CN109029284A - A kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method - Google Patents
A kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method Download PDFInfo
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- CN109029284A CN109029284A CN201810611283.1A CN201810611283A CN109029284A CN 109029284 A CN109029284 A CN 109029284A CN 201810611283 A CN201810611283 A CN 201810611283A CN 109029284 A CN109029284 A CN 109029284A
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/24—Measuring arrangements characterised by the use of optical techniques for measuring contours or curvatures
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
Abstract
The present invention relates to three dimensional point cloud processing and 3 D scene rebuilding technical field, a kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method, the following steps are included: (1) makes scaling board, (2) scaling board three-dimensional point cloud and two dimensional image are acquired, (3) camera calibration, (4) scaling board plane is calculated in camera coordinates system, (5) point face geometrical constraint is established, (6) line face geometrical constraint is constructed, (7) face face geometrical constraint is constructed, (8) calculate the geometric maps relationship of point cloud and image.The present invention has the advantages that the structure to three-dimensional point cloud is analysed in depth, point three kinds of face geometrical constraint, line face geometrical constraint and face face geometrical constraint thoughts are utilized simultaneously, to solve the geometric maps relationship in laser coordinate system midpoint cloud and image coordinate system between image, the geometrical relationship between scaling board plane and laser scanning point is taken full advantage of, to keep the calibration of three-dimensional laser scanner and camera more accurate and reliable.
Description
Technical field
The present invention relates to a kind of three-dimensional laser scanners based on geometrical constraint and camera calibration method, belong to three-dimensional point cloud
Data processing and 3 D scene rebuilding technical field.
Background technique
During digitizing real world, three dimensional point cloud has recorded the geometric attribute and position letter of body surface
Breath, two dimensional image have recorded the colouring information and texture information of body surface, and the depth integration of the two will be formed a kind of emerging
Digital Media, i.e. three-dimensional colour point clouds data, three-dimensional colour point clouds data are the further development of three dimensional point cloud, Ke Yigeng
Add and accurately states real world.In three-dimensional point cloud and two dimensional image fusion process, the calibration of laser scanner and camera is
It determines a most key technology of fusion accuracy, there is stronger theory significance and application value, examined in industry at present
There are more and more applications in the fields such as survey, environment sensing, independent navigation.
There are two types of working methods for three-dimensional laser scanner, and one is realized by the horizontal and vertical rotation of single beam laser
3-D scanning, another kind are to realize 3-D scanning by the transverse rotation of multiple laser, and the three-dimensional of both working methods swashs
The three-dimensional point cloud that photoscanner obtains is that rule mesh is formatted three dimensional point cloud.Three-dimensional laser scanner is main with camera calibration
Refer to: using three-dimensional laser scanner and camera scanning shooting calibration scene, obtaining the three-dimensional point cloud and two of calibration scene respectively
It ties up image and seeks the spin matrix between camera internal reference matrix and three-dimensional laser scanner and camera using camera imaging principle
And translation vector.Determine the geometric maps relationship in laser coordinate system in three-dimensional point cloud and image coordinate system between two dimensional image,
To obtain pixel corresponding to each laser scanning point.
It is found through numerous studies, as follows with three-dimensional laser scanner similar in the present invention and camera calibration method: production is black
White grid scaling board is uniform-distribution with equal-sized circular hole on scaling board.The scaling board is scanned using three-dimensional laser scanner,
Obtain scaling board three-dimensional point cloud.Scaling board is shot using camera simultaneously, obtains the two dimensional image of scaling board.In laser coordinate system
The space coordinate for seeking center of circular hole seeks the pixel coordinate of center of circular hole in camera coordinates system, and building point point geometry constrains,
Inner parameter and external parameter are sought, to realize the calibration of three-dimensional laser scanner and camera.This method there are it is following not
Foot place: 1) when three-dimensional point cloud than it is sparse when, be difficult accurately to calculate the space coordinate of center of circular hole, shadow in laser coordinate system
Ring calibration accuracy；2) deep analysis is not carried out to the structure of three-dimensional point cloud, and it is several to construct to depend on scaling board circular hole unduly
What is constrained, and lacks the development and utilization to its point-line-surface geometrical constraint, the robustness of calibration and accuracy are to be improved.
Summary of the invention
In order to further increase the precision of three-dimensional laser scanner and camera calibration, the present invention provides one kind to be based on geometry
The three-dimensional laser scanner and camera calibration method of constraint.The present invention is shot using three-dimensional laser scanner and camera scanning
When three-dimensional scenic, a kind of scaling method is provided for three-dimensional laser scanner and camera, to solve three-dimensional point cloud in laser coordinate system
With the geometric maps relationship in image coordinate system between two dimensional image, thus realize laser scanner three-dimensional point cloud and camera two dimension
Accurate fusion between image obtains the three-dimensional colour point clouds of scene in real time.
