CN102034238A - Multi-camera system calibrating method based on optical imaging test head and visual graph structure - Google Patents
Multi-camera system calibrating method based on optical imaging test head and visual graph structure Download PDFInfo
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Abstract
The invention provides a multi-camera system calibrating method based on an optical imaging test head and a visual graph structure. The method comprises the following steps: independently calibrating each camera by the optical imaging test head to obtain the initial values of the internal parameter and aberration parameter of each camera; calibrating the multiple cameras two by two, and obtaining the fundamental matrix, polar constraint, rotation matrix and translation vector between every two cameras with a plurality of overlapped regions at a view field by means of linear estimation; building the connection relationship among the multiple cameras according to the graph theory and the visual graph structure, and estimating the rotation vector quantity initial value and translation vector quantity initial value of each camera relative to the referred cameras by a shortest path method; and optimally estimating all the internal parameters and external parameters of the all cameras and the acquired three-dimensional sign point set of the optical imaging test head by a sparse bundling and adjusting algorithm to obtain a high-precision calibrating result. The multi-camera system calibrating method is simple in a calibrating process from the partial situation to the overall situation and from the robust to the precise, ensures high-precise and robust calibration, and is applied to calibrating multi-camera systems with different measurement ranges and different distribution structures.
Description
Technical Field
The invention belongs to the technical field of vision measurement, and relates to a multi-camera system calibration method based on an optical imaging measuring head and a vision graph structure.
Background
The three-dimensional measurement is carried out by using a multi-camera system, and the calibration of the internal parameters and distortion parameters of each camera, the relative poses among the cameras and the pose parameters of a reference coordinate system must be completed firstly. The robustness and the precision of the calibration directly determine the measurement precision of the multi-camera system, so the robustness and the high-precision calibration are the premise and the condition for realizing the high-precision calibration of the multi-camera system.
Camera calibration has long been known and many effective methods have been available over decades. In recent years, due to the unique and obvious characteristics of a multi-camera system on large-scale and large-range measurement, the multi-camera system is widely paid attention to domestic and foreign research, and particularly, the high efficiency and high precision of the multi-camera system become a research hotspot. However, some of the conventional multi-camera calibration methods use electronic theodolites to establish a world coordinate system, thereby increasing the cost and complexity of the system; some adopt three-dimensional, two-dimensional, one-dimensional or 0-dimensional calibration objects, and directly utilize the pose relationship between the internal parameters of a single camera and the cameras to complete the estimation of the calibration parameters of the multi-camera system, so that on one hand, the calibration objects are required to be visible in all the camera fields, on the other hand, the calibration results are influenced by noise, calculation errors, initial parameter errors and the like, and the precision is low; although some methods also adopt a binding adjustment optimization method in the final stage of calibration, the acquisition process of the three-dimensional calibration point set is complex, and extra points need to be discarded, so that the efficiency is low and the robustness is poor.
Disclosure of Invention
The invention aims to provide a multi-camera system calibration method based on an optical imaging measuring head and a visual diagram structure, aiming at the defects or shortcomings of the existing calibration technology. The method can simultaneously complete the internal and external parameter calibration of a single camera and the calibration of a multi-camera system only by one calibrated optical imaging measuring head, is simple, does not need the optical imaging measuring head to be visible in all the camera fields, only needs two or more cameras to be visible in the field, and is suitable for various measurement fields. And the calibration of the multi-camera system is completed from coarse to fine by adopting a visual diagram structure and binding adjustment optimization, so that the robustness and high precision of the result are ensured.
