CN111968089A - L1 median skeleton extraction method based on maximum inscribed sphere mechanism - Google Patents
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Abstract
The invention provides a median skeleton extraction method based on a maximum inscribed sphere mechanism, which relates to the field of image processing and comprises the following steps: acquiring a three-dimensional point cloud data set of a three-dimensional object; acquiring a maximum inscribed sphere and a sphere center of the three-dimensional data according to the three-dimensional point cloud data set, wherein the sphere center is used as a model skeleton point; randomly sampling the three-dimensional point cloud data, performing multiple iterations on initial sampling points, and fixing the regularly arranged sampling points as skeleton branches; connecting the head end and the tail end of the skeleton branch as bridging points with sampling points which are continuously contracted to generate a new skeleton; and expanding the local neighborhood range until the sampling point tends to be stable, and generating a global framework. The invention provides a maximum inscribed sphere mechanism-based L1The median skeleton extraction algorithm sets the neighborhood radius of the maximum inscribed sphere fitting for each sampling point and dynamically enlarges the radius, reduces the iterative convergence times of the algorithm, improves the algorithm efficiency, and improves the extraction efficiencyAnd connecting the taken skeleton branches to optimize and enhance the skeleton extraction result.
Description
Technical Field
The invention relates to the field of image processing, in particular to an L1 median skeleton extraction method based on a maximum inscribed sphere mechanism.
Background
L1Median extractionThe main principle of the skeleton is through L1Solving the mapping of the point cloud data by the median theory, obtaining k adjacent points of the sampling points, introducing a Gaussian weight function to solve the problem of uneven point cloud distribution density, and carrying out multiple iterations to ensure that local L is formed1The median value is small and stable enough to enable the sampling point to shrink to the local center of the neighborhood range, and the skeleton point is obtained.
In the prior art, L1The median skeleton extraction algorithm is suitable for extracting the model skeleton with lower flat curvature and uniform size distribution, and the extraction result of the model algorithm with uneven size distribution and larger curvature is not ideal. L is1When the median skeleton extraction algorithm is initialized, the radius of the global sampling point field is the same, the sampling points are easily affected by point clouds in other regions, so that the convergence of skeleton points is inaccurate, the excessive convergence topological structure of a smaller region is incomplete, the iteration times of the sampling points in a larger region are excessive, and the calculation amount of the algorithm is increased efficiently.
Disclosure of Invention
In order to overcome the problems in the prior art, the invention provides an L1 median skeleton extraction method based on a maximum inscribed sphere mechanism, which comprises the following steps:
step S1, acquiring a three-dimensional point cloud data set of the three-dimensional object;
step S2, acquiring a maximum inscribed sphere and a sphere center of three-dimensional data according to the three-dimensional point cloud data set, wherein the sphere center is used as a model skeleton point;
step S3, randomly sampling the three-dimensional point cloud data, performing multiple iterations on initial sampling points, and fixing the regularly arranged sampling points as skeleton branches;
step S4, taking the head and tail ends of the skeleton branch as bridging points, and connecting the bridging points with sampling points which are continuously contracted to generate a new skeleton;
and S5, expanding the local neighborhood range until the sampling point tends to be stable, and generating a global skeleton.
In this embodiment, in step S2, the method further includes:
step S21, in the three-dimensional point cloud data, the extraction of the maximum inscribed sphere may start from an initial point inside the data model, calculate a vector of the initial point and a closest point of the surface of the data model, and extend the initial point in a negative direction of the vector to adjust the position of the initial point;
step S22, the point position is moved from a position with a low distance field to a position with a high distance field, and the maximum inscribed sphere and the sphere center of the three-dimensional data are searched through iterative adjustment of the algorithm for multiple times;
step S23, the sphere radius is limited by the euclidean distance of the interior points of the data set.
