WO2011079421A1 - 对点云数据进行全局参数化和四边形网格化方法 - Google Patents
对点云数据进行全局参数化和四边形网格化方法 Download PDFInfo
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- WO2011079421A1 WO2011079421A1 PCT/CN2009/001591 CN2009001591W WO2011079421A1 WO 2011079421 A1 WO2011079421 A1 WO 2011079421A1 CN 2009001591 W CN2009001591 W CN 2009001591W WO 2011079421 A1 WO2011079421 A1 WO 2011079421A1
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- main direction
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T17/00—Three dimensional [3D] modelling, e.g. data description of 3D objects
- G06T17/20—Finite element generation, e.g. wire-frame surface description, tesselation
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- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T2210/00—Indexing scheme for image generation or computer graphics
- G06T2210/56—Particle system, point based geometry or rendering
Definitions
- the invention relates to a point cloud data obtained by using a three-dimensional laser scanner for physical measurement in the field of computer graphics and computer vision technology, in particular to a method for global parameterization and quadrilateral meshing of point cloud data. Background technique
- quadrilateral meshes Due to the rapid and accurate development of laser scanners, point cloud data has been widely used in computer-aided design and computer graphics. Usually the original point cloud data does not contain any topology information, so a lot of research work is focused on how to reconstruct the mesh surface from point cloud data. But most of the work has focused on how to produce high-quality triangular patch mesh models, which lack control over the shape and orientation of triangular patches. Due to the tensor product of quadrilateral meshes, quadrilateral meshes have advantages in many areas, such as B-spline fitting, texture mapping, etc., relative to triangular meshes. In particular, quadrilaterals whose directions are consistent with the main direction are more advantageous in modeling because they reflect the symmetry of the geometric model.
- Global parameterization is an effective way to solve quadrilateral meshing.
- Ray (RAY, N., LI, WC, L' E VY, B. , SHEFFER, A., AND ALLIEZ, P. 2006. Periodic global parameterization. ACM Trans. Graph. 25, 4, 1460 - 1485. ) It is proposed to use the periodic global parameterization method to obtain the parameterization result consistent with the main direction.
- the desired quadrilateral meshing is obtained by extracting the contours of the parameterized results. This method results in a high quality quadrilateral mesh without manual intervention.
- Ray's method can only be applied to the surface of the triangle mesh.
- For the point cloud data due to the lack of topological connection between points, it is difficult to directly use the traditional global parameterization method for point cloud data processing. Summary of the invention
- a global parameterization and quadrilateral meshing method for point cloud data includes the following steps:
- Quadrilateral meshing provides an automatic and robust global parameterization method for discrete point cloud data obtained by laser scanning, and uses the parameterized result to obtain quadrilateral meshing which is consistent with the main direction and can reflect the intrinsic geometric features of the model. result.
- FIG. 1 is a basic frame diagram of an algorithm
- FIG. 2 is a flowchart of a main direction calculation
- Figure 3 is a global parameterization flowchart
- Figure 4 is a quadrilateral meshing flow chart
- Figure 5 is a schematic diagram of processing of contour segments
- Figure 6 is the result of the noise-added part model
- Figure 7 is a comparison between the results obtained by the method of the present invention on the point cloud model of the part and the results obtained by the Ray method on the mesh model of the part. detailed description
- the method is mainly divided into three basic steps: • Calculation of the main direction field; Global parameterization; Quadrilateral meshing.
- the specific algorithm for each step will be described in detail below.
- the calculation of the main directional field first requires the normal vector of each point of the point cloud. Because 3D point cloud data generally only has point coordinate information. In order to obtain the curvature tensor information of the point cloud and local triangulation of the point cloud, it is necessary to obtain the normal direction of each point in the point cloud data. First, build a kd tree. In computational geometry, the kd tree is one of the fastest data structures that have been proven to find neighbors. Kd > >> Tree based on point location information, iteratively divided by dichotomy
- the smoothing process makes the main directions of adjacent points as uniform as possible.
- This method defines a function that measures the difference in the main direction between adjacent points of point cloud data. By solving the minimum value of the function, the smoothed main direction can be obtained.
- p is the coefficient of control smoothness, which is the angle between the required main direction and a reference direction, which is defined as any direction on the tangent plane of point i, ", ° is the original main direction and
- the angle of the reference direction, ? y is the direction of the line segment connecting the two points of i, J'.
- the equation can be transformed into a quadratic optimization problem.
- the steepest descent method is used to solve the optimization problem.
- the optimal solution is the angle between the smoothed main direction and the reference direction. The angle can be used to find the smooth main direction.
- the purpose of global parameterization is to find the two scalar functions on the point cloud and ⁇ to find ⁇ and the specific value at each point, so that the maximum principal direction and the minimum principal direction of the point are respectively gradients with two scalar functions. Try to be consistent.
- global parameterization is divided into three steps: local triangulation; calculating the energy function of the point cloud; and finding the optimal solution of the energy function. Partial triangulation has been done in the calculation of the main direction field.
- the method first Define an energy function to measure this difference, defined as follows:
- the equation can be transformed into a quadratic optimization problem.
- the global parameterization result of the point cloud data can be obtained by using the steepest descent method to obtain the optimal solution of the problem.
- the contour of the contour is basically consistent with the main direction, and the contour network constitutes the basic quadrilateral meshing foundation.
- the intersection of the contours is the vertex of the quadrilateral mesh.
