CN110866951A - Correction method for inclination of optical axis of monocular camera - Google Patents
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Abstract
The invention discloses a method for correcting the optical axis inclination of a monocular camera, which comprises the following steps: s1, establishing a camera coordinate system and a body coordinate system; s2, expressed by the plane vector formula:
obtaining a solving formula of the point P under a body coordinate system
S3，pCIs an imaging point of a phase plane represented by a physical point P in a camera coordinate system, and the point P is at O according to the imaging principleCpCOn a straight line, then
Then there are:
in the formula PBRepresenting the position of the P point in a body coordinate system, namely a 3 multiplied by 1 vector;
a 3 × 1 vector, which is the relative position between the camera coordinate system and the origin of the body coordinate system; p is a radical ofCThe coordinates of the point of the P point on the image plane on the camera coordinate system are 3 multiplied by 1 vectors; the invention only needs to establish two coordinate systems, and has simple calculation and small data volume; points which are difficult to be visually measured are predicted by measuring the points which are simple and easy to obtain, the method is simple and easy to realize, and the actual operation scene is more; the coordinate prediction is carried out by adopting a matrix transformation method, and the method is more visual and has high reliability compared with a software data box calculation method.
Description
Technical Field
The invention relates to the technical field of machine vision digital image processing, in particular to a method for correcting the inclination of an optical axis of a monocular camera.
Background
The vision measurement technology is widely applied to the field of non-contact measurement, and compared with stereoscopic vision measurement, monocular vision measurement is simple to use, low in cost and capable of meeting most measurement requirements, so that the application is wider. In practical measurement application, the vertical degree of the optical axis of the camera and an object is a key for ensuring the precision, accuracy and stability of measurement, and because the deviation between the optical axis and the normal of a measured object surface always exists and causes larger measurement error, the precision of three-dimensional coordinates of points on a subsequent extraction plane is reduced, so that the error correction of oblique optical axis measurement is necessary to be researched, and the application of monocular vision measurement in stereo measurement is limited due to the lack of relative information between the optical axis of a lens and a target plane to be measured.
At present, many scholars at home and abroad research the oblique light axis error correction technology, and Chendaqing and the like propose to use a reference measurement technology to overcome the influence caused by the change of the imaging position of the oblique light axis; a method for adjusting the verticality of an optical axis and an objective table based on digital image processing is researched by Gonghao and the like; murata and the like research an optical axis adjusting system for multi-target self-adaptation by using a genetic algorithm; jung Rae Ryoo et al propose an automatically adjusted object lens position scheme within an optical disc drive; thanksgiving and the like researched a correlation method of oblique optical axis digital images based on photogrammetry correction, and applied the two-dimensional DIC technology to three-dimensional measurement, thereby verifying the feasibility of three-dimensional information measurement by adopting a single camera line. However, these methods require correction of the deviation angle formed by the subsequent camera optical axis and the measured plane, which is most originally based on the case where the camera optical axis is absolutely perpendicular to the measured plane, and it is very difficult to satisfy this in two-dimensional measurement. It is therefore desirable to provide a camera optical axis tilt correction method that is simple and easy to operate to ensure the feasibility and robustness of visual measurements.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a monocular camera optical axis inclination correction method, aiming at the condition that the optical axis of a camera is not parallel to a test plane, the monocular camera optical axis inclination error is corrected in vision measurement.
The purpose of the invention is realized by the following technical scheme:
a method for correcting the optical axis inclination of a monocular camera comprises the following steps:
s1, establishing a camera coordinate system and a body coordinate system;
s2, expressed by the plane vector formula:
obtaining a solving formula of the point P under a body coordinate system
S3，pCIs an imaging point of a phase plane represented by a physical point P in a camera coordinate system, and the point P is at O according to the imaging principleCpCOn a straight line, then
Then there are:
in the formula PBRepresenting the position of the P point in a body coordinate system, namely a 3 multiplied by 1 vector;
a 3 × 1 vector, which is the relative position between the camera coordinate system and the origin of the body coordinate system; p is a radical ofCThe coordinates of the point of the P point on the image plane on the camera coordinate system are 3 multiplied by 1 vectors; the point P is located on the plane (fixed with the body coordinate system) where Z is h, and h represents the deviation from the reference plane XOBYwDegree;
S4，PBthe corresponding Z coordinate in the body coordinate system of (a) should be h, where:
and because of
Then there is
Is the ratio of two vector modes;
obtaining P in S3BThe formula (2) is developed into a matrix form:
s5, analyzing the influence of each factor on the calculation precision of the three-dimensional position of the midpoint in the vision measurement, and then performing simulation analysis on three Euler angles, depth differences and four independent variables, and performing partial derivatives on the parameters β, gamma and h to obtain a relational expression;
s6, measuring a visual reference point in the body coordinate system, and measuring the distance between the origin of the body coordinate system and the origin of the camera coordinate system; substituting the data into S5, and solving the influence of each angle and depth of field on the point solution in the body coordinate system;
s7, substituting the influence factor into P in S4BIn the equation (2), the three-dimensional coordinates of the points that are difficult to directly measure in the body coordinate system can be predicted.
