CN110866951B - Method for correcting optical axis inclination of monocular camera - Google Patents
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Abstract
The invention discloses a method for correcting the inclination of an optical axis of a monocular camera, which comprises the following steps: s1, establishing a camera coordinate system and a body coordinate system; s2, a plane vector formula: obtaining a solving formula of the point P in a body coordinate system S3, P C is the imaging point of the phase plane represented by the physical point P in the camera coordinate system, and according to the imaging principle, the point P is on the line O CpC Then there are: Wherein P B represents the position of the P point in the body coordinate system, and is a3 x 1 vector; A 3 x1 vector which is the relative position between the origins of the camera coordinate system and the body coordinate system; p C is the coordinates of the point on the image plane of the P point on the camera coordinate system, 3×1 vector; the invention only needs to establish two coordinate systems, has simple calculation and small data volume; the points which are difficult to directly observe 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 scenes are many; the coordinate prediction is performed by adopting a matrix transformation method, so that 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, compared with the stereoscopic vision measurement, the 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 applications, the vertical degree of the optical axis of the camera and the object is a key for ensuring the measurement precision, accuracy and stability, and because the deviation between the optical axis and the normal line of the object surface to be measured always exists and causes a larger measurement error, the three-dimensional coordinate precision of the point on the subsequent extraction plane is reduced, the error correction of research oblique optical axis measurement is necessary, and because of the lack of relative information between the optical axis of the lens and the object plane to be measured, the application of monocular vision measurement in stereo measurement is limited.
Currently, many scholars at home and abroad research on oblique optical axis error correction technology, chen Daqing and the like propose to use a reference measurement technology to overcome the influence caused by the change of an oblique optical axis imaging position; gong hao et al studied a method of adjusting the perpendicularity of the optical axis and the stage based on digital image processing; murata et al have studied optical axis adjustment systems that employ genetic algorithms for multi-objective adaptation; jung Rae Ryoo et al propose an automatically adjusted objective lens position scheme within an optical disc drive; tang Zhengzong et al studied oblique optical axis digital image correlation methods based on photogrammetry correction and applied two-dimensional DIC techniques to three-dimensional measurements, verifying the feasibility of three-dimensional information measurement using a single camera line. However, these methods all need to correct the deviation angle formed by the optical axis of the subsequent camera and the measured plane by using the most original basis in the case that the optical axis of the camera is absolutely perpendicular to the measured plane, and in two-dimensional measurement, it is very difficult to meet the situation. It is therefore desirable to provide a simple and easy to operate camera optical axis tilt correction method to ensure the feasibility and robustness of visual measurements.
Disclosure of Invention
The invention aims to overcome the defects and shortcomings of the prior art and provides a method for correcting the inclination of the optical axis of a monocular camera.
The aim of the invention is achieved by the following technical scheme:
A method for correcting an optical axis tilt of a monocular camera, comprising the steps of:
S1, establishing a camera coordinate system and a body coordinate system;
S2, a plane vector formula: obtaining the solving formula/>, of the point P in the body coordinate system
S3, P C is the imaging point of the phase plane represented by the physical point P in the camera coordinate system, and according to the imaging principle, the point P is on the line O CpC
Then there are:
Wherein P B represents the position of the P point in the body coordinate system, and is a3 x 1 vector; A 3 x 1 vector which is the relative position between the origins of the camera coordinate system and the body coordinate system; p C is the coordinates of the point on the image plane of the P point on the camera coordinate system, 3×1 vector; the point P is located on the plane z=h (fixedly connected with the body coordinate system), and h represents the degree of deviation from the reference plane XO BYw;
The Z coordinate corresponding to S4, P B in the body coordinate system should be h, where:
And because of Then there is/>Is the ratio of two vector modes;
The formula for obtaining P B in S3 is expanded into a matrix form:
s5, analyzing the influence of each factor on the calculation accuracy of the three-dimensional position of the vision measurement midpoint, and then carrying out simulation analysis on three Euler angles and depth differences and four independent variables; performing partial derivatives on the relation, beta, gamma and h to obtain a relational expression;
s6, measuring a visually visible 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 calculation in the body coordinate system;
S7, substituting the influence factors into the equation of P B in S4, namely predicting the three-dimensional coordinates of the points which are difficult to directly measure in the body coordinate system.