In this embodiment, in step S2, the point cloud data set Q ═ Q in the non-orientationjIn the formula, X is ═ XiDenotes L1Skeleton points obtained by a median method; said X satisfies
The point x in each sampling point set I is obtained by regularizing the sampling dataiThe new coordinates of (a) are:
In the present embodiment, step S3 includes:
gradually enlarging the radius of the neighborhood, and distributing new sampling points at the head and the tail of the framework branch until all the sampling points in the neighborhood are iteratively contracted to form new framework points and are connected into the framework branch.
In the present embodiment, step S4 includes:
step S41, neighbor by KThe point smoothing method comprises screening candidate points of skeleton branches from unmarked sampling points, and calculating the average value of the candidate points
Obtaining the value of the sampling point sigma when sigma isiIf the value is larger than the given threshold value, the unmarked fixed sampling points become skeleton candidate points;
s42, selecting a determined skeleton point from the skeleton candidate points to be connected with the skeleton branch, firstly selecting a point q closest to the skeleton branch from the candidate points, starting searching from the point q along the PCA direction of the skeleton branch, and when an included angle between the candidate point and the skeleton branch meets cos ([ x ] (x) ]ixi-1,xixi+1) Is less than or equal to-0.9, i., -1,0, 1., i.e. the adjacent included angle is less than 15 degrees, the sampling candidate points are merged into the skeleton branch. Calculating the candidate points according to the method, if the number of the sampling points of the newly fused skeleton branch is more than 4, the new skeleton branch is reliable, if the number of the sampling points of the newly fused skeleton branch is less than 4, the newly fused candidate points are removed, and the residual sigma is continued to be calculatediSearching the candidate point with the maximum value; the bridge connection points are end points of the head and the tail of the framework branch, the bridge connection points are not invariable, and when the distance between the nearest candidate point and the bridge connection point is larger than 2 h; when the included angle between the direction of the candidate point and the bridging point is larger than 90 degrees and the distance between the candidate point and the bridging point exceeds three times of the radius of the field, two bridging points appear, and the included angle between the framework branches where the two bridging points are located is larger than 155 degrees, and the two bridging points are combined into one point.
In the present embodiment, step S5 includes:
step S51, for the point cloud model, calculating according to the initial neighborhood radius to obtain the model part skeleton branch, for other parts of the model, the sampling points are not gathered to the center of the model, the neighborhood radius needs to be enlarged, and the sampling points are iterated continuously and shrunk to meet the local L1Obtaining framework branches from the median properties;
step S52, deleting scattered sampling points around the converged skeleton branches if the scattered sampling points exist around the converged skeleton branches, and improving algorithm efficiency and stability; the growth rate of the neighborhood radius is h0/10，h0Maximum inscribed sphere radius of a sample pointRi/4；
And S53, iteratively updating the neighborhood radius at the growth rate until all the sampling points meet the median of the local L1 to obtain the final skeleton.
In this embodiment, in the step S53, the distance d is iterated twice before and after the sampling pointi,i+1<0.0005dboxAnd if the diagonal length of the model bounding box is less than 0.0005, the final skeleton is obtained.
The invention has the beneficial effects that: the invention provides an L based on a maximum inscribed sphere mechanism1And the median framework extraction algorithm sets the neighborhood radius of the maximum inscribed sphere fitting for each sampling point and dynamically enlarges the radius, so that the iterative convergence times of the algorithm are reduced, the algorithm efficiency is improved, and the extracted framework branch connection is optimized to enhance the framework extraction result.
Drawings
Fig. 1 is a flowchart of an L1 median skeleton extraction method based on a maximum inscribed sphere mechanism provided by the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
as shown in fig. 1, the present invention provides a method for extracting a median skeleton of L1 based on a maximum inscribed sphere mechanism, which includes:
step S1, acquiring a three-dimensional point cloud data set of the three-dimensional object;
step S2, acquiring a maximum inscribed sphere and a sphere center of three-dimensional data according to the three-dimensional point cloud data set, wherein the sphere center is used as a model skeleton point;
step S3, randomly sampling the three-dimensional point cloud data, performing multiple iterations on initial sampling points, and fixing the regularly arranged sampling points as skeleton branches;
step S4, taking the head and tail ends of the skeleton branch as bridging points, and connecting the bridging points with sampling points which are continuously contracted to generate a new skeleton;
and S5, expanding the local neighborhood range until the sampling point tends to be stable, and generating a global skeleton.