In order to achieve the above-mentioned object of the invention, it solves present in prior art to topic, the technical solution adopted by the present invention is that:
A kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method, comprising the following steps:
Step 1, production scaling board, for scaling board having a size of 72cm × 72cm, being uniform-distribution with side length thereon is the black of 6cm
White grid；
Step 2, acquisition scaling board three-dimensional point cloud and two dimensional image, fixed three-dimensional laser scanner and camera, by scaling board
Towards three-dimensional laser scanner and camera, scaling board is scanned using three-dimensional laser scanner, obtains the three-dimensional point cloud of scaling board, together
When, scaling board is shot using camera, obtains the two dimensional image of scaling board；The pose for changing scaling board continues to scan on shooting calibration
Plate, to obtain the three-dimensional point cloud P={ P of scaling board under one group of different positions and posej| 1≤j≤m } and two-dimensional image I={ Ij|1≤j
≤ m }, wherein m is scaling board pose number,It is demarcated for j-th of pose
Plate three-dimensional point cloud, For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud,It is
The number of laser scanning point in j pose scaling board three-dimensional point cloud,For jth
A pose scaling board two dimensional image,For ith pixel point in j-th of pose scaling board two dimensional image,
For the number of pixel in j-th of pose scaling board two dimensional image；Laser coordinate system [Ol；X, y, z] origin OlPositioned at laser light
The heart, x/y plane are parallel to three-dimensional laser scanner pedestal；Camera coordinates systemOrigin OcPositioned at camera lens light
The heart,Plane is parallel to image sensor plane；Scaling board coordinate systemOrigin ObPositioned at scaling board upper left
Angular vertex,Plane is located at scaling board plane；Image coordinate system [Oa；U, v] origin OaPositioned at as plane top left corner apex,
Uv plane is located at image sensor plane；
Step 3, camera calibration utilize the tool box Calib and different positions and pose scaling board two-dimensional image I={ I of matlabj|
1≤j≤m }, calculate the external parameter under camera internal reference matrix A and every kind of poseWithWherein,For under j-th of pose
Spin matrix between scaling board coordinate system and camera coordinates system,For scaling board coordinate system and camera coordinates under j-th of pose
Translation vector between system；
Step 4 calculates scaling board plane in camera coordinates system, in camera coordinates system, in j-th of pose of scaling board
Under, with scaling board vectorIndicate scaling board plane,Direction it is parallel with the normal direction of scaling board plane,Size etc.
In camera coordinates system origin to the vertical range of scaling board plane, spin matrix is utilizedAnd translation vectorCalculate scaling board
Vector isWherein,For spin matrixThe 3rd column column vector；
Step 5, a foundation point face geometrical constraint are become scaling board laser scanning point by laser coordinate system using coordinate transform
Camera coordinates system is changed to, and through scaling board laser scanning point in scaling board plane, it is specific to wrap to construct a face geometrical constraint
Include following sub-step:
(a) coordinate transform is utilized, scaling board laser scanning point is transformed into camera coordinates system by laser coordinate system, is expressed
Form is described by formula (1),
In formula,For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud under camera coordinates system,It is sharp
I-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud under light coordinate system, R are laser coordinate system and camera coordinates system
Between spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(b) under camera coordinates system, using scaling board laser scanning point in scaling board plane, building point face geometry is about
Beam, expression-form are described by formula (2),
(c) by formula (2), formula (3) can be calculated,
(d) formula (1) is substituted into formula (3), formula (4) can be calculated,
(e) formula (5) can be obtained by formula (4) expansion,
Wherein,For the spin matrix between laser coordinate system and camera coordinates system, t=
(t1,t2,t3) translation vector between laser coordinate system and camera coordinates system,For camera coordinates system
In j-th of pose scaling board vector,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud
I-th of laser scanning point；
Step 6, building line face geometrical constraint, according to the scanning mode of three-dimensional laser scanner, by scaling board three-dimensional point cloud
If being decomposed into main line point cloud, and straight line fitting is carried out to each line point cloud, obtain fitting a straight line, which is known as demarcating
Plate laser scanning line；Using coordinate transform, scaling board laser scanning line is transformed into camera coordinates system by laser coordinate system, and lead to
Scaling board laser scanning line is crossed in scaling board plane, to construct line face geometrical constraint, specifically includes following sub-step:
(a) three-dimensional laser scanner is there are two types of working method, one is the horizontal and vertical rotation by single beam laser come
Realize 3-D scanning, another kind is to realize 3-D scanning by the transverse rotation of multiple laser, the three of both working methods
Dimension laser scanner obtain three-dimensional point cloud be rule mesh format three dimensional point cloud therefore can be according to three-dimensional point cloud net
The vertical and horizontal of lattice are by scaling board three-dimensional point cloud PjSeveral line point clouds are decomposed into, i.e.,
Wherein,For kth line point cloud in j-th of pose scaling board three-dimensional point cloud, it is distributed on laser scanning line by a series of
Orderly discrete point composition,For the item number of j-th of pose scaling board three-dimensional point cloud centerline cloud；
