CN110807781B - Point cloud simplifying method for retaining details and boundary characteristics - Google Patents
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Abstract
The invention discloses a point for retaining details and boundary characteristicsThe cloud simplifying method comprises the following steps of reading original point cloud model data, obtaining the original point cloud data, performing rasterization processing, and establishing a local k-d tree; fitting the minimum micro tangential plane, and calculating the weighted equivalent resultant force F of the projection points of the point cloud data i And average value F of F when i F, the boundary points are reserved, and a simplified boundary subset PSet1 is obtained; for non-boundary points, its local density ρ is estimated i Partitioning to obtain corresponding subsets; calculating normal vector of non-boundary point according to local density ρ i Calculating local feature factor D i And average value D thereof, respectively selecting threshold value mu for corresponding subset TH When D i /D＞μ TH Reserving the point cloud data to obtain a simplified subset PSet2 of the characteristic points; the method and the device for obtaining the point cloud data set PSet are convenient for obtaining the point cloud model with proper data quantity and no distortion, improve the point cloud compaction efficiency and enable the curved surface detail feature and the boundary feature to be described more accurately.
Description
Technical Field
The invention relates to the field of reverse engineering and mapping research, in particular to a point cloud simplifying method for retaining details and boundary characteristics.
Background
With the continuous development of three-dimensional scanning technology, machine vision and other technologies, three-dimensional point cloud data has been widely used in the fields of industrial detection, reverse engineering, medical diagnosis, cultural relics protection and the like. Meanwhile, as the precision and speed of the non-contact scanning equipment are higher and higher, the acquired point cloud data volume is also increased sharply. In the actual measurement process, dense point clouds of hundreds of thousands or even millions of data points can be obtained, and the generated redundant data points greatly increase the computational load of a computer. Therefore, on the premise of not influencing the characteristics of the object to be detected, the obtained three-dimensional point cloud data is reduced.
In recent years, the reduction of point cloud data is mainly divided into two main methods based on space division and curvature itself. Space division-based methods include a bounding box method, a uniform mesh method, and a triangular mesh method. The bounding box method achieves the purpose of simplifying by keeping the point closest to the center of the grid in each halving grid of the minimum bounding box of the point cloud data. The method has better processing results for the model with large data volume and simple structure, but loses much detail for the model with complex structure and various curvature of the curved surface. The uniform grid method is an optimization method of the bounding box method, and the method is used for simplifying the median point of Z coordinates in the cube by calculating the median point by using median filtering. The method based on triangle gridding needs to triangulate the original point cloud data, and removes partial triangles through normal vectors of the triangles to achieve the purpose of simplification. Curvature-based methods typically require constructing a point cloud topology by K-neighborhood search and fitting a least squares surface, and finally developing different reduction strategies by curvature thresholds. The method has better simplifying effect, but the calculation of the curvature is generally time-consuming, and other schemes for indirectly replacing the calculation of the curvature are generally required to be searched for optimization.
In the prior art, CN101373540B discloses a point cloud reduction method based on parabolic fitting, the method is essentially a reduction algorithm based on curvature threshold, and the time cost in curvature calculation is a disadvantage that the method cannot avoid; CN101021954a discloses a point cloud simplifying method for simplifying curvature calculation, in which the ratio of the distance from a point to be measured to a neighborhood point to the distance from the point to be measured to a fitted micro tangential plane is used for substituting for curvature calculation, and the average value of the approximate curvature and the difference value of the approximate curvature of each point are used as decision thresholds for carrying out point cloud simplifying; CN102890828A discloses a point cloud data simplifying method based on normal included angle, which comprises calculating average value of dot product of normal vector of each point cloud data point and normal vector of point cloud data point in neighborhood, dividing interval and setting sampling ratio by variation of the value, deleting point not conforming to sampling ratio, avoiding complex quadric surface fitting and curvature estimation, however, in practical application, too many parameters are needed to be set manually, and practical effect often varies from experience to experience; CN106373118A discloses a method for simplifying point clouds of complex curved surface parts capable of effectively retaining boundary and local features, the method uses point cloud normal vector and neighborhood point cloud normal vector dot product as threshold values to perform coarse classification, then completes the subdivision of point cloud data through k-means clustering method and Hausdorff distance to complete the simplification of point cloud data, and the result of the k-means clustering method is not stable enough due to the fact that the factors of distance weights are not considered during neighborhood searching and point cloud normal vector calculation, so that unpredictable errors finally appear on boundary feature retention.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art, and provides a point cloud simplifying method for reserving detail and boundary characteristics, which is convenient for acquiring a point cloud model with proper data quantity and no distortion, improves the point cloud simplifying efficiency and ensures that the description of the detail characteristics and the boundary characteristics of a curved surface is more accurate.
