CN114049267A - Improved neighborhood search based statistical and bilateral filtering point cloud denoising method - Google Patents

Improved neighborhood search based statistical and bilateral filtering point cloud denoising method Download PDF

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CN114049267A
CN114049267A CN202111270025.XA CN202111270025A CN114049267A CN 114049267 A CN114049267 A CN 114049267A CN 202111270025 A CN202111270025 A CN 202111270025A CN 114049267 A CN114049267 A CN 114049267A
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马宗方
徐捷
王艳
段明
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Xian University of Architecture and Technology
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Abstract

The invention discloses a statistical and bilateral filtering point cloud denoising method based on improved neighborhood search, which comprises the following steps: step 1, processing point cloud data by using a statistical filtering algorithm based on improved field search to obtain processed point cloud data: step 1.1, obtaining a point cloud two-dimensional plane projection diagram; step 1.2, grid division is carried out to obtain a plurality of rectangles; step 1.3, primarily removing outliers; step 1.4, calculating the average distance corresponding to any point p; step 1.5, calculating the average distance mu and the standard deviation sigma; step 1.6, calculate the maximum threshold dmaxRemoving outlier noise points; and 2, carrying out bilateral filtering on the processed point cloud data obtained in the step 1 to obtain filtered point cloud data. The method of the invention has the advantages of obviously reduced calculated amount and accelerated search rate; in combination with bilateral filtering algorithmsThe point cloud data is managed, so that not only large-scale outlier noise points are removed, but also small-scale noise points in the point cloud are removed, and the limitation of independent use of two algorithms is solved.

