CN116681750A - Self-adaptive point cloud curvature calculation method, device and storage medium thereof - Google Patents
Self-adaptive point cloud curvature calculation method, device and storage medium thereof Download PDFInfo
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Abstract
The application relates to the technical field of point cloud curvature characteristic calculation algorithms, in particular to a self-adaptive point cloud curvature calculation method, equipment and a storage medium thereof, wherein three-dimensional point cloud data are firstly input, then average point distances among the point clouds are obtained, then the method loss characteristics of the point clouds are obtained through the average point distances, then the principal curvature value of each point is calculated, finally the Gaussian curvature of the point is output, the average point distances with certain multiple of the point cloud data are used as KD-Tree search radii for calculating the normal vectors and the curvatures of the point clouds, the radius search is carried out on each point, the normal vectors and the principal curvatures of the point clouds are calculated by adopting a least square method, and the problems of long calculation time, inaccurate calculation results and the like caused by manually setting the KD-Tree search radii when the normal vectors and the curvatures are calculated are avoided; the method solves the problems that the calculation time is long and the result is inaccurate due to the fact that the existing quadric surface fitting is used for calculating the curvature of the point cloud and the curvature of a point which is calculated by the normal vector of the adjacent point.
Description
Technical Field
The application belongs to the technical field of point cloud curvature characteristic calculation algorithms, and particularly relates to a self-adaptive point cloud curvature calculation method, equipment and a storage medium thereof.
Background
In order to measure more complex irregular curved surfaces, extensive and intensive research has been conducted on three-dimensional data acquisition techniques. The technology can be divided into two main types of contact measurement and non-contact measurement, wherein the non-contact measurement is widely applied in a plurality of fields by virtue of the advantages of high measurement efficiency, no damage to the measured object, low environmental requirement and the like. The point cloud is used as one of important result data of non-contact measurement, and has wide application prospect in the fields of reverse engineering, cultural relic restoration and protection, product detection, medical tooth and orthodontic, face-lifting, maxillofacial surgery and the like. The point cloud curvature is a measure of the point cloud bending degree, can represent the trend of the point cloud characteristics in a local curved surface, and provides important information for the extraction and expression of geometric characteristics; the larger the point cloud curvature, the larger the degree of curvature, and the smaller the corresponding radius of curvature, the smaller the curvature circle. The existing curvature calculation method comprises the steps of solving the curvature of the point cloud by quadric surface fitting and solving the curvature of one point by using the normal vector of the adjacent point.
The quadric surface fitting method is to uniformly take n points with a point cloud as a center, fit the quadric surface by using a least square method, and calculate the Gaussian curvature and the average curvature of the data points according to the property of the space curved surface curve. By taking the contribution of the normal vector into consideration by the normal vectors of adjacent points, one adjacent point can be converted into a normal cross-section curve structure, a normal cross-section circle is constructed, and the normal curvature is estimated according to the positions of the two points and the normal vector.
In the traditional method for solving the curvature by using quadric surface fitting neighborhood points, the main curvature direction is an attached result of curvature solving, and when calculation is directly carried out from point cloud, some methods only use the position information of the points and do not use the normal vector information of each point, so that the robustness of the method is poor; there are also methods that use the normal vector information, but they often use the normal vector as a constraint in combination with the first class of methods, increasing the computation time and memory overhead for principal curvature and principal direction model solutions.
Quadric fitting finds the point cloud curvature with the following disadvantages:
all adjacent points of a particular point on the point cloud surface determine the local shape. Estimating the curvature by surface fitting may result in large errors.
The curvature of a point using the normal vector of neighboring points has the following drawbacks:
according to the method, the KD-Tree search radius is set manually, points in the radius are fitted, the normal vector and curvature of the point cloud are calculated, the manually set search radius has a large influence on the calculation of the normal vector and curvature, and the problems of long calculation time, inaccurate results and the like can be caused by improper setting.
Disclosure of Invention
In order to solve the problems, the application adopts the following technical scheme: the self-adaptive point cloud curvature calculating method comprises the following steps of:
s1, inputting three-dimensional point cloud data;
s2, obtaining average point distances among point clouds;
s3, obtaining the legal loss characteristics of the point cloud through average point distances;
s4, calculating a main curvature value of each point;
s5, outputting the Gaussian curvature of the point.
Further, in S2, the input three-dimensional points are traversed, the distance between the nearest point of each point and the current point is calculated, the distances are accumulated and summed, and the average point distance d of the point cloud is obtained by dividing the points.