In this embodiment, in step S2, the method further includes:
step S21, in the three-dimensional point cloud data, the extraction of the maximum inscribed sphere may start from an initial point inside the data model, calculate a vector of the initial point and a closest point of the surface of the data model, and extend the initial point in a negative direction of the vector to adjust the position of the initial point;
step S22, the point position is moved from a position with a low distance field to a position with a high distance field, and the maximum inscribed sphere and the sphere center of the three-dimensional data are searched through iterative adjustment of the algorithm for multiple times;
step S23, the sphere radius is limited by the euclidean distance of the interior points of the data set.
In this embodiment, in step S2, the point cloud data set Q ═ Q in the non-orientationjIn the formula, X is ═ XiDenotes L1Skeleton points obtained by a median method; said X satisfies
The point x in each sampling point set I is obtained by regularizing the sampling dataiThe new coordinates of (a) are:
the above-mentioned
The { gamma } isiI belongs to I as a balance parameter for stabilizing the repulsion relation among sampling points in the sampling data set; and J is a point cloud original data set, mu is a fixed parameter value and can control the repulsion between sampling points, and the parameter value mu is 0.35 obtained by experimental analysis.
In the present embodiment, step S3 includes:
gradually enlarging the radius of the neighborhood, and distributing new sampling points at the head and the tail of the framework branch until all the sampling points in the neighborhood are iteratively contracted to form new framework points and are connected into the framework branch.
In the present embodiment, step S4 includes:
s41, screening candidate points of the skeleton branch from unmarked sampling points by a K neighbor point smoothing method, and obtaining the candidate points of the skeleton branch by a formula
Obtaining the value of the sampling point sigma when sigma isiIf the value is larger than the given threshold value, the unmarked fixed sampling points become skeleton candidate points;
s42, selecting a determined skeleton point from the skeleton candidate points to be connected with the skeleton branch, firstly selecting a point q closest to the skeleton branch from the candidate points, starting searching from the point q along the PCA direction of the skeleton branch, and when an included angle between the candidate point and the skeleton branch meets cos ([ x ] (x) ]ixi-1,xixi+1) Is less than or equal to-0.9, i., -1,0, 1., i.e. the adjacent included angle is less than 15 degrees, the sampling candidate points are merged into the skeleton branch. Calculating the candidate points according to the method, if the number of the sampling points of the newly fused skeleton branch is more than 4, the new skeleton branch is reliable, if the number of the sampling points of the newly fused skeleton branch is less than 4, the newly fused candidate points are removed, and the residual sigma is continued to be calculatediSearching the candidate point with the maximum value; the bridge connection points are end points of the head and the tail of the framework branch, the bridge connection points are not invariable, and when the distance between the nearest candidate point and the bridge connection point is larger than 2 h; when the included angle between the direction of the candidate point and the bridging point is larger than 90 degrees and the distance between the candidate point and the bridging point exceeds three times of the radius of the field, two bridging points appear, and the included angle between the framework branches where the two bridging points are located is larger than 155 degrees, and the two bridging points are combined into one point.
In the present embodiment, step S5 includes:
step S51, for the point cloud model, calculating according to the initial neighborhood radius to obtain the model part skeleton branch, for other parts of the model, the sampling points are not gathered to the center of the model, the neighborhood radius needs to be enlarged, and the sampling points are iterated continuously and shrunk to meet the local L1Obtaining framework branches from the median properties;
step S52, deleting the converged skeleton branch if scattered sampling points exist around the converged skeleton branch, and improving algorithm efficiencyAnd stability; the growth rate of the neighborhood radius is h0/10，h0Maximum inscribed sphere radius R for a sample pointi/4；
And S53, iteratively updating the neighborhood radius at the growth rate until all the sampling points meet the median of the local L1 to obtain the final skeleton.