The aim of the invention is achieved by the following technical scheme:
the point cloud simplifying method for reserving details and boundary features is characterized by comprising the following steps of:
s1, reading original point cloud model data to obtain the original point cloud data;
s2, rasterizing the original point cloud data, and establishing a local k-d tree, wherein the local k-d tree is established, specifically, the k-d tree is established only in the grid where each point cloud data is located and the neighborhood grid thereof; wherein the neighborhood grid of each point cloud data is defined as (l) x ±i,l y ±j,l z ±k)，i,j,k∈[-1,1]；
S3, fitting a minimum micro-tangential plane to the point cloud data and the k neighborhood points of the point cloud data after the rasterization processing, projecting the point cloud data and the k neighborhood points of the point cloud data onto the micro-tangential plane, solving a vector from the projection point of the point cloud data to the neighborhood projection point of the point cloud data, normalizing the vector to obtain normalized dataCalculating the weighted equivalent resultant force F of the projection points of the point cloud data i Further, the average value F of the weighted equivalent resultant force is calculated, if F i If the point cloud data is more than F, the point cloud data is regarded as boundary points, and the boundary points are reserved to obtain a simplified boundary subset PSet1;
s4, for non-boundary points, estimating local density rho in k adjacent domains to which each point cloud data belongs i And proceed withPartitioning to obtain an under-characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 ；
S5, calculating normal vector of non-boundary point, and calculating weighted average value theta of included angle between each point cloud data and normal vector of each point in neighborhood according to distance weight i ；
S6, according to the local density rho i Calculating local characteristic factors, and further calculating average values of the local characteristic factors, wherein the local characteristic factors are respectively an under-characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 Selecting an appropriate threshold mu TH When D i /D＞μ TH When the point cloud data is reserved, otherwise, deleting the point cloud data, and merging the point cloud data sets reserved by each subset to obtain a characteristic point simplified subset PSet2;
and S7, merging the boundary reduced subset PSet1 and the feature point reduced subset PSet2 to obtain a reduced point cloud data set PSet.
Further, the step S2 specifically includes: dividing the side length L of a cube grid according to the random sampling density rho of the point cloud data, wherein the minimum side length L of the cube grid is m times of the sampling density rho, dividing a point cloud data bounding box into space grids, and establishing k neighborhood for each point cloud data.
Further, the partitioning of the point cloud data bounding box into a space grid specifically includes: dividing the point cloud data into grid numbers M according to the x, y and z directions x ,M y ,M z The calculation is as follows:
wherein ,xmax Maximum value of x direction of coordinates, x min Is the minimum value of the coordinate x direction, y max For the maximum value of the coordinate y direction, y min Is the minimum value of the coordinate in the y direction, z max For maximum z direction of coordinates, z min Is the minimum value of the coordinate z direction;for rounding, δ is the expansion.
Further, the sampling density ρ is obtained by the following calculation:
wherein n is the number of the point cloud data which are randomly taken out, the value range of n is 20-30, and d i Is the interval from the closest point of the point cloud data.