In order to achieve the purpose, the invention adopts the technical scheme that:
step 1, establishing hardware:
by adopting a plurality of distributed cameras and an optical imaging measuring head, all the cameras do not require overlapped view field spaces, but require at least two cameras to have overlapped view fields:
and 2, determining the spatial position of each camera, determining one or more spatial positioning points for each camera, and positioning the optical imaging measuring head within the field of view of the calibrated camera according to the principle of spatial positioning point selection, namely in the calibration process of a single camera or multiple cameras. During calibration of a single camera, firstly, a reference positioning block (1) is installed on a corresponding positioning point, an optical imaging measuring head is placed in the field range of each camera and aligned with the reference positioning block (1), the optical imaging measuring head is rotated by taking a measuring tip (2) of the optical imaging measuring head as a circle center, seven mark points (5) on an optical imaging measuring head target body 4 concentrically rotate by taking the measuring tip (2) as the circle center, and the camera acquires a plurality of images of the optical imaging measuring head in different postures; secondly, extracting the central coordinate of each LED sub-pixel in each image by adopting a threshold segmentation and ellipse fitting algorithm, and calculating the central coordinate of each mark point 5 by adopting a gravity center method; finally, recovering the internal parameter matrix and distortion parameters of each camera according to the concentric circle rotation relation of the mark points 5 and the calibrated space distance invariant relation;
step 3, reselecting and positioning the space positioning point, adjusting the posture of the optical imaging measuring head, and ensuring that the optical imaging measuring head is positioned in the overlapped field of view of every two or more cameras; in the overlapped view field, rotating the optical imaging measuring head, simultaneously acquiring the LED images of the mark points of the optical imaging measuring head by the cameras with overlapped view fields, recovering the basic matrix, the essential matrix, the polar line geometric relationship, the rotation matrix and the translation vector between two local cameras through image processing, center recognition and mark point matching and according to the geometric constraint between the mark points;
step 4, taking each camera as a node, taking every two cameras with overlapped fields of view as edges, constructing a visual graph of the multi-camera system, wherein the direction of each edge is determined by the initially calibrated local rotation matrix and the translation vector, and the former camera points to the other camera after transformation; in the visual map, firstly determining a reference camera, starting from the reference camera, establishing a connection relation among all cameras, and calculating a rotation matrix and a translation vector of each camera relative to the reference camera by adopting a shortest path method to realize global initial calibration of a multi-camera system;
step 5, according to the initial calibration result, the mark points acquired, identified and obtained in the step 2 and the step 3 are back projected to a reference camera coordinate system, so that a three-dimensional calibration point set in a world coordinate system is established; performing optimization estimation on all calibration parameters and the three-dimensional calibration point set by adopting a sparse bundling adjustment algorithm to obtain a robust and high-precision calibration result;
step 6, if the calibration result meets the measurement precision requirement, the calibration process is finished; if the three-dimensional calibration point set does not meet the requirement, the number of the positioning points of the optical imaging measuring head is increased, the image is collected again, the identified and reconstructed new three-dimensional calibration points are added to the original marker point set, all calibration parameters and the three-dimensional calibration point set are optimized again by adopting a sparse binding adjustment algorithm, and all parameters are calibrated again.
Each marking point 5 consists of six LEDs, and the center of gravity of the marking point is the center of the marking point.
The step 2 comprises the following steps:
step 21, establishing a camera pinhole projection model:
first, a world coordinate system X is establishedWYWZWCoordinate system X of measuring headtYtZtAn image coordinate scale coordinate system xy and a pixel coordinate system uv, wherein N is 7 mark points on the optical imaging measuring head,indicating the coordinates of the mark point in the measuring head coordinate system,
representing the coordinates of the mark point in the world coordinate system, (R, T) are the rotation and translation parameters of the camera relative to the world coordinate system, K is the internal parameter matrix of the camera, and comprises 5 parameters, namely the horizontal and vertical focal lengths (f)x，fy) The image tilt factor s and the optical center coordinates (u0, v0), (k1, k2, d1, d2) are distortion parameters of a radial direction and a tangential direction respectively, and 7 mark points (5) on the measuring head target surface (4) satisfy the following projection relation:
wherein λ isjIs the projected depth of landmark point j;
indicating the normalized coordinates of the landmark point j on the image.