In this embodiment, in the step S53, the distance d is iterated twice before and after the sampling pointi,i+1<0.0005dboxAnd if the diagonal length of the model bounding box is less than 0.0005, the final skeleton is obtained.
In this embodiment, the initial skeleton of the point cloud obtained by the above algorithm may have the problems of insufficient fineness and roughness of the skeleton connection at the boundary of the skeleton branches, so this embodiment smoothes the point cloud skeleton by using Laplace smoothing and quadrilateral subdivision. The method comprises the following specific steps:
step S61, analyzing the node of each skeleton branch, and calculating each node S except the head end and the tail end of the skeletoniWith neighboring node si-1And si+1If the included angle theta is larger than 50 degrees, adopting Laplace smoothness of one-dimensional space for the node, wherein the formula is si＝si-1/4+si/2+si+1/4。
Step S62, four-point difference subdivision is carried out on each skeleton branch, the Euclidean distance between two adjacent points after subdivision is smaller than a given threshold value, and Laplace smoothing is carried out on the subdivided skeleton branches again
Step S63, searching along the direction of each skeleton branch by taking the first node of each skeleton branch as a starting point, and if the node exceeds a set threshold value 2h0And performing downsampling once to finally extract a smooth framework with uniform framework points.
The invention provides an L based on a maximum inscribed sphere mechanism1And the median framework extraction algorithm sets the neighborhood radius of the maximum inscribed sphere fitting for each sampling point and dynamically enlarges the radius, so that the iterative convergence times of the algorithm are reduced, the algorithm efficiency is improved, and the extracted framework branch connection is optimized to enhance the framework extraction result.
The foregoing detailed description of the preferred embodiments of the invention has been presented. It should be understood that numerous modifications and variations could be devised by those skilled in the art in light of the present teachings without departing from the inventive concepts. Therefore, the technical solutions available to those skilled in the art through logic analysis, reasoning and limited experiments based on the prior art according to the concept of the present invention should be within the scope of protection defined by the claims.
Claims (7)
1. A median skeleton extraction method based on a maximum inscribed sphere mechanism is characterized by comprising the following steps:
step S1, acquiring a three-dimensional point cloud data set of the three-dimensional object;
step S2, acquiring a maximum inscribed sphere and a sphere center of three-dimensional data according to the three-dimensional point cloud data set, wherein the sphere center is used as a model skeleton point;
step S3, randomly sampling the three-dimensional point cloud data, performing multiple iterations on initial sampling points, and fixing the regularly arranged sampling points as skeleton branches;
step S4, taking the head and tail ends of the skeleton branch as bridging points, and connecting the bridging points with sampling points which are continuously contracted to generate a new skeleton;
and S5, expanding the local neighborhood range until the sampling point tends to be stable, and generating a global skeleton.
2. The method for extracting median skeleton according to claim 1, wherein in step S2, the method further comprises:
step S21, in the three-dimensional point cloud data, the extraction of the maximum inscribed sphere may start from an initial point inside the data model, calculate a vector of the initial point and a closest point of the surface of the data model, and extend the initial point in a negative direction of the vector to adjust the position of the initial point;
step S22, the point position is moved from a position with a low distance field to a position with a high distance field, and the maximum inscribed sphere and the sphere center of the three-dimensional data are searched through iterative adjustment of the algorithm for multiple times;
step S23, the sphere radius is limited by the euclidean distance of the interior points of the data set.
3. The method as claimed in claim 1, wherein in step S2, in the unoriented point cloud data set Q ═ Q, the method for extracting median skeleton based on the maximum inscribed sphere mechanismjIn the formula, X is ═ XiDenotes L1Skeleton points obtained by a median method; said X satisfies
The point x in each sampling point set I is obtained by regularizing the sampling dataiThe new coordinates of (a) are:
the above-mentioned
The { gamma } isiI belongs to I as a balance parameter for stabilizing the repulsion relation among sampling points in the sampling data set; and J is a point cloud original data set, mu is a fixed parameter value and can control the repulsion between sampling points, and the parameter value mu is 0.35 obtained by experimental analysis.