Further, the step S3 specifically includes: fitting a micro tangential plane to each point cloud data and the k neighborhood points thereof, wherein the least micro tangential plane is fitted by using a least square method, projecting the point cloud data and the k neighborhood points thereof onto the micro tangential plane, solving the vector from the projection point of the point cloud data to the neighborhood projection point thereof, normalizing the vector to obtain normalized dataWherein j is E [1, k]The method comprises the steps of carrying out a first treatment on the surface of the The weighted equivalent resultant force of the projection points of the point cloud data is calculated as follows:
the total force value represents the distribution condition of neighborhood point cloud data of projection points of the point cloud data, and the total force value represents that the point cloud data is biased to one side;
wherein ,wij Is thatWeighting coefficients of (2); d, d ij Is->I.e. the neighborhood of the projected point of the point cloud data to the point cloud dataThe distance of the projection point;
the average of the weighted equivalent resultant forces is calculated as follows:
the resultant average value represents the average distribution condition of the neighborhood point clouds of each projection point of the point cloud data set;
if F i And if the point cloud data is more than F, the point cloud data is regarded as boundary points, and the boundary points are reserved to obtain a simplified boundary subset PSet1.
Further, the step S4 specifically includes: for non-boundary points, estimating local density rho in k adjacent domain to which each point cloud data belongs i The method comprises the steps of carrying out a first treatment on the surface of the According to ρ i Maximum value ρ of (1) max And a minimum value ρ min Dividing point cloud data of non-boundary points into under-feature point sets S 1 Feature point set S 2 And rich feature point set S 3 The partitioning is calculated as follows:
wherein ,Pi Is random non-boundary point cloud data.
Further, the calculation of the local density ρi is specifically as follows:
wherein ,for the vector from the point cloud data to the neighborhood point cloud +.>The smaller the mean value of (c), the denser the neighborhood in which the point cloud data is located, and the larger ρi.
Further, the method comprises the steps of,the step S5 specifically comprises the following steps: calculating the normal vector of each point cloud data in each subset by a principal component analysis methodAnd calculating a weighted average value theta of the included angles between each point cloud data and the normal vector of each point in the neighborhood according to the distance weight i The calculation is as follows:
wherein ,||pij I is the euclidean distance of the point cloud data to each point in its neighborhood,normal vector of each point in the neighborhood of the point cloud data;
further, the step S6 specifically includes: and calculating a local characteristic factor of the point cloud data according to the local density ρi, wherein the local characteristic factor is calculated as follows:
wherein ,the representation belonging to subset S u And u is [1,2,3 ]]；D i Local characteristic factors of the point cloud data;
calculating the average local characteristic factor of the subset of the point cloud data according to the local characteristic factor of each point cloud data:
wherein ,is a subset S u Is a mean local feature factor of (2);
respectively is an under-characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 A selected threshold mu TH I.e. the corresponding threshold values are respectivelyThe threshold mu TH The value is specifically as follows: under-feature point set S 1 Threshold of->Preferably 0.2, feature point set S 2 Threshold of->Preferably 0.4, and a feature-rich point set S 3 Threshold of->Preferably 0.6, the non-characteristic points, the characteristic points and the rich characteristic points are excessively smooth, so that holes and excessive aggregation of details are avoided.
When D is i /D＞μ TH And when the point cloud data is reserved, otherwise, deleting the point cloud data, and merging the point cloud data sets reserved by each subset to obtain a characteristic point reduced subset PSet2.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention adopts rasterization and local k-d tree to build the topological structure of the point cloud, avoids the overlength of the global k-d tree building time, adopts distance weighting, avoids the influence of remote neighborhood point cloud data on the judgment of boundary points and characteristic points, adopts density weighting, avoids the possible occurrence of hole phenomenon of non-uniform point cloud data characteristic point extraction, and is suitable for a closed point cloud model with obvious boundary characteristics.