Step 22, calibrating image acquisition and marking point identification: selecting a space positioning point according to a principle of space positioning point selection, fixing a reference positioning block (1), rotating an optical imaging measuring head by taking a measuring tip (2) as a circle center, acquiring I1 images with different postures by using a camera, distributing the acquired images in a field space of the camera as much as possible, extracting a sub-pixel center of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center of each mark point by adopting a gravity center method;
step 23, according to the invariance of the radius of the concentric circle, establishing an error function of the distance between each mark point and the measuring tip when the optical imaging measuring head rotates around the measuring tip (2), wherein 7 mark points respectively have the radius rjRotating concentrically around the measuring tip (2), and because the positions of all the mark points are accurately calibrated, the rotating radiuses r of 7 concentric circlesjAnd (3) keeping the radius of the concentric circles unchanged, keeping the distance from each mark point to the measuring tip unchanged during the rotation process of the measuring head, and obtaining a radius error equation for each mark for the I1 rotationally acquired images:
wherein,
denotes an estimated rotation radius r of the jth (j-1, …, 7) index point at the ith rotationjA calibration value representing the turning radius of the jth (j ═ 1, …, 7) index point;
step 24, estimating initial values of internal and external parameters of the camera: solving initial values of a parameter matrix K, a rotation matrix R and a translational vector T in the camera by a radius error function of a minimum formula (3) due to the existence of errors, and estimating an initial value of a distortion parameter by a back projection error minimum
And 25, further improving the calibration precision by adopting a sparse binding adjustment algorithm.
The step 3 comprises the following steps:
step 31, acquiring the measuring head mark point images in the overlapped view field: reselecting and positioning a space positioning point (L1, L2.. once.), adjusting the posture of the optical imaging measuring head to ensure that the optical imaging measuring head is positioned in the overlapped visual field of every two or more cameras, rotating the optical imaging measuring head, and simultaneously acquiring a three-dimensional image of the measuring head marking point by the cameras with overlapped visual fields in the area;
step 32, identifying and matching the mark points of the stereo image: extracting the center of a sub-pixel of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center of each mark point by adopting a gravity center method; fast matching the mark points of the stereo image pair according to the mark point position constraint and the geometric moment invariance rule;
step 33, estimating the fundamental matrix and epipolar geometry:
assuming that the two cameras C1 and C2 have overlapped view field spaces, and no loss of generality, the origin of world coordinates is positioned at the center of the camera C1, and the pose of the camera C1 is (R)1，T1) The pose of the camera C2 is (R, 0)2，T2) The relative relationship between the two cameras is (R, T). ThenImage coordinates of two cameras acquired same-name mark point j
The following relations exist between the following components:
estimating unknown scale parameters from the equation
And
and obtain
WhereinI.e. the required fundamental matrix, and if there are enough pairs of landmark points, the 9 parameters of the fundamental matrix are solved linearly. Meanwhile, in step 2, the intrinsic parameter matrix K of the two cameras C1 and C21，K2Has been calibrated, using coordinate values
(i ═ 1, 2) estimating the epipolar constraint relationship of the stereo images:
wherein,
the method is an essential matrix, and an essential matrix E can be estimated by using a 7-point algorithm;
step 34, estimating the relative pose and scale factor between every two cameras:
because the positions of 7 mark points on the measuring head are known, a rotation matrix R and a translation vector T between every two cameras can be uniquely determined, and when the scale factor is estimated, the normalized radius of the mark point relative to the rotation of the measuring tip is used
And actual nominal radius
The following results were obtained:
taking the average value of 7 point estimates or the average value of N times of measurement as a final scale factor lambda due to the existence of errors;
the step 4 comprises the following steps:
step 41, constructing a visual diagram of the multi-camera system according to a diagram theory:
constructing a visual graph of the multi-camera system by taking each camera as a node and taking every two cameras with overlapped view fields as edges, wherein in the visual graph, the direction of each edge is temporarily determined by an initially calibrated local rotation matrix and a translation vector, and the other camera after transformation is pointed by the previous camera;
step 42, determining the reference cameras, and reestablishing the connection relationship between the cameras:
in the visual map, determining a reference camera, considering the relation with the adjacent camera when selecting the reference camera, and readjusting and establishing the connection relation between the cameras from the reference camera;
step 43, determining the rotation and translation amount of each camera in the reference camera coordinate system by adopting a shortest path method;
solving for the absolute position from the reference camera to each camera using the shortest path, let Ci，Cj，CkThe cameras which are mutually connected on a certain path of the visual map respectively obtain the secondary camera C for every two calibrated camerasiTo CjAnd CjTo CkOf (A) a transformation matrix (R)ij，Tij) And (R)jk，Tjk) From CiTo CkIs calculated by the following equation:
Rik＝RijRjk，Tik＝Tij+RijTjk (9)
and if the number of nodes on the path of the reference camera is more than two, solving by using the above formula for multiple times to finish absolute calibration of all cameras relative to the reference camera.