4. The method for extracting the median skeleton based on the maximum inscribed sphere mechanism according to claim 1, wherein the step S3 includes:
gradually enlarging the radius of the neighborhood, and distributing new sampling points at the head and the tail of the framework branch until all the sampling points in the neighborhood are iteratively contracted to form new framework points and are connected into the framework branch.
5. The method for extracting the median skeleton based on the maximum inscribed sphere mechanism according to claim 1, wherein in step S4, the method comprises:
s41, screening candidate points of the skeleton branch from unmarked sampling points by a K neighbor point smoothing method, and obtaining the candidate points of the skeleton branch by a formula
Obtaining the value of the sampling point sigma when sigma isiIf the value is larger than the given threshold value, the unmarked fixed sampling points become skeleton candidate points;
s42, selecting a determined skeleton point from the skeleton candidate points to be connected with the skeleton branch, firstly selecting a point q closest to the skeleton branch from the candidate points, starting searching from the point q along the PCA direction of the skeleton branch, and when an included angle between the candidate point and the skeleton branch meets cos ([ x ] (x) ]ixi-1,xixi+1) Is less than or equal to-0.9, i., -1,0, 1., i.e. the adjacent included angle is less than 15 degrees, the sampling candidate points are merged into the skeleton branch. Calculating the candidate points according to the method, if the number of the sampling points of the newly fused skeleton branch is more than 4, the new skeleton branch is reliable, if the number of the sampling points of the newly fused skeleton branch is less than 4, the newly fused candidate points are removed, and the residual sigma is continued to be calculatediSearching the candidate point with the maximum value; the bridge connection points are end points of the head and the tail of the framework branch, the bridge connection points are not invariable, and when the distance between the nearest candidate point and the bridge connection point is larger than 2 h; when the included angle between the direction of the candidate point and the bridging point is larger than 90 degrees and the distance between the candidate point and the bridging point exceeds three times of the radius of the field, two bridging points appear, and the included angle between the framework branches where the two bridging points are located is larger than 155 degrees, and the two bridging points are combined into one point.
6. The method for extracting the median skeleton based on the maximum inscribed sphere mechanism according to claim 1, wherein in step S5, the method comprises:
step S51, for the point cloud model, calculating according to the initial neighborhood radius to obtain the model part skeleton branch, for other parts of the model, the sampling points are not gathered to the center of the model, the neighborhood radius needs to be enlarged, and the sampling points are iterated continuously and shrunk to meet the local L1Obtaining framework branches from the median properties;
step S52, branching the converged skeleton, if surroundingIf scattered sampling points exist, the scattered sampling points are deleted, and the efficiency and the stability of the algorithm are improved; the growth rate of the neighborhood radius is h0/10，h0Maximum inscribed sphere radius R for a sample pointi/4；
And S53, iteratively updating the neighborhood radius at the growth rate until all the sampling points meet the median of the local L1 to obtain the final skeleton.
7. The method as claimed in claim 6, wherein in step S53, the distance d is iterated twice before and after the sampling pointi,i+1<0.0005dboxAnd if the diagonal length of the model bounding box is less than 0.0005, the final skeleton is obtained.
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| CN112686799A (en) * | 2020-12-25 | 2021-04-20 | 燕山大学 | Annular forging section line extraction method based on normal vector and L1 median |
| CN114565658A (en) * | 2022-01-14 | 2022-05-31 | 武汉理工大学 | Pore size calculation method and device based on CT technology |
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Cited By (5)
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| CN112465832A (en) * | 2020-11-25 | 2021-03-09 | 重庆大学 | Single-sided tree point cloud skeleton line extraction method and system based on binocular vision |
| CN112465832B (en) * | 2020-11-25 | 2024-04-16 | 重庆大学 | Single-side tree point cloud skeleton line extraction method and system based on binocular vision |
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| CN112686799B (en) * | 2020-12-25 | 2022-05-10 | 燕山大学 | Annular forging section line extraction method based on normal vector and L1 median |
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