Further, in S3, the integer multiple of the average point distance d obtained in S2 is taken as the searching radius r of KD-Tree, and any point P is selected from the three-dimensional points i Radius search using KD-Tree to obtain P i Calculating the mass center of the neighborhood pointFitting and removing centroid to obtain P i Is lost.
Further, in S3, 5 times of the average point distance d of the point cloud is selected as the searching radius r of KD-Tree.
Optionally, in S3, calculating a centroid of the domain pointWhen the formula is as follows:
and uses ax+by+cz+d=0 pair neighbor borrood (P i ) Fitting, wherein each point in the neighborhood subtracts the centroid, and the plane can be simplified to ax+by+cz=0 to finish the barycentering;
then the normal vector of the plane [ X Y Z] T Any three points P are selected from three-dimensional points perpendicular to any vector in the plane 1 、P 2 、P 3 P is obtained by i Is lost:
wherein ,solving by using least square method to obtain point P i Is a normal vector of (2).
Further, in S4, for P i Curvature fitting is carried out on the normal vector of (2) to obtain P i Relative to each neighborhood point P j The normal curvature of (j=0, 2,3,., k-1) is shown by the following formula:
wherein alpha is P i Opposite direction of point normal vector and P i P j Included angle between beta is P i Point normal vector and P j The angle between the point normal vectors.
Further, in S4, there is a relationship between the normal curvature and the principal curvature of the following formula:
and performing least squares fitting by the following formula to obtain principal curvature k 1 And k is equal to 2 ：
Then pass through principal curvature k 1 And k is equal to 2 The gaussian curvature K is obtained as follows:
K＝k 1 k 2 (6)
The gaussian curvature of the final output point.
Meanwhile, the application also provides equipment for calculating the curvature of the self-adaptive point cloud, which comprises the following components:
the system comprises a processor and a memory, wherein the memory is used for storing a computer program, and the processor is used for calling and running the computer program stored in the memory to execute an adaptive point cloud curvature calculation method.
The present application further provides a storage medium for adaptive point cloud curvature calculation, including: for storing a computer program that causes a computer to perform an adaptive point cloud curvature calculation method.
In summary, due to the adoption of the technical scheme, the beneficial effects of the application at least comprise one of the following:
1. the average point distance of certain times of the point cloud data is used as the KD-Tree searching radius of the point cloud normal vector and curvature calculation, the radius search is carried out on each point, the normal vector and the main curvature of the point are calculated by adopting the least square method, and the problems of long calculation time, inaccurate calculation result and the like caused by manually setting the KD-Tree searching radius when the normal vector and the curvature are calculated are avoided;
2. the point cloud curvature is calculated by adopting a self-adaptive method, starting from a normal vector with higher calculation accuracy which is easy to obtain, the point cloud average point distance is used as the KD-Tree searching radius, the point cloud Gaussian curvature is calculated, and the accuracy and the robustness are good;
3. the method solves the problems that the calculation time is long and the result is inaccurate due to the fact that the existing quadric surface fitting is used for calculating the curvature of the point cloud and the curvature of a point which is calculated by the normal vector of the adjacent point.
Drawings
FIG. 1 is a schematic diagram of a Stanford rabbit origin cloud;
FIG. 2 is a schematic view of a 1/5 point cloud with a large curvature for a Stanford rabbit;
FIG. 3 is a schematic view of the original point cloud of the self-made water cup;
FIG. 4 is a schematic view of a 1/5 point cloud with a larger curvature of a self-made cup;
fig. 5 is a flowchart of a method for calculating curvature of an adaptive point cloud.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments. The components of the embodiments of the present application generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the application, as presented in the figures, is not intended to limit the scope of the application, as claimed, but is merely representative of selected embodiments of the application. All other embodiments, based on the embodiments of the application, which are apparent to those of ordinary skill in the art without inventive faculty, are intended to be within the scope of the application.
In addition, the embodiments of the present application and the features of the embodiments may be combined with each other without collision.
As shown in fig. 5, the application discloses a self-adaptive point cloud curvature calculating method, which comprises the following steps:
s1, inputting three-dimensional point cloud data;
s2, obtaining average point distances among point clouds;
s3, obtaining the legal loss characteristics of the point cloud through average point distances;
s4, calculating a main curvature value of each point;
s5, outputting the Gaussian curvature of the point.