The step 5 comprises the following steps:
step 51, obtaining an initial three-dimensional calibration point set
In the step 22 and the step 32, image coordinates of different calibration points of the marker point in all cameras are collected and identified, a three-dimensional sparse calibration point set is obtained by back projection according to all calibration parameters obtained in the previous 4 steps, and errors exist in the reconstructed three-dimensional sparse calibration point set and the calibration parameters due to the fact that a simple connection relation of multiple cameras is used in calibration;
step 52, constructing a back projection error function
Supposing that n three-dimensional coordinate points and m cameras are arranged, the projection coordinate of the ith point on the jth camera image is xijThe parameter of each camera is represented by a vector ajRepresenting, each three-dimensional point by a vector biShowing that the function Q (,) defines the projection of a three-dimensional point on the image surface of the camera, the function d (x, y) represents the Euclidean distance between the image points x and y, and the following back projection error function is established according to the projective geometrical relationship:
and step 53, using the binding adjustment minimized back projection error function to obtain an accurate calibration result.
The back projection error function is a function containing P e □MProblem of non-linear minimization of parameter vectors, P ∈ RMThe parameter vector is formed by the pose parameters of all cameras and a three-dimensional measuring point set X-shaped □NAnd (4) forming.
In order to realize the calibration of the internal and external parameters of a single camera and the relative pose of every two cameras, the invention adopts an optical imaging measuring head as a calibration object, 7 marked points with calibrated positions are arranged on the optical imaging measuring head (each marked point consists of 6 LEDs, the gravity center of the marked point is the center of the marked point), and the internal and external parameters of the cameras are recovered according to the concentric rotation motion relation of the marked points on the target surface of the measuring head around a measuring tip, thereby realizing the rapid calibration. Because the measuring space is large and the visual field of the camera is limited, the invention regards the multi-camera system as a visual graph structure relationship, each camera is a node of the visual graph, the edge of the visual graph represents the overlapped visual field range between the nodes (cameras), the edge of the visual graph has directionality, and the representing pose is changed from the previous camera to the other camera; and optimizing all pose initial parameters of the multi-camera system on a visual map by a shortest path method. Meanwhile, because the noise and the error in the coordinate transformation can influence the overall precision of the system, the invention further adopts a sparse binding adjustment algorithm to carry out optimization adjustment on the acquired three-dimensional mark points and all initial calibration parameters so as to improve the precision of the calibration parameters. By using the method, the overall error of system calibration is greatly reduced, and the robustness of each parameter is obviously improved.
Drawings
Fig. 1 is a schematic diagram of the projection relationship between the optical imaging probe and the camera.
Wherein the reference numerals denote: 1. the measuring head comprises a reference positioning block, 2, a measuring tip, 3, an extension bar, 4, a measuring head target body and 5 and 7 mark points (each mark point consists of 6 LED light spots). XWYWZWRepresenting the world coordinate system, XtYtZtRepresenting a measuring head coordinate system, an xy image coordinate scale coordinate system and uv representing an image pixel coordinate system; P1-P7 represent 7 mark points on the optical imaging measuring head, and r 1-r 7 are distances from the 7 mark points to the measuring tip respectively.
FIG. 2 is a schematic diagram of relative position calibration of two cameras with overlapping fields of view.
Wherein the reference numbers: C1-C8 represent 8 cameras, L1 and L2 represent the positions of positioning points, and R and T represent relative pose transformation relations.
Fig. 3 is a visual diagram construction diagram of a multi-camera system.
Wherein the reference numbers: C1-C8 represent 8 cameras.
Fig. 4 is a schematic diagram illustrating a change in connection relation for determining the front and rear visual images of the reference camera.
Wherein the reference numbers: C1-C8 represent 8 cameras.
Fig. 5 is a schematic diagram of global calibration under a reference camera coordinate system.
Wherein the reference numbers: C1-C8 represent 8 cameras, L1 and L2 represent the positions of positioning points, and R and T represent relative pose transformation relations.
Detailed Description
The invention will be further explained with reference to the drawings.
