CN112053296A - Robust geometric mean filtering grid denoising method - Google Patents
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Abstract
The invention discloses a robust geometric mean filtering grid denoising method, which comprises the following steps: obtaining three-dimensional point coordinates through digital scanning, and obtaining a normal vector n of a grid point through a convex combination method of taubini(ii) a After the normal vector of the grid point is obtained, the average value theta of the included angle of the normal vector is calculatedaverage(ii) a Translating the grid point to a first octave through the translation vector to ensure that the space coordinate of the grid point is a positive value; calculate point VertexiAnd its surrounding 1-neighborhood region N (vertex)j1) angle value ofc(ii) a Drawing the neighborhood points to a central point through a weighted geometric mean filter to keep the characteristics from being passivated, rapidly filtering the non-characteristic area, and updating the vertex position to obtain an updated model; restoring the model to the specified position of the local coordinate system to obtain a grid model after noise reduction; and iterating according to the preset times, and outputting a final noise reduction network model. The denoising method is simple, rapid and robust, uses point space position information to complete denoising, and can keep closedA key feature.
Description
Technical Field
The invention relates to the technical field of spatial information, in particular to a robust geometric mean filtering grid denoising method.
Background
With the continuous development of science and technology, the use of digital scanners is more and more common, people obtain the data of the surface of a three-dimensional object more and more easily through the digital scanners, the density of samples for obtaining the surface data is different and generally mainly divided into point cloud and grid data, the point cloud data has high sampling density and is close to an original model, but the point cloud data has the defects of unclear topological relation and huge point data to be processed; the grid data obviously has detailed topological relation, less data exists, and the low-density sampling of the grid data can have the defect that the model cannot be completely described, but the defects can be complemented by interactive processing. Whether point cloud data or mesh data, is one way to describe three-dimensional models, and the focus of research is on how to process these data. The grid data is used as a basic data object, the data complexity of three-dimensional reconstruction is reduced, noise is inevitably generated in the process of acquiring the grid data by the digital scanner, the accurate representation of a model and the subsequent geometric processing process are seriously influenced by the generation of the noise, and therefore the noise reduction becomes a key step of the digital geometric processing.
Other methods for grid noise reduction are various, such as methods of surface approximation, surface fitting, gaussian curvature flow and the like, and a main research focus at present is how to remove noise on the basis of maintaining key features. Although the current noise reduction algorithm is quite mature, the algorithm has high calculation cost, and the defects that the characteristics are not obvious are still existed.
Disclosure of Invention
The invention aims to provide a robust geometric mean filtering grid denoising method which can rapidly remove noise while effectively maintaining characteristics.
In order to solve the above technical problem, the present invention provides a robust geometric mean filtering grid denoising method, comprising the following steps:
obtaining three-dimensional point coordinates through digital scanning, and obtaining a normal vector n of a grid point through a convex combination method of taubini；
After the normal vectors of the grid points are obtained, vertex is obtained in sequenceiCorresponding 1-neighborhood region N (vertex)j1) and calculating the mean value theta of the angle between normal vectorsaverage；
Translating the grid point to a first octave through the translation vector to ensure that the space coordinate of the grid point is a positive value;
calculate point VertexiAnd its surrounding 1-neighborhood region N (vertex)j1) angle value ofc；
Drawing the neighborhood points to a central point through a weighted geometric mean filter to keep the characteristics from being passivated, rapidly filtering the non-characteristic area, and updating the vertex position to obtain an updated model;
restoring the model to a specified position of a local coordinate system, namely restoring the vertex position of the grid to obtain a grid model after noise reduction;
and iterating according to the preset times, and outputting a final noise reduction network model.
Preferably, a normal vector n of the grid point is obtainediThe formula of (1) is:
wherein f iskRepresenting the vertexiOf related patch set VlMiddle k-th triangular patch, gkIs a triangular plate fkThe center of gravity of the vehicle,
is fkThe corresponding normal vector.
Preferably, the average value theta of the included angle of the normal vector is calculatedaverageSatisfies the formula:
as a preferred scheme, the formula of translating the grid point to the first octave by the translation vector is as follows:
Vi＝Vertexi+c+d：
where Vertex represents the original grid point, c represents the translation vector, and d represents the normal three-dimensional vector.
Preferably, the value of included angle θcSatisfies the calculation formula:
θc＝arccos(ni*nj)。
preferably, the filtering method satisfies the formula:
wherein, thetas＝αθaverageAnd a is an angle coefficient, and the angle coefficient alpha is 0.12.
Preferably, the positions of the vertices of the reduction mesh satisfy the following formula:
preferably, θ satisfies the formula of a gaussian kernel function:
the invention has the following beneficial effects:
the method comprises the steps of calculating an included angle value of a 1-neighborhood point and a normal vector of a central point, calculating an average included angle value of normal vectors of a grid as an angle threshold, and pulling the 1-neighborhood point to the central point by utilizing the low-pass characteristic of a Gaussian kernel function to maintain characteristics; meanwhile, the characteristic of the geometric filter and the high-resistance characteristic of the Gaussian function are used for rapid filtering, so that the running time is saved.
