CN115797460B - Underwater double-target setting method - Google Patents
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Abstract
The invention discloses an underwater double-target determining method, which comprises the following steps of: obtaining left and right camera images of an underwater chessboard graph, establishing an underwater refraction imaging model, and obtaining an underwater target image by using a binocular camera; step 2: performing feature extraction on the image obtained in the step 1 to obtain a coordinate set of the corner points of the calibration plate in the image under a pixel coordinate system, establishing a world coordinate system on the calibration plate to obtain a coordinate set of the corner points of the calibration plate under the world coordinate system, and converting the obtained coordinate set into a camera coordinate system; step 3; based on the coordinate set obtained in the step 2, constructing a forward projection error function to perform nonlinear optimization, and obtaining the intrinsic parameters of the camera and the extrinsic parameters of the left and right cameras by minimizing the re-projection error; step 4: and after obtaining the intrinsic parameters of the camera and the extrinsic parameters of the left and right cameras, calculating a rotation and translation matrix based on the centroid distance increment matrix to obtain the extrinsic parameters of the cameras. The invention optimizes the forward projection error function in a nonlinear manner more accurately and effectively.
Description
Technical Field
The invention belongs to the technical field of underwater binocular vision, and particularly relates to an underwater double-target positioning method.
Background
In the image measurement process and the machine vision application, in order to determine the interrelation between the three-dimensional geometric position of a certain point on the surface of a space object and the corresponding point in the image, a geometric model of camera imaging must be established, the geometric model parameters are camera parameters, the process of solving the parameters is called camera calibration (or camera calibration), the calibration of the camera parameters is a very critical link in the image measurement or the machine vision application, and the accuracy of the calibration result and the stability of the algorithm directly influence the accuracy of the working generating result of the camera.
The camera parameters comprise internal parameters, the internal parameters comprise an internal parameter matrix and a distortion correction matrix, a common calibration method is to take a plurality of poses of a checkerboard or concentric circle target through a camera, then calculate the relationship between world coordinates and pixel coordinates of angular points in the checkerboard or the target, and finally calculate the internal parameters of the camera through a Zhangyou calibration method.
Camera calibration has been widely studied in recent years as an important technique for optical measurement. The traditional calibration method is to establish the relationship between the three-dimensional world and the two-dimensional camera image through the calibration method, and describe the relationship diagram by adopting a pinhole model. Based on the pinhole model, there are many classical methods such as Tsai, heikkila, zhang's calibration, etc.
However, in the implementation of the present invention, it was found that direct underwater binocular calibration leads to a significant increase in the camera due to refraction of light, since the direct underwater calibration converts refraction of light into an effective focal length as compensation, and furthermore, the calculation of the re-projection function is a constant iterative process, which is very time-consuming.
Disclosure of Invention
The invention aims to provide an underwater double-target positioning method.
The aim of the invention is realized by the following technical scheme:
an underwater double-targeting method, comprising the following steps:
step 1: obtaining left and right camera images of an underwater chessboard graph, establishing an underwater refraction imaging model, and obtaining images of the left and right cameras at different positions of the chessboard graph by using a binocular camera;
step 2: performing feature extraction on the converted image obtained in the step 1 to obtain a coordinate set of the corner points of the calibration plate in the image under a pixel coordinate system, establishing a world coordinate system on the calibration plate to obtain a coordinate set of the corner points of the calibration plate under the world coordinate system, and converting the obtained coordinate set into a camera coordinate system;
step 3; based on the coordinate set obtained in the step 2, constructing a forward projection error function to perform nonlinear optimization, and obtaining intrinsic parameters of the camera by minimizing the forward projection error;
step 4: after the intrinsic parameters of the cameras and the rotation and translation matrices of the left and right cameras are obtained, the rotation and translation matrices are calculated based on the centroid distance increment matrix.