The following description will specifically discuss a vision system including 8 cameras as an example. The present invention uses an optical imaging probe as shown in figure 1. The optical imaging measuring head mainly comprises a measuring tip (2), an extension bar (3), a target body (4), 7 mark points (5) and LED light spots. The distribution of 8 cameras is shown in fig. 3, where all cameras do not require overlapping fields of view, but at least every second camera has an overlapping field of view. According to the method, a space positioning point is selected and determined according to the space distribution of 8 cameras, and independent calibration of a single camera and relative pose calibration of every two cameras are completed by utilizing the rotation invariant relation of an optical imaging measuring head around a measuring tip. And then, constructing a connection relation of the multiple cameras according to the graph theory and the visual graph, and completing the calibration of the multiple cameras under a reference camera coordinate system. And finally, globally optimizing the three-dimensional geometric structure and all calibration parameters by adopting a sparse bundling adjustment algorithm in order to eliminate the initial calibration error.
The following describes the steps in a specific order of calibration.
The first stage is as follows: and (4) independently calibrating intrinsic parameters and distortion parameters of the single camera.
The numbers of the cameras are C1-C8, as shown in FIG. 2.
Step 11, establishing a world coordinate system X according to the projection relation between the optical imaging measuring head and the camera shown in figure 1WYWZWCoordinate system X of measuring headtYtZtAn image coordinate scale coordinate system xy and a pixel coordinate system uv.
And step 12, determining the spatial position of each camera, determining one or more spatial positioning points for each camera, and positioning the optical imaging measuring head within the field of view of the calibrated camera according to the principle of spatial positioning point selection, namely in the calibration process of a single camera or multiple cameras. In one shotDuring calibration of the camera, a reference positioning block (1) is fixed on a corresponding positioning point, an optical imaging measuring head rotates by taking a measuring tip (2) as a circle center, the camera is used for collecting I1 images with different postures, and the collected images are distributed in the field space of the camera as much as possible. Extracting the center of a sub-pixel of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center coordinate of each mark point (consisting of 6 LED light spots) by adopting a gravity center method
(I-1, …, I1; j-1, …, 7). Meanwhile, the coordinates of the N-7 mark points on the optical imaging measuring head in the measuring head coordinate system are set as
The coordinates in the world coordinate system are
And (3) establishing a projection relation of the camera according to the formula (1).
And step 13, constructing a radius error equation (2) of each mark point according to the concentric circle radius invariant geometric constraint.
And step 14, a minimized radius error function formula (3) restores the initial values of the intrinsic parameter matrix K, the rotation matrix R and the translational vector T of each camera, and estimates distortion parameters of each camera through the minimum back projection error (K1, K2, d1 and d 2).
And step 15, optimizing internal and external parameters of each camera by adopting a sparse binding adjustment algorithm, and improving the calibration precision.
And a second stage: and calibrating the relative pose of every two cameras with overlapped view fields.
A pair of 8 cameras is arbitrarily selected and grouped in the order of the small number preceding and the large number following.
Step 21, as shown in fig. 2, selecting and positioning an appropriate spatial positioning point (L1, L2,. cndot.), adjusting the posture of the optical imaging probe to ensure that the optical imaging probe is positioned in the overlapped fields of view of every two or more cameras, rotating the optical imaging probe, and simultaneously acquiring a three-dimensional image of a probe mark point by the cameras with overlapped fields of view in the area.
And step 22, extracting the center of the sub-pixel of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center of each mark point by adopting a gravity center method. And quickly matching the mark points of the stereo image pair according to the mark point position constraint and the geometric moment invariance rule.
Step 23, estimating the unknown scale parameters of each pair of cameras according to the formula (4)
And
according to the relationship
Recovering the basic matrix of each two pairs of cameras; and restoring the epipolar constraint relation of each pair of cameras according to the formula (5).
And 24, recovering the rotation matrix R and the translational vector T of each pair of cameras, and calculating a scale factor lambda according to a formula (7) and a formula (8).
And a third stage: and global calibration of the multi-camera system based on the visual map.
Step 31, as shown in fig. 3, a visual diagram of the multi-camera system is constructed by using 8 cameras as nodes and every two cameras with overlapped fields of view as edges. In the visual map, the direction of each edge is temporarily determined by the initially calibrated local rotation matrix and the translation vector, and a directional visual map as shown in fig. 4(a) is constructed.