Drawings
FIG. 1 is a flow chart of a point cloud compaction method for preserving detail and boundary features according to the present invention;
FIG. 2 is a schematic diagram illustrating non-boundary point determination according to an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating boundary point determination according to an embodiment of the present invention;
FIG. 4 is a diagram of an original model of a point cloud according to an embodiment of the present invention;
fig. 5 is a simplified model diagram of a point cloud according to an embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
Examples:
the point cloud simplifying method for retaining detail and boundary features includes the following steps,
firstly, original point cloud data with the number of data points N is read, the point cloud data is subjected to rasterization, and a local k-d tree is established, namely, the side length L of a cube grid is divided according to the random sampling density rho of the point cloud data, the minimum side length L of the cube grid is m times of the sampling density rho, and the value range of m is 1.2-1.5; the method comprises the steps of dividing a point cloud data bounding box into space grids, wherein the dividing of the point cloud data bounding box into space grids specifically comprises the following steps: dividing the point cloud data into grid numbers M according to the x, y and z directions x ,M y ,M z The calculation is as follows:
wherein ,xmax Maximum value of x direction of coordinates, x min Is the minimum value of the coordinate x direction, y max For the maximum value of the coordinate y direction, y min Is the minimum value of the coordinate in the y direction, z max For maximum z direction of coordinates, z min Is the minimum value of the coordinate z direction;for rounding, δ is the expansion;
the grid coordinates of the point cloud data after the rasterization processing are calculated as follows:
wherein (x, y, z) is the geometric coordinates of the point cloud data,for rounding, δ is the expansion;
establishing k neighborhood for each point cloud data, wherein the value range of k is 15-20;
the sampling density ρ is obtained by the following calculation:
wherein n is the number of the point cloud data which are randomly taken out, d i Is the interval from the closest point of the point cloud data. The value range of n is 20-30.
The local k-d tree is built, specifically, each point cloud data only builds a k-d tree on the grid where the point cloud data is located and the neighborhood grid of the point cloud data; wherein the neighborhood grid of each point cloud data is defined as (l) x ±i,l y ±j,l z ±k)，i,j,k∈[-1,1]。
Second step, for each point cloud data p i And k neighborhood points fit a micro-facet, where the least micro-facet is fit using least squares. And the point cloud data p i And the point of the k neighborhood is projected onto a micro-tangential plane to obtain the point cloud data p i The vector from the projection point P to the neighborhood projection point is normalized to obtain normalized dataWherein j is E [1, k]；
Thirdly, calculating weighted equivalent resultant force F of projection points P of the point cloud data i The calculation is as follows:
the total force value represents the distribution condition of the point cloud adjacent to the projection point P, and the total force value represents the deviation of the point cloud data to one side;
wherein ,wij Is thatWeighting coefficients of (2); d, d ij Is->I.e. the distance from the projection point of the point cloud data to the neighborhood projection point of the point cloud data;
the non-boundary point judging schematic diagram is shown in fig. 2, the boundary point judging schematic diagram is shown in fig. 3, if the k neighborhood resultant force value of the projection point is large, the projection point is considered as a boundary point at the moment, otherwise, the distribution of the point is uniform, the point is considered as an internal point, and whether the target point is the boundary point is judged according to the result;
calculate the weighted equivalent resultant force F i Is calculated as follows:
the resultant average value represents the average distribution condition of the neighborhood point clouds of each projection point of the point cloud data set;
if F i If the point cloud data is more than F, the point cloud data is regarded as boundary points, and the boundary points are reserved to obtain a simplified boundary subset PSet1;
fourth, for non-boundary points, estimating local density ρ in k-neighborhood to which each point cloud data belongs i The method comprises the steps of carrying out a first treatment on the surface of the The local density ρ i The calculation of (2) is as follows:
wherein ,for the vector from the point cloud data to the neighborhood point cloud +.>The smaller the mean value of (a), the denser the neighborhood of the point cloud data is, ρ i The larger;
according to ρ i Maximum value ρ of (1) max And a minimum value ρ min Dividing point cloud data of non-boundary points into under-feature point sets S 1 Feature point set S 2 And rich feature point set S 3 The partitioning is calculated as follows:
wherein ,Pi For random non-boundary point cloud data, the density of the corresponding neighborhood is ρ i Is a point of (2).