Further, the step 2 specifically comprises the following steps:
step 2.1: according to the physical size of the calibration plate, world coordinates of all angular points in the calibration plate are obtained, and the angular point coordinate set of the calibration plate under the world coordinate system is defined as P ij Each corner point is positioned on the same plane;
step 2.2: extracting features of the image obtained in the step 1 to obtain a coordinate set of the corner point of the calibration plate under a pixel coordinate system, wherein the coordinate set under the pixel coordinate system is defined as m ij Wherein i represents the sequence number of the image in the image set, and j represents the sequence number of the corner in the image;
step 2.3: converting the coordinates of the corner points of the calibration plate obtained in the step 2.2 under the pixel coordinate system from the pixel coordinate system to the image coordinate system to obtain a coordinate set n ij Then converting the image into a camera coordinate system to obtain a coordinate set p in the camera coordinate system ij The method comprises the steps of carrying out a first treatment on the surface of the Converting the coordinates of the corner obtained in the step 2.1 under the world coordinate system into the camera coordinate system to obtain a corner coordinate P under the camera coordinate system c ；
P c ×P ij ·R+T
Wherein R is the rotation matrix of the left and right cameras, and T is the migration matrix of the left and right cameras; j is the focal length of the camera, u 0 Is the abscissa of the camera optical center in the pixel coordinate system, v 0 Is the ordinate of the camera optical center in the pixel coordinate system.
Further, the step 3 is specifically as follows:
irrespective of the lens thickness, the optical center is the refractive point, and q 0 A direction vector representing the optical path, represented by P i Representing the coordinates of an image point in the camera coordinate system, P w Representing the coordinates of the object point in the camera coordinate system, then P iw A vector representing two points:
P iw ＝P w -P i ＝P c -p ij
handle vector P iw Along n ax Direction and n bx The direction is decomposed:
P iw ＝dot(P iw ,n ax )n ax +P iw⊥
P iw⊥ ＝d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d
wherein,,θ 1 for incident angle of light, θ 2 Is the angle of reflection of the light;
combining the two formulas to obtain a cost function;
P iw ＝d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax
converting the process of solving the parameters into a nonlinear optimization process, and obtaining the camera by minimizing the cost functionIntrinsic parameters, extrinsic parameters of each pair of image left camerasAnd extrinsic parameters of the right camera +.>
arg min||d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax -P iw ||。
Further, the step 4 is specifically as follows:
extrinsic parameters of the left camera of each pair of images obtained according to the step 3Extrinsic parameters of right cameraThe binocular vision system model is constructed as follows:
wherein P is i cl And P i cr Respectively are object points P i Coordinates in the left and right camera coordinate systems, if m pairs of images and n corner points are selected, for the j-th corner point in the i-th pair of images of the left and right coordinates, the coordinates in the left and right camera coordinate systems are:
centroid point of coordinate setAnd->Calculated as follows:
converting origin of each coordinate system into corresponding mass center, and new coordinatesAnd->Can be calculated from the following formula:
the binocular vision system model is combined to obtain:
the translation matrix T is eliminated. The objective function of RT can be written as:
the rotation matrix R may be obtained by minimizing F ex Obtaining;
after the rotation matrix R is obtained, the translation matrix T can be calculated according to the following equation,
the invention has the beneficial effects that:
the invention considers the problem of re-projection caused by refraction of underwater light and the time-consuming problem of calculation of a re-projection function in the double-target calibration process of the underwater robot, and provides a novel calibration method to meet the underwater binocular measurement requirement. The invention establishes an underwater refraction imaging model, and adopts a more accurate and more effective forward projection error function to carry out nonlinear optimization in order to reduce the re-projection error.