Compared with the prior art, the invention has the following beneficial effects:
(1) The invention only needs to establish two coordinate systems, has simple calculation and small data volume;
(2) The method predicts the points which are difficult to directly observe by measuring the points which are easy to obtain, is simple and easy to realize, and has a plurality of actual operation scenes;
(3) The method adopts a matrix transformation method to make coordinate prediction, is more visual than a software data box calculation method, and has high reliability.
Drawings
FIG. 1 is a schematic diagram of the camera coordinate system, the body coordinate system and the world coordinate system of the present invention;
fig. 2 is a schematic view of the single camera optical axis tilt correction of the present invention.
Detailed Description
The present invention will be described in further detail with reference to examples and drawings, but embodiments of the present invention are not limited thereto.
The invention carries out theoretical analysis on measurement errors caused by optical axis inclination in vision measurement, and provides a method for correcting the optical axis inclination of a monocular camera.
As shown in fig. 1 to 2, a method for correcting the inclination of the optical axis of a monocular camera includes the steps of:
S1, establishing a camera coordinate system and a body coordinate system;
S2, a plane vector formula: obtaining the solving formula/>, of the point P in the body coordinate system
S3, P C is the imaging point of the phase plane represented by the physical point P in the camera coordinate system, and according to the imaging principle, the point P is on the line O cpC (M is a variable indicating that a single pixel cannot determine P C)
Then there are:
Wherein P B represents the position of the P point in the body coordinate system, and is a3 x 1 vector; A 3 x 1 vector which is the relative position between the origins of the camera coordinate system and the body coordinate system; p C is the coordinates of the point on the image plane of the P point on the camera coordinate system, 3×1 vector; the point P is located on the plane z=h (fixedly connected with the body coordinate system), and h represents the degree of deviation from the reference plane XO BYw;
The Z coordinate corresponding to S4, P B in the body coordinate system should be h, where:
And because of Then there is/>Is the ratio of two vector modes;
The formula for obtaining P B in S3 is expanded into a matrix form:
s5, analyzing the influence of each factor on the calculation accuracy of the three-dimensional position of the vision measurement midpoint, and then carrying out simulation analysis on three Euler angles and depth differences and four independent variables; performing partial derivatives on the relation, beta, gamma and h to obtain a relational expression;
s6, measuring a visually visible 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 calculation in the body coordinate system;
S7, substituting the influence factors into the equation of P B in S4, namely predicting the three-dimensional coordinates of the points which are difficult to directly measure in the body coordinate system.
Specifically, taking a three-axis table and a high-speed camera scene as an example, in order to realize effective coordinate conversion between the camera and points on a test plane, and further improve the accuracy of the camera in positioning each identification point on the test plane, the invention adopts the following technical scheme under the support of the prior art:
First, a Cartesian coordinate system is established on the camera and the test plane, as shown in FIG. 1, a camera coordinate system and a volume coordinate system, respectively. At this time, it is known from the vector formula:
writing in a matrix form requires that both sides are in the same coordinate system, namely:
wherein P C is the imaging point of the phase plane represented by the physical point P in the camera coordinate system, and according to the imaging principle, the point P is on the line O CpC (M is a variable indicating that a single pixel cannot determine P C). The matrix formula is:
PC＝mpC (3)
(3) Substitution (2), there are:
Where P B denotes the position of the P point in the body coordinate system, 3×1 vector. A 3×1 vector, which is the relative position between the origins of the camera coordinate system and the body coordinate system. P C is the coordinates of the point on the image plane of the P point on the camera coordinate system, 3 x 1 vector. The point P is located on the plane z=h (attached to the body coordinate system), h representing the degree of deviation from the reference plane XO BYw.
In the formula (4), P B is the coordinate of a P point under a body coordinate system; is a translation matrix relative to the camera coordinate system under the body coordinate system to the body coordinate system; /(I) The rotation matrix pc from the camera coordinate system to the body coordinate system is the coordinates of p points in the camera coordinate system; wherein/>Is the ratio of two vector modes.
