CN111856500A - Method for converting three-dimensional plane generalized model between scanner coordinate system and engineering measurement coordinate system - Google Patents
Method for converting three-dimensional plane generalized model between scanner coordinate system and engineering measurement coordinate system Download PDFInfo
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Abstract
The invention provides a method for converting a three-dimensional plane generalized model between a scanner coordinate system (coordinate system 1) and an engineering measurement coordinate system (coordinate system 2), which is called three-dimensional plane (3D plane) conversion and comprises the following steps: 1) in a three-dimensional Cartesian coordinate system, 3D planes are divided into 3 classes according to the coordinate axis where the maximum component of the absolute value of the unit normal vector of the 3D planes is located, and the minimum 3 characteristic parameters are used. 2) And under the condition that the conversion parameters of the two coordinate systems are known, establishing a 3D plane conversion equation of the relation between the characteristic parameters and the conversion parameters of the 3D plane under the two coordinate systems. 3) And establishing a 3D plane error propagation law of the 3D straight line characteristic parameter variance matrix in the coordinate system 2 by using the conversion parameter variance matrix and the 3D straight line characteristic parameter variance matrix in the coordinate system 1. The invention can convert the position and attitude parameters and the errors of the 3D plane on the object in the scanner coordinate system into the engineering measurement coordinate system, thereby facilitating the analysis and research of the linear geometric form of the object.
Description
Technical Field
The invention relates to coordinate conversion of a midpoint in a scanner coordinate system and an engineering measurement coordinate system, surface characteristic parameter conversion and error propagation thereof, belonging to the field of engineering measurement.
Background
At present, point clouds become common data sources in multiple fields such as photogrammetry and remote sensing, computer vision, machine learning and the like, are various in types, and are point clouds, static ground scanning point clouds, ground mobile scanning point clouds, synchronous positioning and drawing point clouds and the like acquired by methods such as airborne laser radar point clouds, photogrammetry and the like according to the data sources. People are always used to observe, express and research objective objects in a geographic space with a plumb line as a datum line and a north direction as a basic direction, and the coordinate system of the geographic space is a geographic reference coordinate system or an engineering measurement coordinate system in the field of surveying and mapping. The coordinate systems of point clouds acquired by different sensor platforms need to be converted into a unified geographical coordinate system, and the process is called point cloud geography in a point cloud processing theory. The academia provides a large number of point cloud geography methods and geography precision evaluation methods aiming at point cloud geography. In the scanning point cloud of the target such as a building, besides points, a large number of linear objects, plane objects and the like are provided, the research on a coordinate conversion model and an error propagation model of the point objects is mature at present, but a good research result is not provided for a characteristic parameter conversion model and an error propagation rule of the plane/linear object, and the invention is invented for the characteristic parameter conversion and the error propagation of a three-dimensional surface object.
Disclosure of Invention
The invention aims to provide a method for converting characteristic parameters of a three-dimensional surface object in point cloud under a scanner coordinate system into an engineering measurement coordinate system and an error propagation rule of the characteristic parameters. The technical scheme is as follows: a method for converting a three-dimensional plane generalized model between a scanner coordinate system and an engineering measurement coordinate system is characterized by comprising the following steps:
1) in a three-dimensional Cartesian coordinate system, a three-dimensional plane is expressed by using minimum characteristic parameters (3), and the 3 characteristic parameters respectively represent the position and the posture of the plane and have definite geometric significance; all planes in the three-dimensional space can be represented by three-dimensional plane equations only containing the 3 characteristic parameters, the three-dimensional plane equations have 3 forms, and the three-dimensional plane equations in the 3 forms are collectively called as a function model of the three-dimensional plane; the 3-order variance matrix of the 3 characteristic parameters forms a random model (also called an error model) of the three-dimensional plane, and the function model and the random model of the three-dimensional plane together form a generalized model of the three-dimensional plane.
2) Under the condition that the conversion parameters of the two coordinate systems are known, the relationship between the characteristic parameters of the three-dimensional plane equations under the two coordinate systems is respectively established, namely 3 three-dimensional plane conversion equations corresponding to the 3 plane equations one by one are deduced.
