| CPC G06T 7/0006 (2013.01) [G06T 3/60 (2013.01); G06T 2207/10028 (2013.01); G06T 2207/30132 (2013.01)] | 4 Claims |
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1. A method for detecting surface flatness of a precast beam based on a three-dimensional point cloud model, comprising the following steps:
(1) performing, according to a specific geometry of a three-dimensional point cloud model of a target component in a three-dimensional coordinate system, coarse calibration and fine calibration on the model sequentially to determine a spatial rotation matrix and perform point cloud coordinate calibration;
(2) determining normal vectors at positions of points of the three-dimensional point cloud model of the component according to a principal component analysis method and a K-nearest-neighbor principle, so that a to-be-detected surface is segmented and extracted by defining a normal vector direction and a coordinate interval; and
(3) iteratively searching for an optimal reference plane according to a form relationship between the to-be-detected surface and the three-dimensional coordinate system and calculating flatness of the surface,
wherein step (1) specifically comprises the following steps:
1.1 setting, for a three-dimensional point cloud model Pt0 of the precast beam, an origin O of an original coordinate system X0Y0Z0 at a centroid of the three-dimensional point cloud model:
 wherein Ptc is a centralized three-dimensional point cloud model; x1 . . . xn are coordinate values of points X0 in Pt0, y1 . . . yn, are coordinate values of Y0, and z1 . . . zn are coordinate values of Z0; and μX is an average value of the coordinate values of the points X0 in Pt0, μY is an average value of the coordinate values of original Y0, and μz is an average value of the coordinate values of original Z0;
1.2 determining, for the precast beam placed horizontally, that a positive direction of an initial Z1 coordinate axis is an opposite direction of gravity and is parallel to a direction of the beam height, making a projection of the three-dimensional point cloud model Ptc onto a plane X0OY0, performing a principal component analysis on the projection to first decentralize a projected point cloud according to a principle of the principal component analysis, calculate a covariance matrix of the decentralized point cloud, and perform singular value decomposition on the covariance matrix to obtain a group of eigenvalues and an eigenvector uniquely corresponding to each eigenvalue, wherein an eigenvector corresponding to the largest eigenvalue is a first principal component, and an eigenvector corresponding to the second largest eigenvalue is a second principal component; and defining a direction of a Y1 coordinate axis as a direction of the first principal component, and defining a direction of an X1 coordinate axis as a direction of the second principal component, to complete calibration of an initial coordinate system X1Y1Z1, that is, coarse calibration of coordinates of the three-dimensional point cloud model; and
1.3 respectively making slices at appropriate positions capable of reflecting features of the beam width, the beam length, and the beam height of the component, wherein thicknesses of the slices are twice a point cloud density; making a projection of points contained in the slices to a slice plane and performing the principal component analysis, fitting the projection to a straight line, and comparing angles between the projected straight line and two coordinate axes; and defining a direction of a coordinate axis with a smaller angle with the projected straight line as the direction of the first principal component according to the principle of the principal component analysis, and defining a direction of an other coordinate axis in the slice plane as the direction of the second principal component, to complete calibration of a final coordinate system XYZ, that is, fine calibration of the coordinates of the three-dimensional point cloud model after the steps are completed for all the directions of the beam width, the beam length, and the beam height; and
calculating, according to an angle between the final coordinate system XYZ and the initial coordinate system X1Y1Z1, rotation matrices Rx, Ry, and Rz corresponding to the point cloud that changes from the initial coordinate system X1Y1Z1 to the final coordinate system XYZ, wherein if a rotation direction of rotating from the initial coordinate system X1Y1Z1 to the final coordinate system XYZ is counterclockwise rotation, the obtained rotation matrices Rx, Ry, and Rz are respectively:
 and
if the rotation direction is clockwise rotation, the obtained rotation matrices Rx, Ry, and Rz are respectively:
 wherein a is an angle between a coordinate system Y1OZ1 and a coordinate system YOZ; β is an angle between a coordinate system X1OZ1 and a coordinate system XOZ; and γ is an angle between a coordinate system X1OY1 and a coordinate system XOY; and obtaining a spatial rotation matrix R=Rx·Ry·Rz according to Rx, Ry, Rz, to implement point cloud coordinate calibration:
Pt=R·Ptc,
wherein Ptc is a centralized three-dimensional point cloud model, and Pt is a three-dimensional point cloud model after coordinate calibration.
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