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention only needs to establish two coordinate systems, and has simple calculation and small data volume;
(2) the method predicts the points difficult to be measured visually by measuring the points which are simple and easy to obtain, is simple and easy to realize, and has more actual operation scenes;
(3) the invention adopts a matrix transformation method to predict the coordinates, and is more intuitive and highly reliable than a software data box calculation method.
Drawings
FIG. 1 is a schematic diagram of the camera coordinate system, the body coordinate system and the world coordinate system setup according to the present invention;
FIG. 2 is a schematic diagram of the optical axis tilt correction of a single camera according to the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but the present invention is not limited thereto.
The invention carries out theoretical analysis on the measurement error caused by the optical axis inclination in the vision measurement, and provides a monocular camera optical axis inclination correction method.
As shown in fig. 1 to 2, a method for correcting the optical axis tilt of a monocular camera includes the following steps:
s1, establishing a camera coordinate system and a body coordinate system;
s2, expressed by the plane vector formula:
obtaining a solving formula of the point P under a body coordinate system
S3，pCIs an imaging point of a phase plane represented by a physical point P in a camera coordinate system, and the point P is at O according to the imaging principlecpCOn a straight line, then
(m is a variable indicating that a single pixel cannot determine PC)
Then there are:
in the formula PBRepresenting the position of the P point in a body coordinate system, namely a 3 multiplied by 1 vector;
a 3 × 1 vector, which is the relative position between the camera coordinate system and the origin of the body coordinate system; p is a radical ofCThe coordinates of the point of the P point on the image plane on the camera coordinate system are 3 multiplied by 1 vectors; the point P is located on the plane (fixed with the body coordinate system) where Z is h, and h represents the deviation from the reference plane XOBYwDegree;
S4，PBthe corresponding Z coordinate in the body coordinate system of (a) should be h, where:
and because of
Then there is
Is the ratio of two vector modes;
obtaining P in S3BThe formula (2) is developed into a matrix form:
s5, analyzing the influence of each factor on the calculation precision of the three-dimensional position of the midpoint in the vision measurement, and then performing simulation analysis on three Euler angles, depth differences and four independent variables, and performing partial derivatives on the parameters β, gamma and h to obtain a relational expression;
s6, measuring a visual reference point in the body coordinate system, and measuring the distance between the origin of the body coordinate system and the origin of the camera coordinate system; substituting the data into S5, and solving the influence of each angle and depth of field on the point solution in the body coordinate system;
s7, substituting the influence factor into P in S4BIn the equation (2), the three-dimensional coordinates of the points that are difficult to directly measure in the body coordinate system can be predicted.
Specifically, taking a scene of a three-axis turntable and a high-speed camera as an example, in order to realize effective coordinate conversion between the camera and a point on a test plane and further improve the accuracy of the camera in positioning each identification point on the test plane, under the support of the prior art, the invention adopts the following technical scheme:
first, cartesian coordinate systems, as shown in fig. 1, a camera coordinate system and a body coordinate system, respectively, are established on the camera and the test plane. At this time, the vector formula shows:
writing in matrix form requires both sides to be under the same coordinate system, that is:
wherein p isCIs an imaging point of a phase plane represented by a physical point P in a camera coordinate system, and the point P is at O according to the imaging principleCpCOn a straight line, then
(m is a variable indicating that a single pixel cannot determine PC). The matrix formula is:
PC＝mpC(3)
(3) substituting (2) then:
in the formula PBRepresenting the position of the point P in the body coordinate system, a 3 x 1 vector.
A 3 x 1 vector is the relative position between the origin of the camera coordinate system with respect to the body coordinate system. p is a radical ofCThe coordinates of the point of the P point on the image plane on the camera coordinate system, a 3 × 1 vector. The point P is located on the plane (fixed with the body coordinate system) where Z is h, and h represents the deviation from the reference plane XOBYwDegree of the disease.