- the connection relationship between the vertices is determined by the connection relationship between the contours.
- the method In order to obtain the final quadrilateral meshing result, as shown in Fig. 4, the method first obtains the equivalent line segments in each triangle, and then processes the redundant contour segments according to certain rules, and finally establishes a quadrilateral mesh. .
- the contours described in the method are formed by concatenation of equal line segments within each triangle.
- the e function values corresponding to its three vertices are respectively, ee k , and the value represented by the contour is ⁇ .
- min ( , 0j ⁇ 0 iso ⁇ max(e i , , define the intersection point; 7, and
- ⁇ are the positions of the two endpoints, respectively.
- ⁇ are the positions of the two endpoints, respectively.
- min( , ⁇ 0 k ) ⁇ e iso ⁇ max( 0,, ⁇ 6 k ) two intersection points can be obtained according to the above method, and the two equal points can be obtained by connecting two intersection points.
- the intersection of the two segments within the triangle is found. This intersection is the intersection of the contour segments. Since the method establishes a partial triangle, there may be cases where the triangles overlap, that is, each edge may be shared by more than two triangles. In order to solve the problem of redundant points caused by triangle overlap, the following rules are adopted to discard or fuse the contour segments obtained by the above method. The rules are as follows:
- the adjacent points of the intersection point are found and connected according to the connection relationship between the contour segments, and a quadrilateral mesh with uniform shape and direction conforming to the main direction can be established. .
- the method described in the present invention was implemented in C++ language and experiments were performed on several different data sets. All experiments were performed on an Intel® CoreTM2 Quad CPU Q6600.
- the 40GHz 4G memory is completed on the PC, and the display part uses the standard OpenGL graphic function. Number library.
- Table 1 gives the time taken for the complexity of the model used in some experiments (the number of points) and the time of the three processes (main direction processing, local triangulation, global parameterization).
- Figure 6 shows the results obtained on a noisy part model with a Gaussian noise with a variance of 0.1.
- Fig. 6(a) shows the main directional field after smoothing on the model
- Fig. 6(b) shows the contours of the two scalar functions corresponding to the parameterized results in red and blue colors, respectively.
- (c) The result of quadrilateral meshing using the above contours. The picture shows that the quadrilateral is evenly distributed and conforms to the geometrical features of the object. This result is processed on the point cloud model to display the results on the mesh surface for display.
- Figure 7 shows a comparison between the results obtained on the part's model using our method on the part's point cloud model and the results obtained using Ray's method on the part's mesh model.
- Fig. 7(a) and Fig. 7(b) show the results of the contour and quadrilateral meshing obtained by the method
- Fig. 7(c) and Fig. 7(d) are the contours and quadrilateral mesh obtained by the Ray method.
- the method only uses the point cloud data of the model without the prior triangle meshing to obtain the same quality results.
- the feature and innovation of this method is to use global triangulation to directly global parameterization and quadrilateral meshing on the point cloud model without reconstructing the triangular mesh surface from point cloud data. Moreover, the method is completely automatic, no manual intervention is required, and the parameter can quickly control the degree of density of the quadrilateral mesh to obtain a quadrilateral mesh of various resolutions.
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CN2009801249381A CN102870139A (zh) | 2009-12-30 | 2009-12-30 | 对点云数据进行全局参数化和四边形网格化方法 |
PCT/CN2009/001591 WO2011079421A1 (zh) | 2009-12-30 | 2009-12-30 | 对点云数据进行全局参数化和四边形网格化方法 |
US13/001,906 US20120013617A1 (en) | 2009-12-30 | 2009-12-30 | Method for global parameterization and quad meshing on point cloud |
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Cited By (5)
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CN102306397A (zh) * | 2011-07-08 | 2012-01-04 | 中国科学院自动化研究所 | 点云数据网格化的方法 |
CN103489221A (zh) * | 2013-09-30 | 2014-01-01 | 中国科学院深圳先进技术研究院 | 四边形网格共形参数化方法 |
CN108765571A (zh) * | 2018-05-29 | 2018-11-06 | 大连九州创智科技有限公司 | 一种大型料堆点云补全方法 |
CN108877476A (zh) * | 2018-05-31 | 2018-11-23 | 北京金阳普泰石油技术股份有限公司 | 一种分层级虚网格获取方法、装置及系统 |
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CN102306397A (zh) * | 2011-07-08 | 2012-01-04 | 中国科学院自动化研究所 | 点云数据网格化的方法 |
CN103489221A (zh) * | 2013-09-30 | 2014-01-01 | 中国科学院深圳先进技术研究院 | 四边形网格共形参数化方法 |
CN108765571A (zh) * | 2018-05-29 | 2018-11-06 | 大连九州创智科技有限公司 | 一种大型料堆点云补全方法 |
CN108877476A (zh) * | 2018-05-31 | 2018-11-23 | 北京金阳普泰石油技术股份有限公司 | 一种分层级虚网格获取方法、装置及系统 |
CN108877476B (zh) * | 2018-05-31 | 2020-05-22 | 北京金阳普泰石油技术股份有限公司 | 一种分层级虚网格获取方法、装置及系统 |
CN109671155A (zh) * | 2018-12-21 | 2019-04-23 | 北京林业大学 | 基于点云数据的表面网格重建方法、系统及相关设备 |
CN109671155B (zh) * | 2018-12-21 | 2023-06-23 | 北京林业大学 | 基于点云数据的表面网格重建方法、系统及设备 |
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