Drawings
FIG. 1 is a binocular calibration flow chart of the present invention;
FIG. 2 is a drawing of a calibration plate acquired under water by a left camera and a right camera;
FIG. 3 is a graph of underwater image point position versus air image point position.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The invention provides a double-target determination method, as shown in fig. 1, the whole flow of the method is as follows:
step 1: carrying out a pool test, obtaining left and right camera images of an underwater chessboard diagram through a binocular camera, defining the origin of a world coordinate system at a first corner point of the upper left corner of the chessboard diagram as shown in fig. 2, and taking the plane of the chessboard diagram as the z=0 plane of the world coordinate system;
step 2: establishing an underwater refraction imaging model, and establishing a relationship between an underwater imaging point and an ideal imaging point in air, as shown in fig. 3;
step 3: according to the physical size of the calibration plate, performing feature calculation on images acquired by the left and right cameras to obtain world coordinates of each corner point in the calibration plate, and defining a coordinate set of the corner point of the calibration plate under the world coordinate system as P ij Each corner point is positioned on the same plane;
step 4: extracting features of the image obtained in the step 1 to obtain a coordinate set of the corner point of the calibration plate under a pixel coordinate system, wherein the coordinate set under the pixel coordinate system is defined as m ij Wherein i represents the sequence number of the image in the image set and j represents the sequence number of the image in the imageA sequence number of the corner point;
step 5: converting the coordinates of the corner points of the calibration plate obtained in the step 4 under the pixel coordinate system from the pixel coordinate system to the image coordinate system to obtain a coordinate set n ij Then converting the image into a camera coordinate system to obtain a coordinate set p in the camera coordinate system ij The method comprises the steps of carrying out a first treatment on the surface of the Converting the coordinates of the corner obtained in the step 3 under the world coordinate system into the camera coordinate system to obtain a corner coordinate P under the camera coordinate system c ；
P c ＝P ij ·R+T
Wherein R is the rotation matrix of the left (right) camera, T is the migration matrix of the left (right) camera, j is the focal length of the camera, u 0 Is the abscissa of the camera optical center in the pixel coordinate system, v 0 Is the ordinate of the camera optical center in the pixel coordinate system;
step 6: irrespective of the lens thickness, the optical center is the refractive point, and q 0 A direction vector representing the optical path, represented by P i Representing the coordinates of an image point in the camera coordinate system, P w Representing the coordinates of the object point in the camera coordinate system, then P iw A vector representing two points:
P iw ＝P w -P i ＝P c -p ij
step 7: handle vector P iw Along n ax Direction and n bx The direction is decomposed and the direction is changed,
P iw ＝dot(P iw ,n ax )n ax +P iw⊥
P iw⊥ ＝d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d
wherein,,θ 1 for incident angle of light, θ 2 Is the angle of reflection of the light;
combining the two formulas to obtain a cost function;
P iw ＝d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax
converting the process of solving the parameters into a nonlinear optimization process, obtaining the intrinsic parameters of the cameras by minimizing the cost function, and obtaining the extrinsic parameters of the left camera of each pair of imagesAnd extrinsic parameters of the right camera +.>
arg min||d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax -P iw ||
Step 8; extrinsic parameters of the left camera of each pair of images obtained according to step 7And extrinsic parameters of the right camera +.>The binocular vision system model is constructed as follows:
wherein P is i cl And P i cr Respectively are object points P i Coordinates in the left and right camera coordinate systems, if m pairs of images and n corner points are selected, for the j-th corner point in the i-th pair of images of the left and right coordinates, the coordinates in the left and right camera coordinate systems are:
centroid point of coordinate setAnd->Calculated as follows:
converting origin of each coordinate system into corresponding mass center, and new coordinatesAnd->Can be calculated from the following formula:
the binocular vision system model is combined to obtain:
the translation matrix T is eliminated. The objective function of RT can be written as:
the rotation matrix R may be obtained by minimizing F ex The method comprises the following steps:
after the rotation matrix R is obtained, the translation matrix T may be calculated according to the following formula:
the above description is only of the preferred embodiments of the present invention and is not intended to limit the present invention, but various modifications and variations can be made to the present invention by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (2)
1. An underwater double-target positioning method is characterized in that: the method comprises the following steps:
step 1: obtaining left and right camera images of an underwater chessboard graph, establishing an underwater refraction imaging model, and obtaining images of the left and right cameras at different positions of the chessboard graph by using a binocular camera;
step 2: performing feature extraction on the converted image obtained in the step 1 to obtain a coordinate set of the corner points of the calibration plate in the image under a pixel coordinate system, establishing a world coordinate system on the calibration plate to obtain a coordinate set of the corner points of the calibration plate under the world coordinate system, and converting the obtained coordinate set into a camera coordinate system;
step 3: based on the coordinate set obtained in the step 2, constructing a forward projection error function to perform nonlinear optimization, and obtaining intrinsic parameters of the camera by minimizing the forward projection error;
irrespective of the lens thickness, the optical center is the refractive point, and q 0 A direction vector representing the optical path, represented by P i Representing the coordinates of an image point in the camera coordinate system, P w Representing the coordinates of the object point in the camera coordinate system, then P iw A vector representing two points:
P iw ＝P w -P i ＝P c -p ij
handle vector P iw Along n ax Direction and n bx The direction is decomposed:
P iw ＝dot(P iw ,n ax )n ax +P iw⊥
P iw⊥ ＝d ow tan(θ1 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d
wherein,,θ 1 for incident angle of light, θ 2 Is the angle of reflection of the light;
combining the two formulas to obtain a cost function;
P iw ＝d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax
converting the process of solving the parameters into a nonlinear optimization process, obtaining the intrinsic parameters of the cameras by minimizing the cost function, and obtaining the extrinsic parameters of the left camera of each pair of imagesAnd extrinsic parameters of the right camera +.>
arg min||d ow tan(θ 1 )S d +(dot(P iw ,n ax )-d ow )tan(θ 2 )S d +dot(P iw ,n ax )n ax -P iw ||；
Step 4: after obtaining the intrinsic parameters of the cameras and the rotation and translation matrixes of the left and right cameras, calculating the rotation and translation matrixes based on the centroid distance increment matrixes;
extrinsic parameters of the left camera of each pair of images obtained according to the step 3Extrinsic parameters of right cameraThe binocular vision system model is constructed as follows:
wherein P is i cl And P i cr Respectively are object points P i Coordinates in the left and right camera coordinate systems, if m pairs of images and n corner points are selected, for the j-th corner point in the i-th pair of images of the left and right coordinates, the coordinates in the left and right camera coordinate systems are:
centroid point of coordinate setAnd->Calculated as follows:
converting origin of each coordinate system into corresponding mass center, and new coordinatesAnd->Can be calculated from the following formula:
the binocular vision system model is combined to obtain:
the translation matrix T is eliminated and the objective function of RT can be written as:
the rotation matrix R may be obtained by minimizing F ex Obtaining;
after the rotation matrix R is obtained, the translation matrix T can be calculated according to the following equation,
2. an underwater double targeting method according to claim 1, characterized in that: the step 2 is specifically as follows:
step 2.1: according to the physical size of the calibration plate, world coordinates of all angular points in the calibration plate are obtained, and the angular point coordinate set of the calibration plate under the world coordinate system is defined as P ij Each corner point is positioned on the same plane;
step 2.2: extracting features of the image obtained in the step 1 to obtain a coordinate set of the corner point of the calibration plate under a pixel coordinate system, wherein the coordinate set under the pixel coordinate system is defined as m ij Wherein i represents the sequence number of the image in the image set, and j represents the sequence number of the corner in the image;
step 2.3: converting the coordinates of the corner points of the calibration plate obtained in the step 2.2 under the pixel coordinate system from the pixel coordinate system to the image coordinate system to obtain a coordinate set n ij Then converting the image into a camera coordinate system to obtain a coordinate set p in the camera coordinate system ij The method comprises the steps of carrying out a first treatment on the surface of the Converting the coordinates of the corner obtained in the step 2.1 under the world coordinate system into the camera coordinate system to obtain a corner coordinate P under the camera coordinate system c ；
P c ＝P ij ·R+T
Wherein P is c Converting the corner points of the calibration plate from a world coordinate system to coordinates under a camera coordinate system; p is p ij Converting pixel points of all angular points of the calibration plate from a pixel coordinate system to an angular point coordinate set under a camera coordinate system; r is the rotation matrix of the left and right cameras, and T is the migration matrix of the left and right cameras; j is the focal length of the camera, u 0 Is the abscissa of the camera optical center in the pixel coordinate system, v 0 Is the ordinate of the camera optical center in the pixel coordinate system.
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