CN113963114A - Discrete boundary point tracking method based on polygon growth - Google Patents
Discrete boundary point tracking method based on polygon growth Download PDFInfo
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- CN113963114A CN113963114A CN202111243783.2A CN202111243783A CN113963114A CN 113963114 A CN113963114 A CN 113963114A CN 202111243783 A CN202111243783 A CN 202111243783A CN 113963114 A CN113963114 A CN 113963114A
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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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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
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- G06T7/10—Segmentation; Edge detection
- G06T7/181—Segmentation; Edge detection involving edge growing; involving edge linking
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- G06T—IMAGE DATA PROCESSING OR GENERATION, IN GENERAL
- G06T7/00—Image analysis
- G06T7/60—Analysis of geometric attributes
- G06T7/64—Analysis of geometric attributes of convexity or concavity
Abstract
The invention discloses a discrete boundary point tracking method based on polygon growth, which is characterized in that on the basis of completing the detection of three-dimensional point cloud hole boundary points, a convex hull of a discrete boundary point set is constructed, and the polygon growth is carried out based on Euclidean distance constraint from points to polygon line segments, so that the region boundary is tracked out from the discrete hole boundary points. The method avoids the need of manually setting a proper parameter threshold value by adopting a Delaunay triangulation method or a rolling sphere method, can accurately track the concave boundary of the point cloud hole, and provides convenience for subsequent object defect area measurement and point cloud hole filling.
Description
Technical Field
The invention relates to a discrete boundary point tracking method based on polygon growth, and belongs to the field of discrete point cloud analysis and processing.
Background
China's manufacturing industry will step forward towards the intelligent manufacturing era with high integration of informatization and industrialization. Under the background, the requirements on the mechanical manufacturing technology of China are higher and higher. At present, people can easily acquire three-dimensional point cloud data of an object to be detected through various sensors such as an optical scanner or a laser radar. The information not only can accurately reflect the real size and shape structure of the object, but also can realize the defect detection of the object by comparing with a CAD model in the production and processing process. Typically, the object defects are represented as holes in the three-dimensional point cloud data. In recent years, many research institutions and scholars at home and abroad research the defects of the point cloud holes, and the boundary points of the point cloud holes can be accurately detected. The boundary points do not have topological relation in space, so a rough and reasonable geometric shape needs to be reconstructed from the discrete hole boundary point set, and the contour information of the point cloud hole is reflected to a certain extent.
The current mature Delaunay triangulation method is to triangulate all points and obtain a concave packet of a point set by deleting long edges; the rolling ball rule is that these points are imagined as nails nailed on a flat surface, rolling with a ball of appropriate radius, capturing the points on the concave packet. However, these point cloud tracking methods have the disadvantage that appropriate thresholds need to be manually set. Therefore, it is of practical significance to research a fast and accurate discrete boundary point tracking method without manual intervention.
Disclosure of Invention
The purpose of the invention is: the method overcomes the defects of the prior art, and provides a discrete boundary point tracking method based on polygon growth, parameters are not required to be set, a discrete boundary point set convex hull can be constructed on the basis of completing point cloud hole boundary point detection, polygon growth is carried out based on Euclidean distance constraint from points to polygon line segments, hole outlines are constructed from discrete hole boundary points, and convenience is brought to subsequent defect area measurement and point cloud hole filling.
The technical scheme adopted for realizing the aim of the invention is a discrete boundary point tracking method based on polygon growth, which comprises the following steps:
s1: projecting N discrete boundary points in the point cloud data to a two-dimensional plane, and establishing a convex hull of the point set by utilizing a Graham scanning method, wherein the convex hull is an M-shaped polygon, and M is less than N;
s2: randomly selecting a point p in the M polygon, namely a non-polygonal contour point, sequentially making a perpendicular line of each side of the polygon, namely a straight line where a line segment is located, and if the foot is located on the line segment, calculating the Euclidean distance between the point and the foot;
s3: comparing the euclidean distances obtained in step S2, and taking the minimum value as the distance from the point p to the polygon;
s4: repeating the step S2 and the step S3 until the distance from each point in the polygon to the polygon is obtained;
s5: screening out the shortest distance from the step S4 to obtain the point closest to the polygon boundary and the corresponding boundary;
s6: inserting the points obtained in the step S5 into the polygon contour points to change a corresponding edge into two edges, thereby forming a new M +1 edge;
s7: assigning M to a new value, i.e., M +1, and repeating steps S2-S6 until all discrete points are inserted into the new polygon contour point, i.e., M-N;
s8: the finally formed polygon is the boundary contour generated by the discrete points.
