretize the contour of the thermal imaging image, and generate point cloud data of the thermal imaging image;

[0081] Compare the point cloud data of the additively manufactured slice layer image and the thermal imaging image, calculate the distance between the discrete points in the two sets of point cloud data, and judge whether the distance is less than or equal to the preset threshold; if the distance is less than or equal to the preset threshold, the printing quality is judged to be qualified; if the distance is greater than the preset threshold, the printing quality is judged to be unqualified.

[0082] The embodiment of the present invention further provides a storage medium, in which a computer program is stored, and when the computer program is executed by a processor, some or all of the steps in each embodiment of the additive manufacturing quality inspection method based on thermal imaging provided by the present invention are implemented. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM) or a random access memory (RAM).

[0083] Those skilled in the art can clearly understand that the technology in the embodiments of the present invention can be implemented by means of software plus a necessary general hardware platform. Based on this understanding, the technical solution in the embodiments of the present invention can be essentially or partly contributed to the prior art in the form of a software product, which can be stored in a storage medium such as ROM / RAM, a magnetic disk, an optical disk, etc., and includes several instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in the various embodiments of the present invention or certain parts of the embodiments.

[0084] The above-described embodiments of the present invention do not limit the protection scope of the present invention.

Claims

1. An additive manufacturing quality inspection system based on thermal imaging, characterized in that: include: Model printing module, data acquisition module, data processing module and data comparison module; The model printing module comprises a powder spreading rod (2), a powder feeding bin (3), a molding bin (4), a platform (5) and a scanning galvanometer (8); the powder feeding bin (3) and the molding bin (4) are arranged on both sides below the platform (5), the powder spreading rod (2) is arranged above the platform (5), and the scanning galvanometer (8) is located above the platform (5); The data acquisition module comprises a photoelectric switch sensor (1), a microcontroller (7) and a thermal imaging camera (9); the photoelectric switch sensor (1) and the thermal imaging camera (9) are arranged above the platform (5); The data processing module and the data comparison module are used to complete data processing and data comparison on the industrial computer (6), respectively; the photoelectric switch sensor (1) and the thermal imaging camera (9) are connected to the microcontroller (7), and the microcontroller (7) is connected to the industrial computer (6); The powder delivery bin (3) is used to deliver printing powder to the platform (5); The powder spreading rod (2) is used to evenly spread the printing powder on the platform (5) to form a powder layer; The molding chamber (4) is a manufacturing chamber for additively manufactured workpieces. The printing powder in the powder feeding chamber (3) is transported to the molding chamber (4) under the drive of the powder spreading rod (2). In the molding chamber (4), the printing powder is melted and bonded together under the heating of the laser beam to form an additively manufactured model. The scanning galvanometer (8) is located above the molding chamber (4) and is used to emit laser light. The laser light scans the powder layer in the molding chamber (4) according to the path of the slice data, so that the printing powder is partially melted and solidified to form an additive manufacturing model. The photoelectric switch sensor (1) is used to send a signal to the microcontroller (7) after detecting that a layer has been printed; The industrial computer (6) is used to send a shooting instruction to the thermal imaging camera (9) after receiving the signal, so as to shoot a thermal imaging image of the layer of the additive manufacturing model; perform binarization processing and edge extraction processing on the thermal imaging image through a data processing module, discretize the contour of the thermal imaging image, and generate point cloud data of the thermal imaging image; compare the point cloud data of the slice layer image of the additive manufacturing and the thermal imaging image through a data comparison module, calculate the distance between the discrete points in the two sets of point cloud data, and judge that the distance is less than or equal to a preset threshold; If the distance is less than or equal to a preset threshold, the printing quality is determined to be qualified; If the distance is greater than a preset threshold, it is determined that the printing quality is unqualified; The binarization process comprises: Compare the pixel threshold with all pixel values ​​of the thermal imaging image. When the pixel value of a certain point is greater than the pixel threshold, the pixel value of the point is set to white; when the pixel value of a certain point is less than the pixel threshold, the pixel value of the point is set to black; the value range of the pixel threshold is 0 to 255; The edge extraction process comprises: The brightness value change rate is regarded as the gradient value, and two 3x3 convolution kernels are used to perform convolution kernel operations on the binary thermal imaging image. The operation methods include: Use a 3x3 convolution kernel in the horizontal direction 3x3 convolution kernel in the vertical direction Traverse the corresponding area in the image; The horizontal direction G is obtained by calculating the weighted sum between pixels. x , vertical direction G y The convolution calculation result of ; The gradient value G is calculated using the gradient calculation formula: Extracting points whose gradient values ​​G are greater than a preset change rate threshold as edge contours of the thermal imaging image, discretizing the contours of the thermal imaging image, and generating point cloud data of the thermal imaging image; Compare the point cloud data of the additive manufacturing slice layer image and the thermal imaging image, and find the distance between the discrete points in the two sets of point cloud data, including: Export the STL file of the additive manufacturing model, the structure of the exported STL model is composed of several triangular facets; when there is a section P with an intersection within the range of any triangular facet, it is considered that the section P is located in a layer of the STL additive manufacturing, and the intersection of the section P and the STL model is recorded as the coordinate (i, j), and all values ​​of (i, j) are recorded as the point cloud data of the slice layer; The point cloud data of the thermal imaging image and slice layer image of the additive manufacturing model are regarded as two discrete irregular point sets P = {p1, p2, ..., p m } and Q={q1,q2,...,q n }, where p1, p2, ..., p m Indicates that there are m points in the point set P, and the subscripts 1 to m are the sequence numbers of the points; q1, q2, ..., q n Indicates that there are n points in the point set Q, and the subscripts 1 to n are the sequence numbers of the points; for each point p in the point set P i , calculate its distance to all points in the point set Q, and take the minimum value d among all distances i Q ; In the formula In the formula, p i represents a point in the point set P; q j represents a point in the point set Q; x i ,y i 、z i Respectively represent point p i The xyz coordinates, x j ,y j 、z j Respectively represent point q j The xyz coordinates of Similarly, for each point q in the point set Q j , calculate its distance to all points in the point set P, and take the minimum value d j P ; In the formula Define the average value Ave(P,Q) of the minimum distance between two sets of points; The value of Ave(P,Q) determines the similarity between two point clouds P and Q. The smaller the value of Ave(P,Q), the more similar the point clouds are.

Images