Fifth step, calculating the normal vector of each point cloud data in each subsetThe subset here comprises the under-feature point set S 1 Feature point set S 2 And rich feature point set S 3 The method comprises the steps of carrying out a first treatment on the surface of the The method comprises the steps of carrying out a first treatment on the surface of the Normal vector of Point cloud data here +.>The estimation method adopts a principal component analysis method, and calculates the weighted average value theta of the included angle between each point cloud data and the normal vector of each point in the neighborhood according to the distance weight i The calculation is as follows:
wherein ,||pij I is the point cloud data to each point in the neighborhood of the point cloud dataThe distance of the euro type,normal vector of each point in the neighborhood of the point cloud data;
sixth step, according to local density ρ i The local characteristic factor of the point cloud data is calculated as follows:
wherein ,the representation belonging to subset S u And u is [1,2,3 ]]；D i Local characteristic factors of the point cloud data;
calculating the average local characteristic factor of the subset of the point cloud data according to the local characteristic factor of each point cloud data:
wherein ,is a subset S u Is a mean local feature factor of (2);
respectively is an under-characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 A selected threshold mu TH I.e. the corresponding threshold values are respectivelyThe threshold mu TH The value is specifically as follows: under-feature point set S 1 Threshold of->Preferably 0.2, feature point set S 2 Threshold of->Preferably 0.4, and a feature-rich point set S 3 Threshold of->Preferably 0.6.
When D is i /D＞μ TH When the point cloud data is reserved, otherwise, deleting the point cloud data, and merging the point cloud data sets reserved by each subset to obtain a characteristic point simplified subset PSet2;
and seventhly, merging the boundary reduced subset PSet1 and the feature point reduced subset PSet2, wherein the merging does not have the problem of deleting duplicate points, and the merging is directly carried out, so that the reduced point cloud data set PSet is obtained.
The point cloud with 10000 cats shown in fig. 4 was subjected to 4400-point reduction in combination with the above steps, and the final reduction result is shown in fig. 5. From the figure, the method provided by the invention well reserves the local and boundary characteristics of the point cloud data, and has beneficial effects on accuracy and simplicity.
The above examples are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above examples, and any other changes, modifications, substitutions, combinations, and simplifications that do not depart from the spirit and principle of the present invention should be made in the equivalent manner, and the embodiments are included in the protection scope of the present invention.
Claims (2)
1. The point cloud simplifying method for reserving details and boundary features is characterized by comprising the following steps of:
s1, reading original point cloud model data to obtain the original point cloud data;
s2, rasterizing the original point cloud data, and establishing a local k-d tree, wherein the local k-d tree is established, specifically, the k-d tree is established only in the grid where each point cloud data is located and the neighborhood grid thereof; wherein the neighborhood grid of each point cloud data is defined as (l) x ±i,l y ±j,l z ±k)，i,j,k∈[-1,1]；
The step S2 specifically comprises the following steps: dividing the side length L of a cube grid according to the random sampling density rho of the point cloud data, wherein the minimum side length L of the cube grid is m times of the sampling density rho, dividing a point cloud data bounding box into space grids, and establishing k neighborhood for each point cloud data;
the method for dividing the point cloud data bounding box into space grids specifically comprises the following steps: dividing the point cloud data into grid numbers M according to the x, y and z directions x ,M y ,M z The calculation is as follows:
wherein ,xmax Maximum value of x direction of coordinates, x min Is the minimum value of the coordinate x direction, y max For the maximum value of the coordinate y direction, y min Is the minimum value of the coordinate in the y direction, z max For maximum z direction of coordinates, z min Is the minimum value of the coordinate z direction;for rounding, δ is the expansion;
the sampling density ρ is obtained by the following calculation:
wherein n is the number of the point cloud data which are randomly taken out, the value range of n is 20-30, and d i Is the interval of the closest point to the point cloud data;
s3, fitting a minimum micro-tangential plane to the point cloud data and the k neighborhood points of the point cloud data after the rasterization processing, projecting the point cloud data and the k neighborhood points of the point cloud data onto the micro-tangential plane, solving a vector from the projection point of the point cloud data to the neighborhood projection point of the point cloud data, normalizing the vector to obtain normalized dataCalculating the weighted equivalent resultant force of the projection points of the point cloud dataF i Further, the average value F of the weighted equivalent resultant force is calculated, if F i If the point cloud data is more than F, the point cloud data is regarded as boundary points, and the boundary points are reserved to obtain a simplified boundary subset PSet1;