(b) least square method is utilized, to line point cloudStraight line fitting is carried out, the direction vector of fitting a straight line is obtainedAnd passing pointThe fitting a straight line is known as scaling board laser scanning line；
(c) coordinate transform is utilized, by the direction vector of scaling board laser scanning lineAnd passing pointBy laser coordinate system
Camera coordinates system is transformed to, expression-form is described by formula (6) and formula (7),
In formula,For under camera coordinates system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction to
Amount,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction vector,For phase
Under machine coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line passing point,It is under laser coordinate system
The passing point of kth laser scanning line in j pose scaling board three-dimensional point cloud, R is between laser coordinate system and camera coordinates system
Spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(d) under camera coordinates system, using scaling board laser scanning line in scaling board plane, i.e. the method for scaling board plane
To the direction vector perpendicular to scaling board laser scanning line, and the passing point of scaling board laser scanning line is in scaling board plane,
Line face geometrical constraint is constructed, expression-form is described by formula (8) and formula (9),
(e) by formula (9), formula (10) can be calculated,
(f) formula (6) and formula (7) are substituted into formula (8) and formula (10) respectively, formula (11) and public affairs can be calculated
Formula (12),
(g) formula (13) can be obtained by formula (11) expansion,
(h) formula (14) can be obtained by formula (12) expansion,
Step 7, building face face geometrical constraint, carry out plane fitting to scaling board three-dimensional point cloud, obtain fit Plane, this is quasi-
It closes plane and is known as scaling board laser scanning face；Using coordinate transform, scaling board laser scanning face is transformed to by laser coordinate system
Camera coordinates system, and be overlapped by scaling board laser scanning face with scaling board plane, to construct face face geometrical constraint, specifically include
Following sub-step:
(a) least square method is utilized, to j-th of pose scaling board three-dimensional point cloud PjPlane fitting is carried out, it is flat to obtain fitting
The normal vector in faceAnd passing pointThe fit Plane is known as scaling board laser and sweeps
Retouch face；
(b) coordinate transform is utilized, by the normal vector d in scaling board laser scanning facejWith passing point ejBy laser coordinate, system is converted
To camera coordinates system, expression-form is described by formula (15) and formula (16),
In formula,For the normal vector in j-th of pose scaling board laser scanning face under camera coordinates system, djFor laser coordinate system
The normal vector in lower j-th of pose scaling board laser scanning face,For j-th of pose scaling board laser scanning face under camera coordinates system
Passing point, ejFor the passing point in j-th of pose scaling board laser scanning face under laser coordinate system, R is laser coordinate system and phase
Spin matrix between machine coordinate system, translation vector of the t between laser coordinate system and camera coordinates system；
(c) it under camera coordinates system, is overlapped using scaling board laser scanning face with scaling board plane, i.e. scaling board plane
Normal vector is parallel with the normal vector in scaling board laser scanning face, and the passing point in scaling board laser scanning face is in scaling board plane
On, to construct face face geometrical constraint, expression-form is described by formula (17) and formula (18),
Wherein, in formula (17) " | | " indicate that vector is parallel；
(d) by formula (18), formula (19) can be calculated,
(e) formula (15) and formula (16) are substituted into formula (17) and formula (19) respectively, formula (20) can be calculated
With formula (21),
(f) formula (22) and formula (23) can be obtained by formula (20) expansion,
(g) formula (24) can be obtained by formula (21) expansion,
Step 8, the geometric maps relationship for calculating point cloud and image have acquired scaling board three under different positions and pose in step 2
Dimension point cloud P={ Pj| 1≤j≤m }, j-th of pose scaling board three-dimensional point cloud
IncludeThe number of a laser scanning point, the then laser scanning point that scaling board three-dimensional point cloud P includes under different positions and pose isJ-th of pose scaling board three-dimensional point cloudIncludeLaser scanning line, then the item number for the laser scanning line that scaling board three-dimensional point cloud P includes under different positions and pose areMeanwhile the scaling board laser scanning that scaling board three-dimensional point cloud P includes under different positions and pose
The number in face is m；Utilize sub-step (f) in sub-step (g) in sub-step (e) in step 5, step 6 and sub-step (h), step 7
With sub-step (g), buildingA formula (5),A formula (13),A formula (14), m formula (22), m formula
(23), m formula (24), simultaneousA formula forms over-determined systems, and expression-form presses formula (25)
Description,
The over-determined systems are solved using least square method, can be obtained the rotation between laser coordinate system and camera coordinates system
Torque battle array R and translation vector t；Using camera pinhole model, internal reference matrix A, spin matrix R and translation vector t, constructs laser and sit
The geometric maps relationship of laser point and pixel in image coordinate system, is described by formula (26) in mark system,
In formula, s is camera amplification coefficient, and (u, v) is pixel coordinate in image coordinate system, and A is to have acquired in step 3
Camera internal reference matrix, R are the spin matrix in step 8 between the laser coordinate system acquired and camera coordinates system, and t is step 8
In translation vector between the laser coordinate system acquired and camera coordinates system, (x, y, z) is that laser point is sat in laser coordinate system
Mark；Complete the calibration of three-dimensional laser scanner and camera.