Further, the specific operation of step S1 includes:
s101: randomly selecting a discrete boundary point in the point cloud, and searching a neighboring point of the point by using a Kdtree neighboring point searching algorithm;
s102: estimating unit normal vectors of the plane where the point and the adjacent points are located by using a Principal Component Analysis (PCA) method, and regarding the unit normal vectors as the unit normal vectors of the point;
s103: repeating the steps S101 and S102 until a unit normal vector of each discrete boundary point is obtained;
s104: summing and unitizing the normal vectors obtained in the step S103 to be used as unit normal vectors of the local projection plane, summing and averaging discrete boundary points to be used as an origin, constructing a least square plane orthogonal coordinate system, projecting the discrete boundary points to the two-dimensional plane, and calculating projection coordinates;
s105: and establishing a convex hull of the discrete boundary point set on a two-dimensional plane by utilizing a Graham (Graham) scanning method.
The invention has the following advantages:
(1) a threshold value is not required to be set, and the human intervention of a Delaunay triangulation method and a rolling sphere method is avoided;
(2) based on the idea of convex hull construction, Euclidean distance criterion is added to realize the polygon growth from the convex hull to the concave hull, so that the concave boundary of the point cloud hole can be tracked more accurately;
(3) the dependence on the point density is not large, and the method is also suitable for a non-uniformly distributed data set;
(4) and a discrete boundary point outline is constructed, so that convenience is provided for subsequent object defect area measurement and point cloud hole filling.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a discrete boundary point constructing an initial convex hull;
FIG. 3 is a schematic diagram of primary polygon growth based on Euclidean distance constraints from points to polygon segments;
FIG. 4 is a schematic diagram of a discrete boundary point tracking process;
fig. 5 is a diagram illustrating the tracking result of the boundary of the bottom hole of the Bunny model.
Detailed Description
The invention discloses a discrete boundary point tracking method based on polygon growth, which can quickly and effectively track the concave boundary of a point cloud hole from a discrete point cloud, and the flow chart is shown in figure 1, and the specific steps are as follows:
s1: projecting N discrete boundary points in the point cloud data to a two-dimensional plane, and establishing a point set convex hull by using a Graham (Graham) scanning method;
specifically, S101: randomly selecting a discrete boundary point in the point cloud, and searching a neighboring point of the point by using a Kdtree neighboring point searching algorithm;
s102: estimating unit normal vectors of the plane where the point and the adjacent points are located by using a Principal Component Analysis (PCA) method, and regarding the unit normal vectors as the unit normal vectors of the point;
s103: repeating the steps S101 and S102 until a unit normal vector of each discrete boundary point is obtained;
s104: summing and unitizing the normal vectors obtained in the step S103 to be used as unit normal vectors of the local projection plane, summing and averaging discrete boundary points to be used as an origin, constructing a least square plane orthogonal coordinate system, projecting the discrete boundary points to the two-dimensional plane, and calculating projection coordinates;
s105: by utilizing a Graham (Graham) scanning method, a discrete boundary point set convex hull is established on a two-dimensional plane, as shown in FIG. 2, the number of discrete boundary points is 12, and the constructed convex hull is a 6-sided polygon.
S2: arbitrarily selecting a point p in a polygoni(i is 5,7,8,9,10,11), sequentially drawing a perpendicular line of a straight line on which each side (line segment) of the polygon is located through the point, and if the point is on the line segment, calculating the Euclidean distance between the point and the point, as shown in FIG. 3, by using a point p5For example, per p5Making an edge p3p4The vertical line of (1) is a point D, and according to a vector product formula, the method comprises the following steps:
let | p4D|＝t|p4p3I, then
When t is more than or equal to 0 and less than or equal to 1, indicating that the foot is on the line segment, and solving the distance
When t is<0 or t>When 1, the foot is on the extension line of the line segment, and the distance is not needed to be solved in the case.