The aim of the design is that the average point distance of certain times of the point cloud data is used as the KD-Tree searching radius of the point cloud normal vector and curvature calculation, the radius search is carried out on each point, the normal vector and the main curvature of the point are calculated by adopting the least square method, and the problems of long calculation time, inaccurate calculation result and the like caused by manually setting the KD-Tree searching radius when the normal vector and the curvature are calculated are avoided; the point cloud curvature is calculated by adopting a self-adaptive method, starting from a normal vector with high calculation accuracy which is easy to obtain, the point cloud average point distance is used as a KD-Tree search radius, the point cloud Gaussian curvature is calculated, the method has good accuracy and robustness, and the problems that the calculation time is long, the result is inaccurate and the like caused by improper setting in the prior quadric surface fitting to calculate the point cloud curvature and the normal vector of the adjacent point to calculate the curvature of one point are solved.
In the implementation, in S2, the input three-dimensional points are traversed, the distance between the nearest point of each point and the current point is calculated, the distances are accumulated and summed, and the average point distance d of the point cloud is obtained by dividing the points. S3, taking the integer multiple of the average point distance d obtained in S2 as the searching radius r of KD-Tree, and selecting any point P in the three-dimensional points i Radius search using KD-Tree to obtain P i Calculating the mass center of the neighborhood pointFitting and removing centroid to obtain P i And (3) selecting 5 times of the average point distance d of the point cloud as the search radius r of KD-Tree.
S3, calculating the mass center of the domain pointWhen the formula is as follows:
and uses ax+by+cz+d=0 pair neighbor borrood (P i ) Fitting is performed, each point in the neighborhood minus the centroid, and the plane can be reduced to ax+by+cz=0, finishing the barycentering;
then the normal vector of the plane [ X Y Z] T Any three points P are selected from three-dimensional points perpendicular to any vector in the plane 1 、P 2 、P 3 P is obtained by i Is lost:
wherein ,solving by using least square method to obtain point P i Is a normal vector of (2).
S4, pair P i Curvature fitting is carried out on the normal vector of (2) to obtain P i Relative to each neighborhood point P j The normal curvature of (j=0, 2,3,., k-1) is shown by the following formula:
wherein alpha is P i Opposite direction of point normal vector and P i P j Included angle between beta is P i Point normal vector and P j The angle between the point normal vectors.
In S4, there is a relationship between the normal curvature and the principal curvature of the following equation:
and performing least squares fitting by the following formula to obtain principal curvature k 1 And k is equal to 2 ：
Then pass through principal curvature k 1 And k is equal to 2 The gaussian curvature K is obtained as follows:
K＝k 1 k 2 (6)
The gaussian curvature of the final output point.
The aim of the design is that the average point distance of certain times of the point cloud data is used as the KD-Tree searching radius of the point cloud normal vector and curvature calculation, the radius search is carried out on each point, the normal vector and the main curvature of the point are calculated by adopting the least square method, and the problems of long calculation time, inaccurate calculation result and the like caused by manually setting the KD-Tree searching radius when the normal vector and the curvature are calculated are avoided; the method solves the problems that the calculation time is long and the result is inaccurate due to the fact that the existing quadric surface fitting is used for calculating the curvature of the point cloud and the curvature of a point which is calculated by the normal vector of the adjacent point.
As shown in fig. 1 and fig. 2, in order to verify the correctness and efficiency of the adaptive point cloud curvature calculation method provided in this embodiment, curvature calculation is performed on the stanfu rabbit point cloud, 1/5 point cloud with a larger curvature is extracted, the result is shown in fig. 1 and fig. 2, the number of the stanfu rabbit point cloud is 35947, the calculation time is 0.487s, as shown in fig. 3 and fig. 4, curvature calculation is performed on the self-made cup point cloud, the number of the self-made cup point cloud is 785322, and the calculation time is 93.679s.
The embodiment also provides a device for calculating the curvature of the self-adaptive point cloud, which comprises:
the system comprises a processor and a memory, wherein the memory is used for storing a computer program, and the processor is used for calling and running the computer program stored in the memory to execute an adaptive point cloud curvature calculation method.
The processor may be a central processing unit (Central Processing Unit, CPU), but also other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), field programmable gate arrays (FieldProgrammable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory may be an internal memory unit or an external memory device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital Card (SD), a Flash Card (Flash Card), etc. Further, the memory may also include both internal storage units and external storage devices. The memory is used for storing the computer program and other programs and data, and may also be used for temporarily storing data that has been or is to be output.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, the specific names of the functional units and modules are only for distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus/terminal device and method may be implemented in other manners. For example, the apparatus/terminal device embodiments described above are merely illustrative, e.g., the division of the modules or units is merely a logical function division, and there may be additional divisions in actual implementation, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection via interfaces, devices or units, which may be in electrical, mechanical or other forms.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in the embodiments of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated modules/units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present application may implement all or part of the flow of the method of the above embodiment, or may be implemented by a computer program to instruct related hardware, where the computer program may be stored in a computer readable storage medium, and when the computer program is executed by a processor, the computer program may implement the steps of each of the method embodiments described above. Wherein the computer program comprises computer program code which may be in the form of source code, object code, executable files or some intermediate form or the like. The computer readable medium may include any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (RAM, random Access Memory), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth.