3) Under the condition that two coordinate system transformation parameter variance matrixes are known, an error propagation rule of three-dimensional plane characteristic parameters in a scanner coordinate system is deduced, and the rule is called a three-dimensional plane error propagation law for short.
The method for converting the three-dimensional plane generalized model between the scanner coordinate system and the engineering measurement coordinate system is characterized in that in the step 1), according to the difference of the maximum absolute value component in the three-dimensional plane normal vector, 3 expression forms of the three-dimensional plane equation can be written as
Ex:x+axy+bxz+cx＝0 (1a)
Ey:ayx+y+byz+cy＝0(1b)
Ez:azx+bzy+z+cz＝0 (1c)
In the formula, ExRepresenting a first class of three-dimensional planes not parallel to the x-axis, EyRepresenting a second type of three-dimensional plane not parallel to the y-axis, EzRepresenting non-parallelism of a third kindIn the z-axis three-dimensional plane. a isi,bi,ciAnd (i ═ x, y, z) is a characteristic parameter of the three-dimensional plane. (1) Is characterized in that
The characteristic parameters are few and independent. One of the conventional methods is as follows: using unit normal vectors of planes
And the distance d from the plane to the coordinate origin, 4 characteristic parameters in total represent the three-dimensional plane, the equation is that lX + mY + nZ + d is 0, and l2+m2+n2The conventional method has a disadvantage of characteristic parameter correlation, and the correlation between characteristic parameters needs to be considered when data is processed.
And the three-dimensional plane equation of 3 expression forms can express all three-dimensional planes in a three-dimensional coordinate system. The second conventional method is: using plane normal vectors
The 3 components of (1) represent three-dimensional planes as characteristic parameters, and the equation is that Ax + By + Cz +1 is 0, and the traditional method has the defect that the plane passing through the coordinate origin cannot be expressed.
And thirdly, the characteristic parameters represent the position and the posture of the three-dimensional plane in a three-dimensional Cartesian coordinate system, and the geometric meaning of the three-dimensional plane is clear. Taking the third type of three-dimensional plane as an example, the geometric meanings of the characteristic parameters are respectively as follows: the three-dimensional plane normal vector n is perpendicular to the plane E and points to the coordinate origin O, and the projection length of n on the z-axis is 1, the projection lengths on the x-axis and the y-axis are a and b, respectively, and c is the distance from the plane to the coordinate origin (as shown in fig. 1). a. b determining the attitude of the plane E, and calculating the attitude angle of the three-dimensional plane from a and b
ω, κ, c determine the position of plane E.
Fourthly, the random model of the characteristic parameters a, b and c is expressed by a variance matrix
In application, ExCorresponding to the front side of the object, EyCorresponding to the side of the object, EzCorresponding to the horizontal plane of the object.
The method for converting the three-dimensional plane generalized model between the scanner coordinate system and the engineering measurement coordinate system is characterized in that in the step 2), the transformation parameters of the two coordinate systems are known
And the characteristic parameter q ═ a, b, c of the three-dimensional plane E in the scanner coordinate system o-xyz]TDetermining a characteristic parameter Q ═ A, B, C in an engineering measurement coordinate system O-XYZ]TThe process of (1) is called three-dimensional plane forward conversion, and vice versa is three-dimensional plane reverse conversion, the forward and reverse conversion is called three-dimensional plane conversion, and the forward and reverse conversion are respectively expressed by matrixes
The above equations (1) and (2) are respectively a function model and a random model of a three-dimensional plane, a, b and c represent characteristic parameters of a three-dimensional plane equation,
ω and κ represent attitude angles of the three-dimensional plane.