The medicine have the advantages that a kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method, including
Following steps: (1) production black and white grid scaling board, (2) acquisition scaling board three-dimensional point cloud and two dimensional image, (3) camera calibration,
(4) scaling board plane is calculated in camera coordinates system, (5) establish point face geometrical constraint, and (6) establish line face geometrical constraint, and (7) are built
Facade face geometrical constraint, (8) calculate the geometric maps relationship of point cloud and image.Compared with the prior art, advantages of the present invention exists
In: the structure of three-dimensional point cloud is analysed in depth, while about using point face geometrical constraint, line face geometrical constraint and face face geometry
Three kinds of thoughts of beam, it is sufficiently sharp to solve the geometric maps relationship in laser coordinate system midpoint cloud and image coordinate system between image
With the geometrical relationship between scaling board plane and laser scanning point, to make the calibration of three-dimensional laser scanner and camera more
Accurately and reliably.
Detailed description of the invention
Fig. 1 is the method for the present invention flow chart of steps.
Fig. 2 is black and white grid scaling board schematic diagram.
Fig. 3 is a cloud and Image Acquisition schematic diagram.
In figure: being (a) scaling board, be (b) three-dimensional laser scanner and camera.
Fig. 4 is that j-th of pose scaling board vector calculates schematic diagram.
In figure: being (a) j-th of pose scaling board, be (b) camera coordinates system.
Fig. 5 is a face geometrical constraint building schematic diagram.
In figure: being (a) j-th of pose scaling board, be (b) camera coordinates system.
Fig. 6 is line face geometrical constraint building schematic diagram.
In figure: being (a) j-th of pose scaling board, be (b) camera coordinates system.
Fig. 7 is face face geometrical constraint building schematic diagram.
In figure: being (a) j-th of pose scaling board, be (b) camera coordinates system.
Fig. 8 is a cloud and image co-registration result figure.
Specific embodiment
The present invention will be further explained below with reference to the attached drawings.
As shown in Figure 1, a kind of three-dimensional laser scanner based on geometrical constraint and camera extrinsic calibration method, including it is following
Step:
Step 1, production scaling board, scaling board are uniform-distribution with the black and white that side length is 6cm having a size of 72cm × 72cm thereon
Grid, as shown in Figure 2.
Step 2, acquisition scaling board three-dimensional point cloud and two dimensional image, fixed three-dimensional laser scanner and camera, by scaling board
Towards three-dimensional laser scanner and camera, scaling board is scanned using three-dimensional laser scanner, obtains the three-dimensional point cloud of scaling board, together
When, scaling board is shot using camera, obtains the two dimensional image of scaling board；The pose for changing scaling board continues to scan on shooting calibration
Plate, to obtain the three-dimensional point cloud P={ P of scaling board under one group of different positions and posej| 1≤j≤m } and two-dimensional image I={ Ij|1≤j
≤ m }, wherein m is scaling board pose number,It is demarcated for j-th of pose
Plate three-dimensional point cloud, For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud,It is
The number of laser scanning point in j pose scaling board three-dimensional point cloud,For jth
A pose scaling board two dimensional image,For ith pixel point in j-th of pose scaling board two dimensional image,
For the number of pixel in j-th of pose scaling board two dimensional image；Laser coordinate system [Ol；X, y, z] origin OlPositioned at laser light
The heart, x/y plane are parallel to three-dimensional laser scanner pedestal；Camera coordinates systemOrigin OcPositioned at camera lens light
The heart,Plane is parallel to image sensor plane；Scaling board coordinate systemOrigin ObPositioned at scaling board upper left
Angular vertex,Plane is located at scaling board plane；Image coordinate system [Oa；U, v] origin OaPositioned at as plane top left corner apex, uv
Plane is located at image sensor plane, as shown in Figure 3.
Step 3, camera calibration utilize the tool box Calib and different positions and pose scaling board two-dimensional image I={ I of matlabj|
1≤j≤m }, calculate the external parameter under camera internal reference matrix A and every kind of poseWithWherein,For under j-th of pose
Spin matrix between scaling board coordinate system and camera coordinates system,For scaling board coordinate system and camera coordinates under j-th of pose
Translation vector between system.
Step 4 calculates scaling board plane in camera coordinates system, in camera coordinates system, in j-th of pose of scaling board
Under, with scaling board vectorIndicate scaling board plane,Direction it is parallel with the normal direction of scaling board plane,Size etc.