the step S3 specifically comprises the following steps: fitting a micro tangential plane to each point cloud data and the k neighborhood points thereof, wherein the least micro tangential plane is fitted by using a least square method, projecting the point cloud data and the k neighborhood points thereof onto the micro tangential plane, solving the vector from the projection point of the point cloud data to the neighborhood projection point thereof, normalizing the vector to obtain normalized dataWherein j is E [1, k]The method comprises the steps of carrying out a first treatment on the surface of the The weighted equivalent resultant force of the projection points of the point cloud data is calculated as follows:
wherein ,wij Is thatWeighting coefficients of (2); d, d ij Is->I.e. the distance from the projection point of the point cloud data to the neighborhood projection point of the point cloud data;
the average of the weighted equivalent resultant forces is calculated as follows:
wherein N is the total number of the point cloud data;
if F i If the point cloud data is more than F, the point cloud data is regarded as boundary points, and the boundary points are reserved to obtain a simplified boundary subset PSet1;
s4, for non-boundary points, estimating local density rho in k adjacent domains to which each point cloud data belongs i And partitioning to obtain a feature point set S 1 Feature point set S 2 And rich feature point set S 3 ；
The step S4 specifically includes: for non-boundary points, estimating local density rho in k adjacent domain to which each point cloud data belongs i The method comprises the steps of carrying out a first treatment on the surface of the According to ρ i Maximum value ρ of (1) max And a minimum value ρ min Dividing point cloud data of non-boundary points into under-feature point sets S 1 Feature point set S 2 And rich feature point set S 3 The partitioning is calculated as follows:
wherein ,Pi Random non-boundary point cloud data;
the local density ρ i The calculation of (2) is as follows:
wherein ,a vector from the point cloud data to the neighborhood point cloud;
s5, calculating normal vector of non-boundary point, and calculating weighted average value theta of included angle between each point cloud data and normal vector of each point in neighborhood according to distance weight i ；
The step S5 specifically comprises the following steps: calculating the normal vector of each point cloud data in each subset by a principal component analysis methodAnd calculating a weighted average value theta of the included angles between each point cloud data and the normal vector of each point in the neighborhood according to the distance weight i The calculation is as follows:
wherein ,||pij I is the euclidean distance of the point cloud data to each point in its neighborhood,normal vector of each point in the neighborhood of the point cloud data;
s6, according to the local density rho i Calculating local feature factor D i Further, the average value D is calculated to be respectively the under characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 A selected threshold mu TH I.e. the corresponding threshold values are respectivelyWhen D is i /D＞μ TH When the point cloud data is reserved, otherwise, deleting the point cloud data, and merging the point cloud data sets reserved by each subset to obtain a characteristic point simplified subset PSet2;
the step S6 specifically includes: according to local density ρ i The local characteristic factor of the point cloud data is calculated as follows:
wherein ,the representation belonging to subset S u And u is [1,2,3 ]]；D i Local characteristic factors of the point cloud data;
calculating the average local characteristic factor of the subset of the point cloud data according to the local characteristic factor of each point cloud data:
wherein ,is a subset S u Is a mean local feature factor of (2);
respectively is an under-characteristic point set S 1 Feature point set S 2 And rich feature point set S 3 A selected threshold mu TH I.e. the corresponding threshold values are respectively
When D is i /D＞μ TH When the point cloud data is reserved, otherwise, deleting the point cloud data, and merging the point cloud data sets reserved by each subset to obtain a characteristic point simplified subset PSet2;
and S7, merging the boundary reduced subset PSet1 and the feature point reduced subset PSet2 to obtain a reduced point cloud data set PSet.
2. The method for point cloud compaction with preservation of detail and boundary features according to claim 1, wherein the threshold μ TH The value is specifically as follows: under-feature point set S 1 Threshold of (2)Is 0.2, feature point set S 2 Threshold of->Is 0.4, and is rich in feature point set S 3 Threshold of->0.6.
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| CN111815611B (en) * | 2020-07-14 | 2024-03-22 | 南京航空航天大学 | Round hole feature extraction method for rivet hole measurement point cloud data |
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