Description

Improved neighborhood search based statistical and bilateral filtering point cloud denoising method
Technical Field
The invention belongs to the technical field of 3D point cloud data processing, and particularly relates to a point cloud denoising method based on statistics and bilateral filtering of search in the improvement field.
Background
With the development of three-dimensional reconstruction technology, 3D point cloud data is more and more widely used in the reconstruction process. The non-contact point cloud data acquisition method has very important application in the fields of artificial intelligence, industrial production, medicine and the like due to high precision, high resolution and sampling speed. The point cloud data obtained by the three-dimensional laser scanning equipment presents a disordered and scattered state, and in addition, due to the influences of factors such as the surface roughness of a target object, the equipment precision, the ambient illumination and the like, the obtained 3D point cloud is inevitably influenced by noise points. The serious influence of the noise point not only can seriously influence the subsequent feature extraction and matching, the reconstruction precision and the point cloud data identification rate. Therefore, it has been the focus of research to remove noise points from point cloud data and obtain a complete and usable point cloud.
There are also many filtering algorithms related to denoising for disordered point clouds or partially ordered point clouds. The statistical filtering algorithm is to calculate the average distance between a point and a point cloud in a k neighborhood through calculation, and the point outside a certain range can be regarded as outlier rejection, but small-scale noise in the point cloud cannot be well removed. Bilateral filtering is mainly to make the data points of the point cloud move to the edge along the normal vector, so that some internal noise of the point cloud can be removed, and the noise can be smoothed by making the point cloud move to the surface and enhancing the edge information. But the de-noising effect on outlier isolated noise points is not good. In addition, when the traditional statistical filtering algorithm is used for searching the point cloud neighborhood, the rasterization on the space is utilized for searching, so that the calculation amount is large, and the searching speed is low.
Disclosure of Invention
The invention aims to provide a statistics and bilateral filtering point cloud denoising method based on improved neighborhood search, which projects point cloud data to a plane, carries out grid division and searches in 9 adjacent rectangles, thus solving the problems of low neighborhood searching speed and large calculation amount of the traditional statistical filtering algorithm and the problem of limitation that noise points with different scales cannot be well removed when only statistical filtering or bilateral filtering is used.
In order to achieve the purpose, the invention adopts the following technical scheme to solve the problem:
a statistics and bilateral filtering point cloud denoising method based on improved neighborhood search specifically comprises the following steps:
step 1, processing point cloud data by using a statistical filtering algorithm based on improved field search to obtain processed point cloud data: the method comprises the following substeps:
step 1.1, selecting a projection direction of a side view or a top view according to the distribution condition of large-scale outlier noise points in point cloud data to obtain a point cloud two-dimensional plane projection diagram;
step 1.2, carrying out grid division on point cloud data in a point cloud two-dimensional plane projection graph to obtain a plurality of rectangles;
step 1.3, if the number of the points of the rectangle where the p points are located is less than the sum of the numbers of the points in all adjacent rectangles of the rectangle where the p points are located, rejecting the p points as outliers;
step 1.4, calculating the average distance between any point p and all points in the adjacent rectangle of the rectangle where the point p is located;
step 1.5, calculating the average distance mu and the standard deviation sigma of each point in the whole point cloud data obtained in the step 1.3:
step 1.6, calculating by using a formula 4 to obtain a maximum threshold value d according to the average distance mu and the standard deviation sigmamaxComparing the average distance of each point to all points in the adjacent rectangle of the rectangle to which the point is located with a maximum threshold dmaxRemoving the points exceeding the maximum threshold value as outlier noise points;
step 2, carrying out bilateral filtering on the processed point cloud data obtained in the step 1 to obtain filtered point cloud data, and comprising the following substeps:
step 2.1, searching the processed point cloud data obtained in the step 1 to obtain each data point piK neighborhood of (2)k(pi) Evaluating each data point piThe normal vector of (a);
step 2.2, calculating to obtain Gaussian kernel functions wc (x) and Ws (y);
step 2.3, calculating a bilateral filtering factor lambda according to the Gaussian kernel function wc (x) and Ws (y);
and 2.4, calculating the data points after bilateral filtering, and updating corresponding points in the point cloud data obtained in the step 1 by using the obtained data points until all the data points are updated.
Further, in step 1.4, the average distance d between any point p and all points in the adjacent rectangle of the rectangle where the point p is located is calculated by using formula (1)k；