And step 32, in the visual map, using C8 as a reference camera, readjusting and establishing a connection relationship between the cameras, and determining a new directional visual map by using a shortest path method, as shown in fig. 4 (b).
Step 33, determining the rotation and translation amount of each camera in the reference camera coordinate system according to formula (9), as shown in fig. 5. Thus, the absolute calibration of all cameras relative to the reference camera is initially completed.
A fourth stage: and carrying out global optimization calibration based on sparse binding adjustment.
Step 41, reconstructing a three-dimensional sparse calibration point set X epsilon □ through back projection according to the initial calibration parametersN。
And 42, establishing a back projection error minimum function (10) by all the calibration data and the three-dimensional point set.
And 43, using the binding adjustment minimized back projection error function to obtain an accurate calibration result.
The fifth stage: and further optimizing and estimating the calibration parameters until the three-dimensional measurement calibration precision requirement is met.
The invention is characterized in that:
the calibration method uses the imaging measuring head with fixed optical mark points to calibrate the internal and external parameters of the camera and the relative pose between the cameras, does not need any other equipment, and has simple method and low cost.
The calibration method does not need the optical imaging measuring head to be visible in all the camera view fields, only needs to be visible in the overlapped view fields of every two cameras, is suitable for multi-camera systems with different distribution structures, and can be used for small-scale space calibration and large-scale space calibration.
The visual map and the binding adjustment optimization algorithm adopted by the calibration method can obviously improve the calibration efficiency, robustness and precision.
Claims (7)
1. A multi-camera system calibration method based on an optical imaging measuring head and a visual diagram structure is characterized by comprising the following steps:
step 1, establishing hardware:
by adopting a plurality of distributed cameras and an optical imaging measuring head, all the cameras do not require overlapped view field spaces, but require at least two cameras to have overlapped view fields:
and 2, determining the spatial position of each camera, determining one or more spatial positioning points for each camera, and positioning the optical imaging measuring head within the field of view of the calibrated camera according to the principle of spatial positioning point selection, namely in the calibration process of a single camera or multiple cameras. During calibration of a single camera, firstly, a reference positioning block (1) is installed on a corresponding positioning point, an optical imaging measuring head is placed in the field range of each camera and aligned with the reference positioning block (1), the optical imaging measuring head is rotated by taking a measuring tip (2) of the optical imaging measuring head as a circle center, seven mark points (5) on an optical imaging measuring head target body 4 concentrically rotate by taking the measuring tip (2) as the circle center, and the camera acquires a plurality of images of the optical imaging measuring head in different postures; secondly, extracting the central coordinate of each LED sub-pixel in each image by adopting a threshold segmentation and ellipse fitting algorithm, and calculating the central coordinate of each mark point 5 by adopting a gravity center method; finally, recovering the internal parameter matrix and distortion parameters of each camera according to the concentric circle rotation relation of the mark points 5 and the calibrated space distance invariant relation;
step 3, reselecting and positioning the space positioning point, adjusting the posture of the optical imaging measuring head, and ensuring that the optical imaging measuring head is positioned in the overlapped field of view of every two or more cameras; in the overlapped view field, rotating the optical imaging measuring head, simultaneously acquiring the LED images of the mark points of the optical imaging measuring head by the cameras with overlapped view fields, recovering the basic matrix, the essential matrix, the polar line geometric relationship, the rotation matrix and the translation vector between two local cameras through image processing, center recognition and mark point matching and according to the geometric constraint between the mark points;
step 4, taking each camera as a node, taking every two cameras with overlapped fields of view as edges, constructing a visual graph of the multi-camera system, wherein the direction of each edge is determined by the initially calibrated local rotation matrix and the translation vector, and the former camera points to the other camera after transformation; in the visual map, firstly determining a reference camera, starting from the reference camera, establishing a connection relation among all cameras, and calculating a rotation matrix and a translation vector of each camera relative to the reference camera by adopting a shortest path method to realize global initial calibration of a multi-camera system;
step 5, according to the initial calibration result, the mark points acquired, identified and obtained in the step 2 and the step 3 are back projected to a reference camera coordinate system, so that a three-dimensional calibration point set in a world coordinate system is established; performing optimization estimation on all calibration parameters and the three-dimensional calibration point set by adopting a sparse bundling adjustment algorithm to obtain a robust and high-precision calibration result;
step 6, if the calibration result meets the measurement precision requirement, the calibration process is finished; if the three-dimensional calibration point set does not meet the requirement, the number of the positioning points of the optical imaging measuring head is increased, the image is collected again, the identified and reconstructed new three-dimensional calibration points are added to the original marker point set, all calibration parameters and the three-dimensional calibration point set are optimized again by adopting a sparse binding adjustment algorithm, and all parameters are calibrated again.