The conversion method of the three-dimensional plane generalized model between the scanner coordinate system and the engineering measurement coordinate system is characterized in that in the step 3), two coordinate system conversion parameters T and a variance matrix delta thereof are knownTAnd the characteristic parameter q and the variance matrix delta of the three-dimensional plane E in the scanner coordinate system o-xyzqThe error propagation rule of the characteristic parameters of the three-dimensional plane in the engineering measurement coordinate system is
In the formula HTJacobian matrix, K, being the partial derivative of Q with respect to TqJacobian matrix of partial derivatives of Q with Q, of the form
Drawings
FIG. 1 is a geometric meaning of a third class of three-dimensional planar feature parameters;
fig. 2 is a memorial archway drawing of first-stage surveying and mapping, fig. 3 is a memorial archway drawing of second-stage surveying and mapping (soaking in rainwater), fig. 4 is a memorial archway drawing of third-stage surveying and mapping (construction process of square), fig. 5 is a memorial archway drawing of fourth-stage surveying and mapping (completion of square application), fig. 6 is a memorial archway drawing of fifth-stage surveying and mapping (reinforcement maintenance), and fig. 7 is a memorial archway drawing of sixth-stage surveying and mapping (completion measurement); figure 8 is a global view of the inclination of the building element, figure 9 is a partial view of the inclination of the building element, and figure 10 is a view of the inclination of the stone pillar of the building element; FIG. 11 is a result of extraction of a three-dimensional scan point cloud surface object for a memorial archway.
Detailed Description
The technical scheme of the invention is further explained by combining the attached drawings.
A conversion method of a three-dimensional plane generalized model between a scanner coordinate system and an engineering measurement coordinate system comprises three-dimensional straight line parameterization, three-dimensional plane conversion and three-dimensional plane characteristic parameter error propagation rules of the scanner coordinate system:
1. three-dimensional linear parameterization of scanner coordinate system
In step 1), the scanner coordinate system o-xyz is a three-dimensional cartesian coordinate system, the point cloud is firstly segmented to extract a three-dimensional plane object, the three-dimensional plane object is parameterized by a fitting method, and the three-dimensional plane object is classified and expressed as follows according to a function model
Ex:x+axy+bxz+cx＝0 (1a)
Ey:ayx+y+byz+cy＝0 (1b)
Ez:azx+bzy+z+cz＝0 (1c)
In the formula, ExRepresenting a first class of three-dimensional planes not parallel to the x-axisFlour, EyRepresenting a second type of three-dimensional plane not parallel to the y-axis, EzRepresenting a third class of three-dimensional planes that are not parallel to the z-axis. a isi,bi,ciAnd (i ═ x, y, z) is a characteristic parameter of the three-dimensional plane.
2. Three-dimensional planar transformation
In step 2), the transformation parameters of two coordinate systems are known
And the characteristic parameter q ═ a, b, c of the three-dimensional plane E in the scanner coordinate system o-xyz]TDetermining a characteristic parameter Q ═ A, B, C in an engineering measurement coordinate system O-XYZ]TThe process of (1) is called three-dimensional plane forward conversion, and vice versa is three-dimensional plane reverse conversion, the forward and reverse conversion is called three-dimensional plane conversion, and the forward and reverse conversion are respectively expressed by matrixes
The following is a derivation of the specific form of the above formula: knowing the transformation parameters of two coordinate systems
If the scanner coordinate system midpoint P (X, Y, Z) is converted to P (X, Y, Z) in the engineering measurement coordinate system, the conversion equation is
Formula medium rotation torque array
Is marked as
(3) The formula is expressed in pure form as
In the O-XYZ and O-XYZ coordinate systems, the first class of three-dimensional plane equations is
Substituting the formula (4) into the formula (5),
after arrangement, the first three-dimensional plane positive conversion model can be obtained as
The positive conversion models of the three-dimensional planes of the second kind and the third kind can be obtained by the same method
In the formula, xS＝(r11XS+r21YS+r31ZS)，yS＝(r12XS+r22YS+r32ZS)，zS＝(r13XS+r23YS+r33ZS)。
The deduced inverse transformation models of the 3-class three-dimensional planes are respectively
3. Three-dimensional plane error propagation law
In step 3), two coordinate system conversion parameters T and variance matrix delta thereof are knownTAnd the characteristic parameter q and the variance matrix delta of the three-dimensional plane E in the scanner coordinate system o-xyzqThe error propagation rule of the characteristic parameters of the three-dimensional plane in the engineering measurement coordinate system is
In the formula HTJacobian matrix, K, being the partial derivative of Q with respect to TqJacobian matrix of partial derivatives of Q with Q, of the form
Obtaining two Jacobian matrixes H and K according to the (7), (8) and (9), substituting the two Jacobian matrixes H and K into the formula (13), and obtaining a variance matrix delta of characteristic parameters of the three-dimensional plane under the engineering measurement coordinate systemQ。
4. Typical applications (deformation monitoring)
The Shandong Weifang Anqiu City was a four-post three-room three-storied house of Stone structure, the general height was 9.65 m, the Longmen square beam and the Ming-room eaves tower were 3.4 m and 1.68 m, respectively. The memorial archways are provincial ancient buildings and are influenced by factors such as foundation sinking, wind and rain, artificial damage and the like all the year round, and the memorial archways have the problems of serious overall inclination, local inclination, part damage, falling and the like, as shown in figure 1. In order to accurately reflect the overall deformation condition of the memorial archway, obtain the real-time memorial archway morphological characteristics and predict the change trend of the memorial archway, the memorial archway is subjected to multi-period fine mapping.