In camera coordinates system origin to the vertical range of scaling board plane, as shown in figure 4, utilizing spin matrixAnd translation vector
Calculating scaling board vector isWherein,For spin matrixThe 3rd column column vector.
Step 5, a foundation point face geometrical constraint are become scaling board laser scanning point by laser coordinate system using coordinate transform
Camera coordinates system is changed to, and through scaling board laser scanning point in scaling board plane, it is specific to wrap to construct a face geometrical constraint
Include following sub-step:
(a) coordinate transform is utilized, scaling board laser scanning point is transformed into camera coordinates system by laser coordinate system, is expressed
Form is described by formula (1),
In formula,For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud under camera coordinates system,It is sharp
I-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud under light coordinate system, R are laser coordinate system and camera coordinates system
Between spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(b) under camera coordinates system, using scaling board laser scanning point in scaling board plane, building point face geometry is about
Beam, as shown in figure 5, its expression-form is described by formula (2),
(c) by formula (2), formula (3) can be calculated,
(d) formula (1) is substituted into formula (3), formula (4) can be calculated,
(e) formula (5) can be obtained by formula (4) expansion,
Wherein,For the spin matrix between laser coordinate system and camera coordinates system, t=
(t1,t2,t3) translation vector between laser coordinate system and camera coordinates system,For camera coordinates system
In j-th of pose scaling board vector,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud
I-th of laser scanning point.
Step 6, building line face geometrical constraint, according to the scanning mode of three-dimensional laser scanner, by scaling board three-dimensional point cloud
If being decomposed into main line point cloud, and straight line fitting is carried out to each line point cloud, obtain fitting a straight line, which is known as demarcating
Plate laser scanning line；Using coordinate transform, scaling board laser scanning line is transformed into camera coordinates system by laser coordinate system, and lead to
Scaling board laser scanning line is crossed in scaling board plane, to construct line face geometrical constraint, specifically includes following sub-step:
(a) three-dimensional laser scanner is there are two types of working method, one is the horizontal and vertical rotation by single line laser come
Realize 3-D scanning, another kind is to realize 3-D scanning by the transverse rotation of multi-thread laser, the three of both working methods
Dimension laser scanner obtain three-dimensional point cloud be rule mesh format three dimensional point cloud therefore can be according to three-dimensional point cloud net
The vertical and horizontal of lattice are by scaling board three-dimensional point cloud PjSeveral line point clouds are decomposed into, i.e.,
Wherein,For kth line point cloud in j-th of pose scaling board three-dimensional point cloud, it is distributed on laser scanning line by a series of
Orderly discrete point composition,For the item number of j-th of pose scaling board three-dimensional point cloud centerline cloud；
(b) least square method is utilized, to line point cloudStraight line fitting is carried out, the direction vector of fitting a straight line is obtainedAnd passing pointThe fitting a straight line is known as scaling board laser scanning line,
As shown in Figure 6；
(c) coordinate transform is utilized, by the direction vector of scaling board laser scanning lineAnd passing pointBy laser coordinate system
Camera coordinates system is transformed to, expression-form is described by formula (6) and formula (7),
In formula,For under camera coordinates system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction to
Amount,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction vector,For phase
Under machine coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line passing point,It is under laser coordinate system
The passing point of kth laser scanning line in j pose scaling board three-dimensional point cloud, R is between laser coordinate system and camera coordinates system
Spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(d) under camera coordinates system, using scaling board laser scanning line in scaling board plane, i.e. the method for scaling board plane
To the direction vector perpendicular to scaling board laser scanning line, and the passing point of scaling board laser scanning line is in scaling board plane,
Line face geometrical constraint is constructed, as shown in fig. 6, its expression-form is described by formula (8) and formula (9),
(e) by formula (9), formula (10) can be calculated,
(f) formula (6) and formula (7) are substituted into formula (8) and formula (10) respectively, formula (11) and public affairs can be calculated
Formula (12),
(g) formula (13) can be obtained by formula (11) expansion,
(h) formula (14) can be obtained by formula (12) expansion,
Step 7, building face face geometrical constraint, carry out plane fitting to three-dimensional point cloud, obtain fit Plane, the fit Plane
Referred to as scaling board laser scanning face；Using coordinate transform, scaling board laser scanning face is transformed into camera by laser coordinate system and is sat