P in formula (4)BIs the coordinate of the point P under the body coordinate system;
is a translation matrix from the camera coordinate system to the body coordinate system relative to the body coordinate system;
a rotation matrix pc from a camera coordinate system to a body coordinate system is the coordinate of a point p under the camera coordinate system; wherein
Is the ratio of the two vector modes.
And P isBThe corresponding Z coordinate in the body coordinate system should be h, and then (1) can obtain:
wherein
Formula (5) is substituted for formula (4) by:
r in formula (6)ij(i, j ═ 1, …, 3) is affected only by three euler angles, h is the depth difference, and four independent variables (α, γ, h).
To analyze the effect of each factor on the accuracy of the calculation of the three-dimensional position of the point in the visual measurement, the three euler angles and depth differences (α, γ, h) mentioned above, four independent variables, were then subjected to simulation analysis.
Will be provided with
pC、
The formula (6) is substituted by:
the parameters in the formula are as follows:
r11＝cosαcosβ
r12＝sinαcosβ
r13＝-sinβ
r21＝-sinαcosγ+cosαsinβsinγ
r22＝cosαcosγ+sinαsinβsinγ
r23＝cosβsinγ
r31＝sinαsinγ+cosαsinβcosγ
r32＝-cosαsinγ+sinαsinβsinγ
r33＝cosβcosγ
secondly, to PBThe relational expressions are obtained by performing the partial derivatives for α, β, γ, and h.
When α is subjected to partial derivation, β, γ, and h are known quantities, and therefore:
similarly, when β is subjected to partial derivation, α, γ, and h are known amounts, and there are:
similarly, when the partial derivatives are calculated for γ, α, β, and h are known amounts, and there are:
finally, the depth of field h is derived, and α, β and gamma are set as known quantities at the moment, including:
and thirdly, measuring the distances between the obvious identification points under a plurality of body coordinate systems and the distance between the original point of the camera coordinate system and the original point of the set body coordinate system by using a measuring tool reaching the precision required by the experiment.
The influence of α, β, h on the point P in the body coordinate system is obtained by substituting the measured data into the equations (8), (9), (10) and (11). the influence quantity is substituted into the unknown point obtaining equation, and the method can be used for obtaining the point coordinates which are difficult to directly measure in the body coordinate system.
The invention only needs to establish two coordinate systems, and has simple calculation and small data volume; points which are difficult to be visually measured are predicted by measuring the points which are simple and easy to obtain, the method is simple and easy to realize, and the actual operation scene is more; the coordinate prediction is carried out by adopting a matrix transformation method, and the method is more visual and has high reliability compared with a software data box calculation method.
The present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents and are included in the scope of the present invention.
Claims (1)
1. A method for correcting the optical axis inclination of a monocular camera, comprising the steps of:
s1, establishing a camera coordinate system and a body coordinate system;
s2, expressed by the plane vector formula:
obtaining a solving formula of the point P under a body coordinate system
S3，pCIs an imaging point of a phase plane represented by a physical point P in a camera coordinate system, and the point P is at O according to the imaging principleCPCOn a straight line, then
Then there are:
in the formula PBRepresenting the position of the P point in a body coordinate system, namely a 3 multiplied by 1 vector;
a 3 × 1 vector, which is the relative position between the camera coordinate system and the origin of the body coordinate system; p is a radical ofCThe coordinates of the point of the P point on the image plane on the camera coordinate system are 3 multiplied by 1 vectors; the point P is located on the plane (fixed with the body coordinate system) where Z is h, and h represents the deviation from the reference plane XOBYwDegree;
S4，PBthe corresponding Z coordinate in the body coordinate system of (a) should be h, where:
and because of
Then there is
Is the ratio of two vector modes;
obtaining P in S3BThe formula (2) is developed into a matrix form:
s5, analyzing the influence of each factor on the calculation precision of the three-dimensional position of the midpoint in the vision measurement, and then performing simulation analysis on three Euler angles, depth differences and four independent variables, and performing partial derivatives on the parameters β, gamma and h to obtain a relational expression;
s6, measuring a visual reference point in the body coordinate system, and measuring the distance between the origin of the body coordinate system and the origin of the camera coordinate system; substituting the data into S5, and solving the influence of each angle and depth of field on the point solution in the body coordinate system;
s7, substituting the influence factor into P in S4BIn the equation (2), the three-dimensional coordinates of the points that are difficult to directly measure in the body coordinate system can be predicted.
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