2. The method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 1, characterized in that: each marking point 5 consists of six LEDs, and the center of gravity of the marking point is the center of the marking point.
3. The method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 1, characterized in that: the step 2 comprises the following steps:
step 21, establishing a camera pinhole projection model:
first, a world coordinate system X is establishedWYWZWCoordinate system X of measuring headtYtZtAn image coordinate scale coordinate system xy and a pixel coordinate system uv, wherein N is 7 mark points on the optical imaging measuring head,
indicating the coordinates of the mark point in the measuring head coordinate system,representing the coordinates of the mark point in a world coordinate system, (R, T) are rotation and translation parameters of the camera relative to the world coordinate system, K is an internal parameter matrix of the camera, and the internal parameter matrix comprises 5 parameters which are respectively a horizontal focal distance and a vertical focal distance(fx，fy) The image tilt factor s and the optical center coordinates (u0, v0), (k1, k2, d1, d2) are distortion parameters of a radial direction and a tangential direction respectively, and 7 mark points (5) on the measuring head target surface (4) satisfy the following projection relation:
wherein λ isjIs the projected depth of landmark point j;
indicating the normalized coordinates of the landmark point j on the image.
Step 22, calibrating image acquisition and marking point identification: selecting a space positioning point according to a principle of space positioning point selection, fixing a reference positioning block (1), rotating an optical imaging measuring head by taking a measuring tip (2) as a circle center, acquiring I1 images with different postures by using a camera, distributing the acquired images in a field space of the camera as much as possible, extracting a sub-pixel center of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center of each mark point by adopting a gravity center method;
step 23, according to the invariance of the radius of the concentric circle, establishing an error function of the distance between each mark point and the measuring tip when the optical imaging measuring head rotates around the measuring tip (2), wherein 7 mark points respectively have the radius rjRotating concentrically around the measuring tip (2), and because the positions of all the mark points are accurately calibrated, the rotating radiuses r of 7 concentric circlesjAnd (3) keeping the radius of the concentric circles unchanged, keeping the distance from each mark point to the measuring tip unchanged during the rotation process of the measuring head, and obtaining a radius error equation for each mark for the I1 rotationally acquired images:
wherein,
denotes an estimated rotation radius r of the jth (j-1, …, 7) index point at the ith rotationjA calibration value representing the turning radius of the jth (j ═ 1, …, 7) index point;
step 24, estimating initial values of internal and external parameters of the camera: solving initial values of a parameter matrix K, a rotation matrix R and a translational vector T in the camera by a radius error function of a minimum formula (3) due to the existence of errors, and estimating an initial value of a distortion parameter by a back projection error minimum
And 25, further improving the calibration precision by adopting a sparse binding adjustment algorithm.