Mark system, and be overlapped by scaling board laser scanning face with scaling board plane, to construct face face geometrical constraint, specifically include following son
Step:
(a) least square method is utilized, to j-th of pose scaling board three-dimensional point cloud PjPlane fitting is carried out, it is flat to obtain fitting
The normal vector in faceAnd passing pointThe fit Plane is known as scaling board laser
Scanning surface, as shown in Figure 7；
(b) coordinate transform is utilized, by the normal vector d in scaling board laser scanning facejWith passing point ejBy laser coordinate, system is converted
To camera coordinates system, expression-form is described by formula (15) and formula (16),
In formula,For the normal vector in j-th of pose scaling board laser scanning face under camera coordinates system, djFor laser coordinate system
The normal vector in lower j-th of pose scaling board laser scanning face,For j-th of pose scaling board laser scanning face under camera coordinates system
Passing point, ejFor the passing point in j-th of pose scaling board laser scanning face under laser coordinate system, R is laser coordinate system and phase
Spin matrix between machine coordinate system, translation vector of the t between laser coordinate system and camera coordinates system；
(c) it under camera coordinates system, is overlapped using scaling board laser scanning face with scaling board plane, i.e. scaling board plane
Normal vector is parallel with the normal vector in scaling board laser scanning face, and the passing point in scaling board laser scanning face is in scaling board plane
On, to construct face face geometrical constraint, expression-form is described by formula (17) and formula (18),
Wherein, in formula (17) " | | " indicate that vector is parallel；
(d) by formula (18), formula (19) can be calculated,
(e) formula (15) and formula (16) are substituted into formula (17) and formula (19) respectively, formula (20) can be calculated
With formula (21),
(f) formula (22) and formula (23) can be obtained by formula (20) expansion,
(g) formula (24) can be obtained by formula (21) expansion,
Step 8, the geometric maps relationship for calculating point cloud and image have acquired scaling board three under different positions and pose in step 2
Dimension point cloud P={ Pj| 1≤j≤m }, j-th of pose scaling board three-dimensional point cloud
IncludeThe number of a laser scanning point, the then laser scanning point that scaling board three-dimensional point cloud P includes under different positions and pose isJ-th of pose scaling board three-dimensional point cloudIncludeLaser scanning line, then the item number for the laser scanning line that scaling board three-dimensional point cloud P includes under different positions and pose areMeanwhile the scaling board laser scanning that scaling board three-dimensional point cloud P includes under different positions and pose
The number in face is m；Utilize sub-step (f) in sub-step (g) in sub-step (e) in step 5, step 6 and sub-step (h), step 7
With sub-step (g), buildingA formula (5),A formula (13),A formula (14), m formula (22), m formula
(23), m formula (24), simultaneousA formula forms over-determined systems, and expression-form presses formula (25)
Description,
The over-determined systems are solved using least square method, can be obtained the rotation between laser coordinate system and camera coordinates system
Torque battle array R and translation vector t；Using camera pinhole model, internal reference matrix A, spin matrix R and translation vector t, constructs laser and sit
The geometric maps relationship of laser point and pixel in image coordinate system, is described by formula (26) in mark system,
In formula, s is camera amplification coefficient, and (u, v) is pixel coordinate in image coordinate system, and A is to have acquired in step 3
Camera internal reference matrix, R are the spin matrix in step 8 between the laser coordinate system acquired and camera coordinates system, and t is step 8
In translation vector between the laser coordinate system acquired and camera coordinates system, (x, y, z) is that laser point is sat in laser coordinate system
Mark；The calibration for completing three-dimensional laser scanner and camera can accurately merge two using the required geometric maps relationship of calibration
Image and three-dimensional point cloud are tieed up, three-dimensional colour point clouds are obtained, as shown in figure 8, the upper left corner is the X-Y scheme that camera shooting obtains in figure
Picture, right side are the three-dimensional point cloud that three-dimensional laser scanner scans, and the lower left corner is that three-dimensional point cloud merges to obtain with two dimensional image
Three-dimensional colour point clouds, can be clearly seen that white wall in two dimensional image, white ground, brown timber, navy blue iron gate
Color and three-dimensional point cloud in wall, ground, timber, iron gate position be accurately fused together, form true three-dimensional
Colour point clouds.
The invention has the advantages that: the structure of three-dimensional point cloud is analysed in depth, while utilizing a face geometrical constraint, line face
Three kinds of thoughts of geometrical constraint and face face geometrical constraint, to solve in laser coordinate system midpoint cloud and image coordinate system between image
Geometric maps relationship takes full advantage of the geometrical relationship between scaling board plane and laser scanning point, so that three-dimensional laser be made to sweep
The calibration for retouching instrument and camera is more accurate and reliable.