Figure BDA0003328413620000021
Wherein d isjK is the sum of the number of points in all adjacent rectangles of the rectangle in which the point p is located.
Further, in step 1.5, the average distance μ and the standard deviation σ are calculated by using formula 2 and formula 3:
Figure BDA0003328413620000022
Figure BDA0003328413620000031
wherein n is the total number of the point cloud data obtained in step 1.3, and in the embodiment, n is 1920040; dkiThe average distance of the ith point from all points in its neighboring rectangle is obtained from step 1.4.
Further, in step 1.6, the maximum threshold value d is calculated by using formula 4max：
dmax＝μ+α×σ (4)
Wherein α is a proportionality coefficient, and α is 0.1.
Further, in the step 2.1, each data point p is obtained by using Kdtree neighborhood searchiK neighborhood of (2)k(pi)；
Each data point p is estimated by a principal component analysis-based methodiThe normal vector of (a); the operation is as follows:
constructing a covariance matrix C by using a formula 5, calculating an eigenvector v corresponding to the minimum eigenroot lambda of the covariance matrix C, and taking the eigenvector v as a data point piIs estimated approximately.
Figure BDA0003328413620000032
Wherein p issFor any point, p, in the processed point cloud data obtained in step 1sIs a data point piK is the number of points in the k neighborhood of point p.
Further, in the step 2.2, gaussian kernel functions wc (x) and ws (y) are calculated according to equations 6 and 7. They respectively correspond to the spatial domain to control smooth and frequency domains to control edge preservation;
Figure BDA0003328413620000033
wherein σcThe parameter is used for controlling the smooth smoothness of the point cloud, and is taken as the radius of the k neighborhood of the measured point;
Figure BDA0003328413620000034
wherein σsThe parameter is a parameter for controlling the point cloud characteristic maintenance, and is taken as the standard deviation of the neighborhood points of the measured point.
Further, in step 2.3, the bilateral filtering factor λ is calculated by using formula 8:
Figure BDA0003328413620000035
wherein p isjIs piN is any point in the k neighborhood of (1)iAnd nj are respectively a point piAnd point pjThe normal vector of (2).
Further, the bilateral filtered data points are calculated using equation 9:
pl＝pi+λni (9)
wherein p isiFor the ith point in the point cloud data obtained after the processing in the step 1, lambda is a bilateral filtering factor, and niIs the normal vector of the point, plIs the updated data point.
Compared with the prior art, the invention has the following beneficial effects:
compared with the neighborhood searching method of the traditional statistical filtering algorithm, the method has the advantages that the calculated amount is obviously reduced, and the searching speed is accelerated; the point cloud data is processed by combining with the bilateral filtering algorithm, so that not only are noise points of large-scale outliers removed, but also small-scale noise points in the point cloud are removed, and the limitation of independent use of the two algorithms is solved.
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FIG. 1 is a diagram of an embodiment of a point cloud data source;
FIG. 2 is a side view of a point cloud undergoing search based on improved neighborhood in an embodiment of the present invention;
FIG. 3 is a diagram of the denoising effect of a statistical filtering algorithm based on improved neighborhood search according to an embodiment of the present invention;
FIG. 4 is a diagram of denoising effect by bilateral filtering algorithm in the embodiment of the present invention;
FIG. 5 is a diagram of denoising effects of statistics and bilateral filtering algorithms based on improved neighborhood search according to an embodiment of the present invention.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention discloses a statistics and bilateral filtering point cloud denoising method based on improved neighborhood search, which is implemented according to the following steps as shown in figure 1:
step 1, processing point cloud data by using a statistical filtering algorithm based on improved field search to obtain processed point cloud data, and specifically implementing the following steps:
step 1.1, selecting the projection direction of a side view or a top view according to the distribution condition of large-scale outlier noise points in the point cloud data to obtain a point cloud two-dimensional plane projection diagram, as shown in fig. 2.
Step 1.2, carrying out grid division on point cloud data in a point cloud two-dimensional plane projection graph to obtain a plurality of rectangles;
therefore, after the point cloud data is subjected to grid division to obtain rectangles, when k neighborhood points of any point in the point cloud data are searched, 9 rectangles in total in the rectangle where the point is located or the adjacent rectangle of the point can be searched, and compared with the traditional neighborhood searching in a space, the calculation amount is reduced, and the efficiency is obviously improved.
Step 1.3, if the number of points of the rectangle where any point p is located is less than the sum of the number of points in all adjacent rectangles of the rectangle where the point is located, removing the point p as an outlier;
step 1.4, calculating the average distance d between any point p and all points in the adjacent rectangle of the rectangle where the point p is located by using the formula (1)k；
Figure BDA0003328413620000051