4. The method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 1, characterized in that: the step 3 comprises the following steps:
step 31, acquiring the measuring head mark point images in the overlapped view field: reselecting and positioning a space positioning point (L1, L2.. once.), adjusting the posture of the optical imaging measuring head to ensure that the optical imaging measuring head is positioned in the overlapped visual field of every two or more cameras, rotating the optical imaging measuring head, and simultaneously acquiring a three-dimensional image of the measuring head marking point by the cameras with overlapped visual fields in the area;
step 32, identifying and matching the mark points of the stereo image: extracting the center of a sub-pixel of each LED light spot by adopting a threshold segmentation and ellipse fitting algorithm, and estimating the center of each mark point by adopting a gravity center method; fast matching the mark points of the stereo image pair according to the mark point position constraint and the geometric moment invariance rule;
step 33, estimating the fundamental matrix and epipolar geometry:
assuming that the two cameras C1 and C2 have overlapped view field spaces, and no loss of generality, the origin of world coordinates is positioned at the center of the camera C1, and the pose of the camera C1 is (R)1，T1) The pose of the camera C2 is (R, 0)2，T2) The relative relationship between the two cameras is (R, T). The image coordinates of the same-name mark point j acquired by the two cameras
The following relations exist between the following components:
estimating unknown scale parameters from the equation
And
and obtain
Wherein
I.e. the required fundamental matrix, and if there are enough pairs of landmark points, the 9 parameters of the fundamental matrix are solved linearly. Meanwhile, in step 2, the intrinsic parameter matrix K of the two cameras C1 and C21，K2Has been calibrated, using coordinate values
(i ═ 1, 2) estimating the epipolar constraint relationship of the stereo images:
wherein,
the method is an essential matrix, and an essential matrix E can be estimated by using a 7-point algorithm;
step 34, estimating the relative pose and scale factor between every two cameras:
because the positions of 7 mark points on the measuring head are known, a rotation matrix R and a translation vector T between every two cameras can be uniquely determined, and when the scale factor is estimated, the normalized radius of the mark point relative to the rotation of the measuring tip is used
And the actual calibrated radius rjThe following can be obtained:
taking the average value of 7 point estimates or the average value of N times of measurement as a final scale factor lambda due to the existence of errors;
5. the method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 1, characterized in that: the step 4 comprises the following steps:
step 41, constructing a visual diagram of the multi-camera system according to a diagram theory:
constructing a visual graph of the multi-camera system by taking each camera as a node and taking every two cameras with overlapped view fields as edges, wherein in the visual graph, the direction of each edge is temporarily determined by an initially calibrated local rotation matrix and a translation vector, and the other camera after transformation is pointed by the previous camera;
step 42, determining the reference cameras, and reestablishing the connection relationship between the cameras:
in the visual map, determining a reference camera, considering the relation with the adjacent camera when selecting the reference camera, and readjusting and establishing the connection relation between the cameras from the reference camera;
step 43, determining the rotation and translation amount of each camera in the reference camera coordinate system by adopting a shortest path method;
solving for the absolute position from the reference camera to each camera using the shortest path, let Ci，Cj，CkThe cameras which are mutually connected on a certain path of the visual map respectively obtain the secondary camera C for every two calibrated camerasiTo CjAnd CjTo CkOf (A) a transformation matrix (R)ij，Tij) And (R)jk，Tjk) From CiTo CkIs calculated by the following equation:
Rik＝RijRjk，Tik＝Tij+RijTjk (9)
and if the number of nodes on the path of the reference camera is more than two, solving by using the above formula for multiple times to finish absolute calibration of all cameras relative to the reference camera.
6. The method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 1, characterized in that: the step 5 comprises the following steps:
step 51, obtaining an initial three-dimensional calibration point set
In the step 22 and the step 32, image coordinates of different calibration points of the marker point in all cameras are collected and identified, a three-dimensional sparse calibration point set is obtained by back projection according to all calibration parameters obtained in the previous 4 steps, and errors exist in the reconstructed three-dimensional sparse calibration point set and the calibration parameters due to the fact that a simple connection relation of multiple cameras is used in calibration;
step 52, constructing a back projection error function
Supposing that n three-dimensional coordinate points and m cameras are arranged, the projection coordinate of the ith point on the jth camera image is xijThe parameter of each camera is represented by a vector ajRepresenting, each three-dimensional point by a vector biShowing that the function Q (,) defines the projection of a three-dimensional point on the image surface of the camera, the function d (x, y) represents the Euclidean distance between the image points x and y, and the following back projection error function is established according to the projective geometrical relationship:
and step 53, using the binding adjustment minimized back projection error function to obtain an accurate calibration result.
7. The method for calibrating a multi-camera system based on an optical imaging probe and a visual pattern structure according to claim 5, wherein: the back projection error function is a function containing P e □MProblem of non-linear minimization of parameter vectors, P ∈ RMThe parameter vector is formed by the pose parameters of all cameras and a three-dimensional measuring point set X-shaped □NAnd (4) forming.
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