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Fig. 1 is a flowchart of a robust geometric mean filtering grid denoising method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Referring to fig. 1, a robust geometric mean filtering mesh denoising method in a preferred embodiment of the present invention includes the following steps:
obtaining three-dimensional point coordinates through digital scanning, and obtaining a normal vector n of a grid point through a convex combination method of taubini；
After the normal vectors of the grid points are obtained, vertex is obtained in sequenceiCorresponding 1-neighborhood region N (vertex)j1) and calculating the mean value theta of the angle between normal vectorsaverage；
Translating the grid point to a first octave through the translation vector to ensure that the space coordinate of the grid point is a positive value;
calculate point VertexiAnd its surrounding 1-neighborhood region N (vertex)j1) angle value ofc；
Drawing the neighborhood points to a central point through a weighted geometric mean filter to keep the characteristics from being passivated, rapidly filtering the non-characteristic area, and updating the vertex position to obtain an updated model;
restoring the model to a specified position of a local coordinate system, namely restoring the vertex position of the grid to obtain a grid model after noise reduction;
iteration is carried out according to the preset times, and a final noise reduction network model is output; wherein the best effect is achieved when the iteration number is 3.
Specifically, the robust geometric mean filtering grid denoising method according to the preferred embodiment of the present invention calculates the angle between the 1-neighborhood point and the normal vector of the central point, calculates the average angle between the normal vectors of the grid as the threshold of the angle, and uses the low-pass characteristic of the gaussian kernel function to pull the 1-neighborhood point to the central point for feature preservation; meanwhile, the characteristic of the geometric filter and the high-resistance characteristic of the Gaussian function are used for rapid filtering, so that the running time is saved.
In the preferred embodiment of the present invention, the normal vector n of the grid point is obtainediThe formula of (1) is:
wherein f iskRepresenting the vertexiOf related patch set VlMiddle k-th triangular patch, gkIs a triangular plate fkThe center of gravity of the vehicle,
is fkThe corresponding normal vector.
In a preferred embodiment of the invention, the mean value θ of the normal vector angle is calculatedaverageSatisfies the formula:
in the preferred embodiment of the present invention, the translation vector translates the grid point to the first octave by the formula:
Vi＝Vertexi+c+d：
where Vertex represents the original grid point, c represents the translation vector, and d represents the normal three-dimensional vector.
In the preferred embodiment of the invention, the included angle value θcSatisfies the calculation formula:
θc＝arccos(ni*nj)。
in the preferred embodiment of the present invention, the filtering method satisfies the formula:
wherein, thetas＝αθaverageAnd a is an angle coefficient, and the angle coefficient alpha is 0.12.
In the preferred embodiment of the present invention, the positions of the vertices of the reduction mesh satisfy the formula:
in a preferred embodiment of the present invention, θ satisfies the formula of a gaussian kernel function:
the above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and substitutions can be made without departing from the technical principle of the present invention, and these modifications and substitutions should also be regarded as the protection scope of the present invention.
Claims (8)
1. A robust geometric mean filtering grid denoising method is characterized by comprising the following steps:
obtaining three-dimensional point coordinates through digital scanning, and obtaining a normal vector n of a grid point through a convex combination method of taubini；
After the normal vectors of the grid points are obtained, vertex is obtained in sequenceiCorresponding 1-neighborhood region N (vertex)j1) and calculating the mean value theta of the angle between normal vectorsaverage；
Translating the grid point to a first octave through the translation vector to ensure that the space coordinate of the grid point is a positive value;
calculate point VertexiAnd its surrounding 1-neighborhood region N (vertex)j1) angle value ofc；
Drawing the neighborhood points to a central point through a weighted geometric mean filter to keep the characteristics from being passivated, rapidly filtering the non-characteristic area, and updating the vertex position to obtain an updated model;
restoring the model to a specified position of a local coordinate system, namely restoring the vertex position of the grid to obtain a grid model after noise reduction;
and iterating according to the preset times, and outputting a final noise reduction network model.
2. The robust geometric mean filtering mesh denoising method of claim 1, wherein: obtainingNormal vector n of grid pointiThe formula of (1) is:
wherein f iskRepresenting the vertexiOf related patch set VlMiddle k-th triangular patch, gkIs a triangular plate fkThe center of gravity of the vehicle,
is fkThe corresponding normal vector.
3. The robust geometric mean filtering mesh denoising method of claim 1, wherein: calculating the average value theta of the included angle of the normal vectoraverageSatisfies the formula:
4. the robust geometric mean filtering mesh denoising method of claim 1, wherein: the translation vector translates the grid point to the first octave by the formula:
Vi＝Vertexi+c+d：
where Vertex represents the original grid point, c represents the translation vector, and d represents the normal three-dimensional vector.
5. The robust geometric mean filtering mesh denoising method of claim 1, wherein: included angle value thetacSatisfies the calculation formula:
θc＝arccos(ni*nj)。
6. the robust geometric mean filtering mesh denoising method of claim 4, wherein: the filtering method satisfies the formula:
wherein, thetas＝αθaverageAnd a is an angle coefficient, and the angle coefficient alpha is 0.12.
7. The robust geometric mean filtering mesh denoising method of claim 4, wherein: the reduction mesh vertex position satisfies the formula:
8. the robust geometric mean filtering mesh denoising method of claim 1, wherein: wherein θ satisfies the gaussian kernel function formula:
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| CN117197000A (en) * | 2023-11-06 | 2023-12-08 | 武汉中观自动化科技有限公司 | Quick grid denoising method and device and electronic equipment |
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| CN107274367A (en) * | 2017-06-16 | 2017-10-20 | 东北电力大学 | A kind of 3-D geometric model denoising method described based on architectural feature |
| CN111479982A (en) * | 2017-11-15 | 2020-07-31 | 吉奥奎斯特系统公司 | In-situ operating system with filter |
| CN108447038A (en) * | 2018-03-27 | 2018-08-24 | 北京工业大学 | A kind of mesh denoising method based on non local full variation operator |
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| CN117197000A (en) * | 2023-11-06 | 2023-12-08 | 武汉中观自动化科技有限公司 | Quick grid denoising method and device and electronic equipment |
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