Claims (1)
1. a kind of three-dimensional laser scanner based on geometrical constraint and camera calibration method, it is characterised in that the following steps are included:
Step 1, production scaling board, scaling board are uniform-distribution with the black and white grid that side length is 6cm having a size of 72cm × 72cm thereon
Lattice；
Step 2, acquisition scaling board three-dimensional point cloud and two dimensional image, fixed three-dimensional laser scanner and camera, by scaling board towards
Three-dimensional laser scanner and camera scan scaling board using three-dimensional laser scanner, obtain the three-dimensional point cloud of scaling board, meanwhile,
Scaling board is shot using camera, obtains the two dimensional image of scaling board；The pose for changing scaling board, continues to scan on shooting scaling board,
To obtain the three-dimensional point cloud P={ P of scaling board under one group of different positions and posej| 1≤j≤m } and two-dimensional image I={ Ij|1≤j≤
M }, wherein m is scaling board pose number,For j-th of pose scaling board
Three-dimensional point cloud, For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud,For jth
The number of laser scanning point in a pose scaling board three-dimensional point cloud,For jth
A pose scaling board two dimensional image,For ith pixel point in j-th of pose scaling board two dimensional image,
For the number of pixel in j-th of pose scaling board two dimensional image；Laser coordinate system [Ol；X, y, z] origin OlPositioned at laser light
The heart, x/y plane are parallel to three-dimensional laser scanner pedestal；Camera coordinates systemOrigin OcPositioned at camera lens light
The heart,Plane is parallel to image sensor plane；Scaling board coordinate systemOrigin ObPositioned at scaling board upper left
Angular vertex,Plane is located at scaling board plane；Image coordinate system [Oa；U, v] origin OaPositioned at as plane top left corner apex, uv
Plane is located at image sensor plane；
Step 3, camera calibration utilize the tool box Calib and different positions and pose scaling board two-dimensional image I={ I of matlabj|1≤j
≤ m }, calculate the external parameter under camera internal reference matrix A and every kind of poseWithWherein,To be demarcated under j-th of pose
Spin matrix between plate coordinate system and camera coordinates system,For scaling board coordinate system under j-th of pose and camera coordinates system it
Between translation vector；
Step 4 calculates scaling board plane in camera coordinates system, in camera coordinates system, under j-th of pose of scaling board, uses
Scaling board vectorIndicate scaling board plane,Direction it is parallel with the normal direction of scaling board plane,Size be equal to phase
Machine coordinate origin utilizes spin matrix to the vertical range of scaling board planeAnd translation vectorCalculate scaling board vector
ForWherein,For spin matrixThe 3rd column column vector；
Step 5, a foundation point face geometrical constraint are transformed to scaling board laser scanning point by laser coordinate system using coordinate transform
Camera coordinates system, and by scaling board laser scanning point in scaling board plane, to construct a face geometrical constraint, specifically include with
Lower sub-step:
(a) coordinate transform is utilized, scaling board laser scanning point is transformed into camera coordinates system, expression-form by laser coordinate system
It is described by formula (1),
In formula,For i-th of laser scanning point in j-th of pose scaling board three-dimensional point cloud under camera coordinates system,For laser seat
Mark is i-th of laser scanning point in lower j-th of pose scaling board three-dimensional point cloud, and R is between laser coordinate system and camera coordinates system
Spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(b) under camera coordinates system, using scaling board laser scanning point in scaling board plane, building point face geometrical constraint,
Expression-form is described by formula (2),
(c) by formula (2), formula (3) can be calculated,
(d) formula (1) is substituted into formula (3), formula (4) can be calculated,
(e) formula (5) can be obtained by formula (4) expansion,
Wherein,For the spin matrix between laser coordinate system and camera coordinates system, t=(t1,t2,
t3) translation vector between laser coordinate system and camera coordinates system,It is j-th in camera coordinates system
Pose scaling board vector,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud i-th swash
Optical scanning point；
Step 6, building line face geometrical constraint decompose scaling board three-dimensional point cloud according to the scanning mode of three-dimensional laser scanner
If for main line point cloud, and carrying out straight line fitting to each line point cloud, fitting a straight line is obtained, which is known as scaling board and swashs
Optical scanning line；Using coordinate transform, scaling board laser scanning line is transformed into camera coordinates system by laser coordinate system, and pass through mark
Fixed board laser scanning line, to construct line face geometrical constraint, specifically includes following sub-step in scaling board plane:
(a) there are two types of working methods for three-dimensional laser scanner, and one is realized by the horizontal and vertical rotation of single line laser
3-D scanning, another kind are to realize 3-D scanning by the transverse rotation of multi-thread laser, and the three-dimensional of both working methods swashs
Photoscanner obtain three-dimensional point cloud be rule mesh format three dimensional point cloud therefore can be according to three-dimensional point cloud grid
Vertical and horizontal are by scaling board three-dimensional point cloud PjSeveral line point clouds are decomposed into, i.e.,Wherein,For kth line point cloud in j-th of pose scaling board three-dimensional point cloud, by it is a series of be distributed in it is orderly on laser scanning line
Discrete point composition,For the item number of j-th of pose scaling board three-dimensional point cloud centerline cloud；
(b) least square method is utilized, to line point cloudStraight line fitting is carried out, the direction vector of fitting a straight line is obtainedAnd passing pointThe fitting a straight line is known as scaling board laser scanning line；