Wherein d isjThe distance from any point p to each point in the adjacent rectangle of the rectangle in which the point p is positioned is defined, and k is the sum of the number of the points in all the adjacent rectangles of the rectangle in which the point p is positioned;
step 1.5, calculating the average distance mu and the standard deviation sigma of the ith point in the overall point cloud data obtained in the step 1.3 by respectively using a formula 2 and a formula 3:
Figure BDA0003328413620000052
Figure BDA0003328413620000053
wherein n is the total number of the point cloud data obtained in step 1.3, and in the embodiment, n is 1920040; dkiThe average distance of the ith point to all points in the adjacent rectangle of the rectangle in which the ith point is located is obtained in step 1.4;
step 1.6, calculating by using a formula 4 according to the average distance mu and the standard deviation sigma to obtain the maximum dmaxComparing the average distance of each point to all points in the adjacent rectangle of the rectangle to which the point is located with a maximum threshold dmaxRemoving the points exceeding the maximum threshold value as outlier noise points;
dmax＝μ+α×σ (4)
wherein α is a proportionality coefficient, and α is 0.1.
The processed point cloud data is obtained through the improved neighborhood search statistical filtering algorithm in the step 1, and large-scale outliers can be filtered, as shown in fig. 3, when the original point cloud is compared, the large-scale outliers are rapidly filtered, and the edge information of the point cloud is well retained.
And 2, in order to obtain satisfactory point cloud data, carrying out bilateral filtering on the processed point cloud data obtained in the step 1 to obtain filtered point cloud data. The method is implemented according to the following steps:
step 2.1, for the processed point cloud data obtained in the step 1, each data point p is obtained by using Kdtree neighborhood searchiK neighborhood of (2)k(pi) Each data point p is obtained by Principal Component Analysis (PCA) based estimationiThe normal vector of (a); the operation of the principal component analysis method is specifically as follows:
constructing a covariance matrix C by using a formula 5, calculating an eigenvector v corresponding to the minimum eigenroot lambda of the covariance matrix C, and taking the eigenvector v as a data point piIs estimated approximately.
Figure BDA0003328413620000054
Wherein p issFor any point, p, in the processed point cloud data obtained in step 1sIs a data point piK is the number of points in the k neighborhood of point p;
and 2.2, calculating to obtain Gaussian kernel functions wc (x) and Ws (y) according to the formula 6 and the formula 7. They respectively correspond to the spatial domain to control smooth and frequency domains to control edge preservation;
Figure BDA0003328413620000061
wherein σcThe parameter is used for controlling the smooth smoothness of the point cloud, and is taken as the radius of the k neighborhood of the measured point. It reflects the ratio of the bilateral filtering in the distance space, the larger the value is, the smoother the point cloud.
Figure BDA0003328413620000062
Wherein σsThe parameter is a parameter for controlling the point cloud characteristic maintenance, and is taken as the standard deviation of the neighborhood points of the measured point. It represents the effect of the normal vector angle on the bilateral filtering, with a larger value indicating better retention of the edge characteristics.
Step 2.3, according to the gaussian kernel function wc (x) and ws (y), calculating a bilateral filtering factor λ by using a formula 8:
Figure BDA0003328413620000063
wherein p isjIs piN is any point in the k neighborhood of (1)iAnd nj are respectively a point piAnd point pjThe normal vector of (a);
step 2.4, calculating the data points after bilateral filtering by using a formula 9, and updating corresponding points in the point cloud data obtained in the step 1 by using the obtained data points until all the data points are updated:
pl＝pi+λni (9)
wherein p isiFor the first point cloud data obtained after the processing of the step 1i points, λ is a bilateral filter factor, niIs the normal vector of the point, plIs the updated data point.
As shown in fig. 5, the effect of performing bilateral filtering on the point cloud data obtained in step 1 in step 2 is that small-scale noise interfering in the point cloud is better removed, the edge of the point cloud is smoother, and a satisfactory effect is obtained.
In order to verify the effectiveness of the method of the invention, 20 different point cloud data sets are selected for comparison processing.
As can be seen from Table 1, compared with the method which only uses the traditional filtering algorithm or the bilateral filtering algorithm and cannot simultaneously remove the noise of the point cloud with small scale and large scale, the method has the advantages that the effect of the method is obviously superior to the two algorithms, for example, the speed is averagely improved by 1.25s compared with the traditional statistical filtering algorithm.
TABLE 1 duration comparison of statistical filtering in the present invention with conventional statistical filtering
Figure BDA0003328413620000071
As can be seen from Table 2, compared with the conventional statistical filtering and bilateral filtering methods, the denoising effect of the method provided by the invention is improved by 10.4% compared with the average statistical filtering and 6.3% compared with the average denoising effect of the bilateral filtering algorithm.
TABLE 2 post-filtering point comparison of the method of the present invention with statistical filtering and bilateral filtering
Figure BDA0003328413620000072