The Z coordinate of P B corresponding to the body coordinate system should be h, and is obtained by (1):
Wherein the method comprises the steps of
The substitution of formula (5) into formula (4) is:
R ij (i, j=1, …, 3) in the formula (6) is affected by only three euler angles, h is the depth difference, and four independent variables (α, β, γ, h).
To analyze the effect of factors on the accuracy of the calculation of the three-dimensional position of the midpoint of the visual measurement, simulation analysis was then performed on the three euler angles and depth differences (α, β, γ, h) mentioned above, four independent variables.
Will bepC、/>The formula (6) includes:
wherein each parameter is as follows:
r11＝cosαcosβ
r12＝sinαcosβ
r13＝-sinβ
r21＝-sinαcosγ+cosαsinβsinγ
r22＝cosαcosγ+sinαsinβsinγ
r23＝cosβsinγ
r31＝sinαsinγ+cosαsinβcosγ
r32＝-cosαsinγ+sinαsinβsinγ
r33＝cosβcosγ
next, P B is biased with respect to α, β, γ, and h to obtain a relational expression.
In the case of performing the bias on α, since β, γ, and h are all known amounts, there are:
similarly, when deriving β, α, γ, and h are set to known amounts, and there are:
similarly, when deriving γ, α, β, and h are set to known amounts, and there are:
Finally, deriving the depth of view h, and setting alpha, beta and gamma as known quantities at the moment, wherein the method comprises the following steps:
and thirdly, measuring the distances among the obvious identification points in a plurality of individual coordinate systems and the distances between the origin of the camera coordinate system and the origin of the established individual coordinate system by using a measuring tool which achieves the precision required by the experiment.
The measured data are substituted into the formulas (8), (9), (10) and (11) to obtain the influence of alpha, beta and h on the point P under the body coordinate system. The influence quantity is substituted into an unknown point calculation formula, and can be used for calculating point coordinates which are difficult to directly measure in a body coordinate system.
The invention only needs to establish two coordinate systems, has simple calculation and small data volume; the points which are difficult to directly observe 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 scenes are many; the coordinate prediction is performed by adopting a matrix transformation method, so that the method is more visual and has high reliability compared with a software data box calculation method.
The foregoing is illustrative of the present invention and is not to be construed as limiting thereof, but rather as various changes, modifications, substitutions, combinations, and simplifications which may be made therein without departing from the spirit and principles of the invention are intended to be included within the scope of the invention.
Claims (1)
1. A method for correcting an inclination of an optical axis of a monocular camera, comprising the steps of:
S1, establishing a camera coordinate system and a body coordinate system;
S2, a plane vector formula: obtaining a solving formula of the point P in a body coordinate system
S3, P c is the imaging point of the phase plane represented by the physical point P in the camera coordinate system, and according to the imaging principle, the point P is on the line O CpC
Then there are:
Where P B denotes the position of the P point in the volumetric coordinate system, 3X 1 vector: A 3 x 1 vector which is the relative position between the origins of the camera coordinate system and the body coordinate system; p C is the coordinates of the point on the image plane of the P point on the camera coordinate system, 3×1 vector; the point P is located on the plane z=h, h representing the degree of deviation from the reference plane X 1OBY1;
The Z coordinate corresponding to S4, P B in the body coordinate system should be h, where:
And because of Then there is/>Is the ratio of two vector modes;
The formula for obtaining P B in S3 is expanded into a matrix form:
S5, analyzing the influence of each factor on the calculation accuracy of the three-dimensional position of the vision measurement midpoint, and then carrying out simulation analysis on three Euler angles alpha, beta, gamma and depth differences h and four independent variables; performing partial derivatives on alpha, beta and gamma to obtain a relational expression;
S6, measuring a visually visible 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 to obtain the influence of three Euler angles alpha, beta, gamma and depth difference h on the midpoint of the body coordinate system
S7, substituting three Euler angles alpha, beta, gamma and depth difference h into a solving formula of P B in S4, and predicting three-dimensional coordinates of points which are difficult to directly measure in a body coordinate system;
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