(c) coordinate transform is utilized, by the direction vector of scaling board laser scanning lineAnd passing pointBy laser coordinate, system is converted
To camera coordinates system, expression-form is described by formula (6) and formula (7),
In formula,For under camera coordinates system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction vector,For under laser coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line direction vector,For camera
Under coordinate system in j-th of pose scaling board three-dimensional point cloud kth laser scanning line passing point,For jth under laser coordinate system
The passing point of kth laser scanning line in a pose scaling board three-dimensional point cloud, R is between laser coordinate system and camera coordinates system
Spin matrix, translation vector of the t between laser coordinate system and camera coordinates system；
(d) under camera coordinates system, using scaling board laser scanning line in scaling board plane, i.e., the normal direction of scaling board plane is hung down
Directly in the direction vector of scaling board laser scanning line, and the passing point of scaling board laser scanning line carrys out structure in scaling board plane
Line face geometrical constraint is built, expression-form is described by formula (8) and formula (9),
(e) by formula (9), formula (10) can be calculated,
(f) formula (6) and formula (7) are substituted into formula (8) and formula (10) respectively, formula (11) and formula can be calculated
(12),
(g) formula (13) can be obtained by formula (11) expansion,
(h) formula (14) can be obtained by formula (12) expansion,
Step 7, building face face geometrical constraint, carry out plane fitting to scaling board three-dimensional point cloud, obtain fit Plane, and the fitting is flat
Face is known as scaling board laser scanning face；Using coordinate transform, scaling board laser scanning face is transformed into camera by laser coordinate system
Coordinate system, and be overlapped by scaling board laser scanning face with scaling board plane, to construct face face geometrical constraint, specifically include following
Sub-step:
(a) least square method is utilized, to j-th of pose scaling board three-dimensional point cloud PjPlane fitting is carried out, the method for fit Plane is obtained
VectorAnd passing pointThe fit Plane is known as scaling board laser scanning face；
(b) coordinate transform is utilized, by the normal vector d in scaling board laser scanning facejWith passing point ejBy laser coordinate, system transforms to phase
Machine coordinate system, expression-form are described by formula (15) and formula (16),
In formula,For the normal vector in j-th of pose scaling board laser scanning face under camera coordinates system, djIt is under laser coordinate system
The normal vector in j pose scaling board laser scanning face,For the warp in j-th of pose scaling board laser scanning face under camera coordinates system
It crosses a little, ejFor the passing point in j-th of pose scaling board laser scanning face under laser coordinate system, R is that laser coordinate system and camera are sat
Spin matrix between mark system, translation vector of the t between laser coordinate system and camera coordinates system；
(c) it under camera coordinates system, is overlapped using scaling board laser scanning face with scaling board plane, i.e. the normal direction of scaling board plane
Amount is parallel with the normal vector in scaling board laser scanning face, and the passing point in scaling board laser scanning face is come in scaling board plane
Building face face geometrical constraint, expression-form are described by formula (17) and formula (18),
Wherein, in formula (17) " | | " indicate that vector is parallel；
(d) by formula (18), formula (19) can be calculated,
(e) formula (15) and formula (16) are substituted into formula (17) and formula (19) respectively, formula (20) and public affairs can be calculated
Formula (21),
(f) formula (22) and formula (23) can be obtained by formula (20) expansion,
(g) formula (24) can be obtained by formula (21) expansion,
Step 8, the geometric maps relationship for calculating point cloud and image have acquired scaling board three-dimensional point under different positions and pose in step 2
Cloud P={ Pj| 1≤j≤m }, j-th of pose scaling board three-dimensional point cloud
IncludeThe number of a laser scanning point, the then laser scanning point that scaling board three-dimensional point cloud P includes under different positions and pose isJ-th of pose scaling board three-dimensional point cloudIncludeLaser scanning line, then the item number for the laser scanning line that scaling board three-dimensional point cloud P includes under different positions and pose areMeanwhile the scaling board laser scanning that scaling board three-dimensional point cloud P includes under different positions and pose
The number in face is m；Utilize sub-step (f) in sub-step (g) in sub-step (e) in step 5, step 6 and sub-step (h), step 7
With sub-step (g), buildingA formula (5),A formula (13),A formula (14), m formula (22), m formula
(23), m formula (24), simultaneousA formula forms over-determined systems, and expression-form presses formula (25)
Description,
The over-determined systems are solved using least square method, can be obtained the spin moment between laser coordinate system and camera coordinates system
Battle array R and translation vector t；Using camera pinhole model, internal reference matrix A, spin matrix R and translation vector t, laser coordinate system is constructed
The geometric maps relationship of pixel, is described by formula (26) in middle laser point and image coordinate system,
In formula, s is camera amplification coefficient, and (u, v) is pixel coordinate in image coordinate system, and A is the camera acquired in step 3
Internal reference matrix, R are spin matrix between the laser coordinate system acquired and camera coordinates system in step 8, t be in step 8
Translation vector between the laser coordinate system acquired and camera coordinates system, (x, y, z) are laser point coordinates in laser coordinate system；It is complete
At the calibration of three-dimensional laser scanner and camera.
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