S3: the euclidean distances obtained in step S2 are compared, and the minimum value is defined as a point piDistance to the polygon. At point p5For example, the step S2 can be executedTo obtain two Euclidean distances, p respectively5To the edge p3p4Distance value of p5To the edge p4p6By comparison, p is5To the edge p4p6As the point p5Distance d to polygon5。
S4: repeating the steps S2 and S3 until each point p in the polygon is obtainediDistance d to polygoni(i＝5,7,8,9,10,11)。
S5: the shortest distance d is screened out from the step S45Obtaining the point p closest to the polygon boundary5And corresponding boundary p4p6。
S6: the point p acquired in step S55Inserted into a polygon outline point, edge p4p6Growing into two sides p4p5And p5p6Forming a new 7-sided polygon.
S7: repeating the steps S2-S6 until all the discrete points are inserted into the new polygon contour points, as shown in FIG. 4, wherein (i) - (sixth) represents the process of polygon growth;
s8: the finally formed 12-sided polygon is the boundary contour generated by the discrete points.
The method is fully verified in experiments, and the discrete boundary points of 4 groups of holes at the bottom of the Stanford Bunny model are tracked, and the effect is shown in figure 5, which shows that the method can well track the point cloud hole boundary with the topological relation of the discrete points, and the dependence on the point density is not large.
Claims (2)
1. A discrete boundary point tracking method based on polygon growth is characterized by comprising the following steps:
s1: projecting N discrete boundary points in the point cloud data to a two-dimensional plane, and establishing a convex hull of the point set by utilizing a Graham scanning method, wherein the convex hull is an M-shaped polygon, and M is less than N;
s2: randomly selecting a point p in the M polygon, namely a non-polygonal contour point, sequentially making a perpendicular line of each side of the polygon, namely a straight line where a line segment is located, and if the foot is located on the line segment, calculating the Euclidean distance between the point and the foot;
s3: comparing the euclidean distances obtained in step S2, and taking the minimum value as the distance from the point p to the polygon;
s4: repeating the step S2 and the step S3 until the distance from each point in the polygon to the polygon is obtained;
s5: screening out the shortest distance from the step S4 to obtain the point closest to the polygon boundary and the corresponding boundary;
s6: inserting the points obtained in the step S5 into the polygon contour points to change a corresponding edge into two edges, thereby forming a new M +1 edge;
s7: assigning M to a new value, i.e., M +1, and repeating steps S2-S6 until all discrete points are inserted into the new polygon contour point, i.e., M ═ N;
s8: the finally formed polygon is the boundary contour generated by the discrete points.
2. The discrete boundary point tracking method based on polygon growing according to claim 1, wherein: the step S1 includes the following steps:
s101: randomly selecting a discrete boundary point in the point cloud, and searching a neighboring point of the point by using a Kdtree neighboring point searching algorithm;
s102: estimating unit normal vectors of the plane where the point and the adjacent points are located by utilizing a Principal Component Analysis (PCA) method, and regarding the unit normal vectors as the unit normal vectors of the point;
s103: repeating the steps S101 and S102 until a unit normal vector of each discrete boundary point is obtained;
s104: summing and unitizing the normal vectors obtained in the step S103 to be used as unit normal vectors of the local projection plane, summing and averaging discrete boundary points to be used as an origin, constructing a least square plane orthogonal coordinate system, projecting the discrete boundary points to the two-dimensional plane, and calculating projection coordinates;
s105: and establishing a discrete boundary point set convex hull on a two-dimensional plane by utilizing a Graham scanning method.
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| CN117236937A (en) * | 2023-11-13 | 2023-12-15 | 国网天津市电力公司宝坻供电分公司 | Power distribution network defect positioning method and device based on security domain concave visualization |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN117236937A (en) * | 2023-11-13 | 2023-12-15 | 国网天津市电力公司宝坻供电分公司 | Power distribution network defect positioning method and device based on security domain concave visualization |
| CN117236937B (en) * | 2023-11-13 | 2024-02-27 | 国网天津市电力公司宝坻供电分公司 | Power distribution network defect positioning method and device based on security domain concave visualization |
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