The memorial archway structure is a masonry structure and is built up by carving green stone blocks. The deformation is judged by visual observation:
(1) the foundation has more obvious uneven settlement as shown in figure 2;
(2) the 4 mingsheng stone columns have inclination and distortion as shown in figure 4;
(3) inclining a bright gantry purlin;
(4) each part (block) of the gantry purlin has relative inclination, as shown in figure 3.
The measurement adopts the combination of a three-dimensional laser scanning technology and a traditional precision measurement technology, the deformation observation of more than 20 brickworks is carried out for 6 periods, 1-3 planes on each brickworks are used as deformation elements, the posture and the position of each brickworks in each period are calculated by using the technology of the patent, and abundant data support is provided for the rescue and the protection of cultural relics.
During the measurement scanning, the scanning precision of a single station is 20 kilogrations, the resolution of the rarefied point cloud is 2cm, more than 3 spherical control targets are distributed in a scanning view field, and the radius of each spherical target is 0.1 m. The geographic reference plane coordinate system adopts a CGCS2000 coordinate system, the central meridian of the experimental area is 117 degrees, the elevation coordinate system adopts a yellow sea 85 elevation coordinate system, and the projection mode is Gaussian projection.
The practical application comprises the following main steps: firstly, scanning cloud data of two adjacent stations, and carrying out geography on one station point cloud through a standard control point. And secondly, selecting and extracting the homonymous plane in the geographic point cloud and the point cloud of another station. And thirdly, calculating the geographic parameters by using the technology of the patent respectively. Fourthly, the geography parameters obtained by the technology of the patent are used for carrying out geography on the point cloud of the other station. And fifthly, detecting the geographical precision through the standard control points of the test area and the distributed control targets.
Practice proves that:
1. the three-dimensional plane model can comprehensively reflect the posture and position change of a deformable body. Especially for cultural relics with a multi-masonry structure, the three-dimensional laser scanning technology can measure the deformation of exposed masonry with plane characteristics.
2. The method can be used for three-dimensional plane point cloud splicing of scanning overlapping areas of all stations, and if more than 3 three-dimensional planes have acquired characteristic parameters of two coordinate systems, coordinate conversion parameters are calculated by formulas (7) - (9).
3. The three-dimensional laser scanning technology is a non-contact measurement technology, cannot cause secondary damage to the cultural relics, and is beneficial to cultural relic protection.
Claims (4)
1. A method for converting a three-dimensional plane generalized model between a scanner coordinate system and an engineering measurement coordinate system (hereinafter referred to as two coordinate systems) is characterized by comprising the following steps:
1) in a three-dimensional Cartesian coordinate system, a three-dimensional plane is expressed by using minimum characteristic parameters (3), and the 3 characteristic parameters respectively represent the position and the posture of the plane and have definite geometric significance; all planes in the three-dimensional space can be represented by three-dimensional plane equations only containing the 3 characteristic parameters, the three-dimensional plane equations have 3 forms, and the three-dimensional plane equations in the 3 forms are collectively called as a function model of the three-dimensional plane; the 3-order variance matrix of the 3 characteristic parameters forms a random model (also called an error model) of the three-dimensional plane, and the function model and the random model of the three-dimensional plane together form a generalized model of the three-dimensional plane.
2) Under the condition that the conversion parameters of the two coordinate systems are known, the relationship between the characteristic parameters of the three-dimensional plane equations in the two coordinate systems is respectively established, namely 3 three-dimensional plane conversion equations corresponding to the 3 plane equations one by one are deduced.