Claims (8)

1. A statistics and bilateral filtering point cloud denoising method based on improved neighborhood search is characterized by comprising the following steps:
step 1, processing point cloud data by using a statistical filtering algorithm based on improved field search to obtain processed point cloud data: the method comprises the following substeps:
step 1.1, selecting a projection direction of a side view or a top view according to the distribution condition of large-scale outlier noise points in point cloud data to obtain a point cloud two-dimensional plane projection diagram;
step 1.2, carrying out grid division on point cloud data in a point cloud two-dimensional plane projection graph to obtain a plurality of rectangles;
step 1.3, if the number of the points of the rectangle where the p points are located is less than the sum of the numbers of the points in all adjacent rectangles of the rectangle where the p points are located, rejecting the p points as outliers;
step 1.4, calculating the average distance between any point p and all points in the adjacent rectangle of the rectangle where the point p is located;
step 1.5, calculating the average distance mu and the standard deviation sigma of each point in the whole point cloud data obtained in the step 1.3:
step 1.6, calculating by using a formula 4 to obtain a maximum threshold value d according to the average distance mu and the standard deviation sigmamaxComparing the average distance of each point to all points in the adjacent rectangle of the rectangle to which the point is located with a maximum threshold dmaxRemoving the points exceeding the maximum threshold value as outlier noise points;
step 2, carrying out bilateral filtering on the processed point cloud data obtained in the step 1 to obtain filtered point cloud data, and comprising the following substeps:
step 2.1, searching the processed point cloud data obtained in the step 1 to obtain each data point piK neighborhood of (2)k(pi) Evaluating each data point piThe normal vector of (a);
step 2.2, calculating to obtain Gaussian kernel functions wc (x) and Ws (y);
step 2.3, calculating a bilateral filtering factor lambda according to the Gaussian kernel function wc (x) and Ws (y);
and 2.4, calculating the data points after bilateral filtering, and updating corresponding points in the point cloud data obtained in the step 1 by using the obtained data points until all the data points are updated.
2. Statistics for improving neighborhood search as recited in claim 1And a bilateral filtering point cloud denoising method, characterized in that, in the step 1.4, the formula (1) is adopted to calculate the average distance d between any point p and all points in the adjacent rectangle of the rectangle where the point p is locatedk；
Figure FDA0003328413610000011
Wherein d isjK is the sum of the number of points in all adjacent rectangles of the rectangle in which the point p is located.
3. The method for denoising point clouds by improving statistics of neighborhood search and bilateral filtering according to claim 1, wherein in the step 1.5, the mean distance μ and the standard deviation σ are calculated by using formula 2 and formula 3:
Figure FDA0003328413610000021
Figure FDA0003328413610000022
wherein n is the total number of the point cloud data obtained in step 1.3, and in the embodiment, n is 1920040; dkiThe average distance of the ith point from all points in its neighboring rectangle is obtained from step 1.4.
4. The method for improving statistics of neighborhood search and bilateral filtering point cloud denoising of claim 1, wherein in step 1.6, the maximum threshold d is obtained by calculation using formula 4max：
dmax＝μ+α×σ (4)
Wherein α is a proportionality coefficient, and α is 0.1.
5. The improved neighborhood of claim 1The statistical and bilateral filtering point cloud denoising method for searching is characterized in that in the step 2.1, each data point p is obtained by using Kdtree neighborhood searchiK neighborhood of (2)k(pi)；
Each data point p is estimated by a principal component analysis-based methodiThe normal vector of (a); the operation is as follows:
constructing a covariance matrix C by using a formula 5, calculating an eigenvector v corresponding to the minimum eigenroot lambda of the covariance matrix C, and taking the eigenvector v as a data point piIs estimated approximately.
Figure FDA0003328413610000023
Wherein p issFor any point, p, in the processed point cloud data obtained in step 1sIs a data point piK is the number of points in the k neighborhood of point p.
6. The method of claim 1, wherein in step 2.2, gaussian kernel functions wc (x) and ws (y) are calculated by formula 6 and formula 7. They respectively correspond to the spatial domain to control smooth and frequency domains to control edge preservation;
Figure FDA0003328413610000024
wherein σcThe parameter is used for controlling the smooth smoothness of the point cloud, and is taken as the radius of the k neighborhood of the measured point;
Figure FDA0003328413610000025
wherein σsThe parameter is a parameter for controlling the point cloud characteristic maintenance, and is taken as the standard deviation of the neighborhood points of the measured point.
7. The method for improving statistics of neighborhood search and bilateral filtering point cloud denoising as claimed in claim 1, wherein in said step 2.3, bilateral filtering factor λ is calculated by using formula 8:
Figure FDA0003328413610000031
wherein p isjIs piN is any point in the k neighborhood of (1)iAnd nj are respectively a point piAnd point pjThe normal vector of (2).
8. The method of improving statistical and bilateral filtering point cloud denoising of neighborhood search of claim 1,
the bilateral filtered data points are calculated using equation 9:
pl＝pi+λni (9)
wherein p isiFor the ith point in the point cloud data obtained after the processing in the step 1, lambda is a bilateral filtering factor, and niIs the normal vector of the point, plIs the updated data point.
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Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114897026A (en) * 2022-05-24 2022-08-12 上海枢光科技有限公司 Point cloud filtering method
CN115984147A (en) * 2023-03-17 2023-04-18 汉斯夫(杭州)医学科技有限公司 Point cloud self-adaptive processing method, device and medium based on dental scanner
CN116843563A (en) * 2023-06-25 2023-10-03 成都飞机工业（集团）有限责任公司 Point cloud noise reduction processing method
CN116955444A (en) * 2023-06-15 2023-10-27 共享易付(广州)网络科技有限公司 Method and system for mining collected noise points based on big data analysis

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114897026A (en) * 2022-05-24 2022-08-12 上海枢光科技有限公司 Point cloud filtering method
CN115984147A (en) * 2023-03-17 2023-04-18 汉斯夫(杭州)医学科技有限公司 Point cloud self-adaptive processing method, device and medium based on dental scanner
CN115984147B (en) * 2023-03-17 2023-09-15 汉斯夫(杭州)医学科技有限公司 Dental scanner-based point cloud self-adaptive processing method, device and medium
CN116955444A (en) * 2023-06-15 2023-10-27 共享易付(广州)网络科技有限公司 Method and system for mining collected noise points based on big data analysis
CN116843563A (en) * 2023-06-25 2023-10-03 成都飞机工业（集团）有限责任公司 Point cloud noise reduction processing method

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