In this embodiment, a computer storage medium is further provided, in which a computer program is stored, where the computer storage medium may be one of a magnetic random access memory, a read-only memory, a programmable read-only memory, an erasable programmable read-only memory, an electrically erasable programmable read-only memory, a flash memory, a magnetic surface memory, and an optical disc, and may also be various devices including one or any combination of the foregoing, such as a mobile phone, a computer, a tablet device, etc., where the computer program can drive a system for resolving log data conflicts in different formats, and where the computer program processor can perform an adaptive point cloud curvature calculation method.
Finally, it should be noted that: the foregoing description of the preferred embodiments of the present application is not intended to be limiting, but rather, it will be apparent to those skilled in the art that the foregoing description of the preferred embodiments of the present application can be modified or equivalents can be substituted for some of the features thereof, and any modification, equivalent substitution, improvement or the like that is within the spirit and principles of the present application should be included in the scope of the present application.
Claims (9)
1. The self-adaptive point cloud curvature calculating method is characterized by comprising the following steps of:
s1, inputting three-dimensional point cloud data;
s2, obtaining average point distances among point clouds;
s3, obtaining the legal loss characteristics of the point cloud through average point distances;
s4, calculating a main curvature value of each point;
s5, outputting the Gaussian curvature of the point.
2. The adaptive point cloud curvature calculation method according to claim 1, wherein: and S2, traversing the input three-dimensional points, calculating the distance between the nearest point of each point and the current point, accumulating and summing the distances, and dividing the distances by the points to obtain the average point distance d of the point cloud.
3. The adaptive point cloud curvature calculation method according to claim 2, wherein: s3, taking the integer multiple of the average point distance d obtained in S2 as the searching radius r of KD-Tree, and selecting any point P in the three-dimensional points i Radius search using KD-Tree to obtain P i Calculating the mass center of the neighborhood pointFitting and removing centroid to obtain P i Is lost.
4. A method for computing curvature of an adaptive point cloud according to claim 3, wherein: and S3, selecting 5 times of the average point distance d of the point cloud as the search radius r of KD-Tree.
5. A method for computing curvature of an adaptive point cloud according to claim 3, wherein: s3, calculating the mass center of the domain pointWhen the formula is as follows:
and uses ax+by+cz+d=0 pair neighbor borrood (P i ) Fitting, wherein each point in the neighborhood subtracts the centroid, and the plane can be simplified to ax+by+cz=0 to finish the barycentering;
then the normal of the plane [ XYZ] T Any three points P are selected from three-dimensional points perpendicular to any vector in the plane 1 、P 2 、P 3 P is obtained by i Is lost:
wherein ,solving by using least square method to obtain point P i Is a normal vector of (2).
6. The adaptive point cloud curvature computing method according to claim 5, wherein: s4, pair P i Curvature fitting is carried out on the normal vector of (2) to obtain P i Relative to each neighborhood point P j The normal curvature of (j=0, 2,3,., k-1) is shown by the following formula:
wherein alpha is P i Opposite direction of point normal vector and P i P j Included angle between beta is P i Point normal vector and P j The angle between the point normal vectors.
7. The adaptive point cloud curvature computing method according to claim 6, wherein: in S4, there is a relationship between the normal curvature and the principal curvature of the following equation:
and performing least squares fitting by the following formula to obtain principal curvature k 1 And k is equal to 2 ：
Then pass through principal curvature k 1 And k is equal to 2 The gaussian curvature K is obtained as follows:
K＝k 1 k 2 (6)
The gaussian curvature of the final output point.
8. An apparatus for adaptive point cloud curvature computation, comprising:
a processor and a memory for storing a computer program, the processor being adapted to invoke and run the computer program stored in the memory for performing the method according to any of claims 1 to 7.
9. A storage medium for adaptive point cloud curvature computation, characterized in that: for storing a computer program that causes a computer to perform the method of any one of claims 1 to 7.
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| CN117968667A (en) * | 2024-04-02 | 2024-05-03 | 国网江苏省电力有限公司常州供电分公司 | SLAM point cloud map construction method and system for loop detection of inspection robot |
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| CN117968667A (en) * | 2024-04-02 | 2024-05-03 | 国网江苏省电力有限公司常州供电分公司 | SLAM point cloud map construction method and system for loop detection of inspection robot |
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