3) Under the condition that two coordinate system transformation parameter variance matrixes are known, an error propagation rule of three-dimensional plane characteristic parameters in a scanner coordinate system is deduced, and the rule is called a three-dimensional plane error propagation law for short.
2. The method for transforming the generalized model of three-dimensional plane between the scanner coordinate system and the engineering measurement coordinate system as claimed in claim 1, wherein in step 1), 3 expressions of the equation of three-dimensional plane can be written as follows according to the difference of the maximum component of the absolute value in the normal vector of three-dimensional plane
Ex:x+axy+bxz+cx＝0 (1a)
Ey:ayx+y+byz+cy＝0 (1b)
Ez:azx+bzy+z+cz＝0 (1c)
In the formula, ExRepresenting a first class of three-dimensional planes not parallel to the x-axis, EyRepresenting a second type of three-dimensional plane not parallel to the y-axis, EzRepresenting a third class of three-dimensional planes that are not parallel to the z-axis. a isi,bi,ciAnd (i ═ x, y, z) is a characteristic parameter of the three-dimensional plane. (1) Is characterized in that
The characteristic parameters are few and independent. One of the conventional methods is as follows: using unit normal vectors of planes
And the distance d from the plane to the coordinate origin, 4 characteristic parameters in total represent the three-dimensional plane, the equation is that lX + mY + nZ + d is 0, and l2+m2+n2The conventional method has a disadvantage of characteristic parameter correlation, and the correlation between characteristic parameters needs to be considered when data is processed.
And the three-dimensional plane equation of 3 expression forms can express all three-dimensional planes in a three-dimensional coordinate system. The second conventional method is: using plane normal vectors
The 3 components of (1) represent three-dimensional planes as characteristic parameters, and the equation is that Ax + By + Cz +1 is 0, and the traditional method has the defect that the plane passing through the coordinate origin cannot be expressed.
And thirdly, the characteristic parameters represent the position and the posture of the three-dimensional plane in a three-dimensional Cartesian coordinate system, and the geometric meaning of the three-dimensional plane is clear. Taking the third type of three-dimensional plane as an example, the geometric meanings of the characteristic parameters are respectively as follows: the three-dimensional plane normal vector n is perpendicular to the plane E and points to the coordinate origin O, and the projection length of n on the z-axis is 1, the projection lengths on the x-axis and the y-axis are a and b, respectively, and c is the distance from the plane to the coordinate origin (as shown in fig. 1). a. b determining the attitude of the plane E, and calculating the attitude angle of the three-dimensional plane from a and b
ω, κ, c determine the position of plane E.
Fourthly, the random model of the characteristic parameters a, b and c is expressed by a variance matrix
In application, ExCorresponding to the front side of the object, EyCorresponding to the side of the object, EzCorresponding to the horizontal plane of the object.
The above equations (1) and (2) are respectively a function model and a random model of a three-dimensional plane, a, b and c represent characteristic parameters of the three-dimensional plane equation,
ω and κ represent attitude angles of the three-dimensional plane.
3. The method for transforming the generalized model of three-dimensional plane between the scanner coordinate system and the engineering measurement coordinate system as claimed in claim 1, wherein in step 2), the transformation parameters of the two coordinate systems are known
And the characteristic parameter q ═ a, b, c of the three-dimensional plane E in the scanner coordinate system o-xyz]TDetermining a characteristic parameter Q ═ A, B, C in an engineering measurement coordinate system O-XYZ]TThe process of (1) is called three-dimensional plane forward conversion, and vice versa is three-dimensional plane reverse conversion, the forward and reverse conversion is called three-dimensional plane conversion, and the forward and reverse conversion are respectively expressed by matrixes
4. The method for transforming the generalized model of three-dimensional plane between the scanner coordinate system and the engineering measurement coordinate system as claimed in claim 1, wherein in step 3), two coordinate system transformation parameters T and their variance matrix Δ are knownTAnd the characteristic parameter q and the variance matrix delta of the three-dimensional plane E in the scanner coordinate system o-xyzqThree-dimensional planar features in an engineering measurement coordinate systemThe error propagation rule of the characteristic parameters is
In the formula HTJacobian matrix, K, being the partial derivative of Q with respect to TqJacobian matrix of partial derivatives of Q with Q, of the form
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