CN105046715A - Space analytic geometry-based line-scan camera calibration method - Google Patents

Abstract

The invention provides a space analytic geometry-based line-scan camera calibration method and belongs to the line-scan CCD camera calibration field. The space analytic geometry-based line-scan camera calibration method is especially suitable for fast, accurate and flexible calibration of line-scan cameras. According to the calibration method, a new target is designed, and space analysis geometrical relationships are utilized, and the parameters of a line-scan camera can be obtained based on a vector method, and therefore, rapid calibration of the camera can be realized. With the method adopted, calibration accuracy can be ensured without making a precise target required, and the target is not required to move precisely according to a prescribed direction; and the plane of the target and the plane of the camera are not required to be parallel to each other, and therefore, the arrangement position and attitude of the camera can be arbitrary, and the flexibility of the calibration of the line-scan camera can be effectively improved. The space analytic geometry-based line-scan camera calibration method of the invention has the advantages of fast calibration speed, high accuracy, flexible operation and the like. With the space analytic geometry-based line-scan camera calibration method adopted, a precise target is not required to be produced, and fast calibration of the line-scan camera under harsh environment conditions can be realized.

Description

A kind of line-scan digital camera scaling method based on interspace analytic geometry

Technical field

The invention belongs to linear array CCD camera and demarcate field, particularly relate under rugged environment condition, fast, accurately and neatly linear array CCD camera is demarcated.

Background technology

The demarcation of camera parameter is unusual the key link, and the precision of its calibration result and the stability of calibration algorithm directly have influence on the accuracy of related system net result.Therefore, camera calibration is photogrammetric and one of the most basic, most important technology in computer vision technique.

Line-scan digital camera has the advantages that visual field is wide, sample frequency is high, resolution is high, and its process one dimensional image signal has unrivaled advantage, is widely used in high-acruracy survey.Utilize line-scan digital camera to carry out the tasks such as vision measurement, first need to demarcate the inside and outside parameter of line-scan digital camera.The demarcation of camera is generally first utilize the calibration point and the pixel coordinate of its correspondence that in local space, three-dimensional coordinate is known, sets up the equation comprising camera inside and outside parameter, then obtains the inside and outside parameter of camera by solving overdetermined linear system.Utilize the parameter of camera calibration during actual measurement, and solve its three dimensional space coordinate according to the image coordinates of measurement point is counter.

The scaling method of area array cameras is a lot, and its calibration technique is very ripe.Because the image-generating unit of line-scan digital camera only has row, easily lose feature point for calibration, this makes the scaling method of a lot of area array cameras not be suitable for the demarcation of line-scan digital camera.In the calibration process of line-scan digital camera, choosing of unique point is a difficult problem always.Therefore, the problem of calibrating research of line-scan digital camera is fewer.

The people such as Duan Fajie propose a kind of linear array CCD camera calibration technique based on two-step approach, and parameter to be calibrated is divided into two groups by the method, then demarcates respectively, this simplify calibration process.But the method requires that carrying out micro-stepping with known increment to target by micrometric displacement two-dimentional work bench on Y or Z-direction moves, and scaling method is dumb.The people such as luna propose one and improve one's methods, and have by making one the movement that multiple plane-parallel stereo target avoids target.But the method imaging features point is less, the parameter of camera accurately can not be reflected, and very high to the making accuracy requirement of target.The method for making of the plane target drone that the people such as prince's occasion proposes efficiently solves the problem that feature point for calibration is easily lost.But its caliberating device requires that camera target surface is parallel to plane target drone, and requires that plane target drone will all the time perpendicular to precise guide rail in micro-stepping moving process.Zhu, a state in the Zhou Dynasty your people such as grade that continues have studied a kind of scaling method of the line-scan digital camera utilizing laser tracker to assist.The method devises a kind of plane target drone be made up of many straight lines and six gauge points, does not require that target strictly moves by the direction of specifying and distance, but still needs repeatedly to move freely target, to obtain abundant unique point.

Compared with area array cameras, line-scan digital camera has obvious advantage in process one dimensional image signal, and it is widely used in high-precision measurement.But, less to the demarcation of line-scan digital camera research both at home and abroad, and the scaling method of a lot of area array cameras be not suitable for the demarcation of line-scan digital camera.After the various scaling methods that other people propose in research, the present invention proposes a kind of linear array CCD camera to be carried out fast, the method for accurate, flexible calibration.The advantage of the method has: target makes simple, and without the need to moving target mark; The attitude of timing signal camera can be any, do not require that camera target surface is parallel with target plane; The accuracy of demarcating is high, speed is fast.For the occasion at a few thing bad environments, such as forge and press factory, shipyard etc., the advantageous ground of this scaling method is more obvious.

Summary of the invention

In order to improve accuracy and the dirigibility of line-scan digital camera demarcation, the invention provides a kind of line-scan digital camera scaling method based on interspace analytic geometry, the target solving the existence of existing scaling method makes the problems such as various particular/special requirement is more, stated accuracy is not high in complexity, calibration process.In order to avoid target is excessive, made 3 little targets, 3 little targets can be placed on any position within the scope of viewing field of camera.This method utilizes vector method nominal light axial vector, replaces and demarcates rotation matrix, is more suitable for the vision measurement system resolving spatial point three-dimensional coordinate based on interspace analytic geometry theory.

The present invention is realized by following technical scheme:

Based on a line-scan digital camera scaling method for interspace analytic geometry, it is characterized in that, comprise the following steps:

1) world coordinate system is set up;

2) the coordinate O=(XYZ) of described camera photocentre O in world coordinate system is measured;

3) make and lay the plane target drone of demarcation;

4) take the image of respective point on each target with linear array CCD camera, obtain the pixel coordinate of respective point.Then, by the Special Targets target calculation method made, impact point P is obtained ₁, P ₂, P ₃world coordinates.

5) described 3 calibration for cameras focal distance f, figure principal point U is utilized ₀with camera light axial vector

Preferably, described world coordinate system is set up by third party's instrument.

Preferably, described third party's instrument is total powerstation.

Preferably, in step 2) in, utilize the mechanical dimension of CCD camera, by total powerstation determination camera photocentre coordinate O=(XYZ);

Preferably, in step 3) in, make 3 plane target drones equally, and be placed in camera within sweep of the eye.Each target solves the world coordinates of an impact point, altogether P ₁, P ₂, P ₃the world coordinates of three impact points.

Preferably, in step 5) in, described demarcation content comprises further:

5.1) focal distance f and figure principal point U is calculated ₀;

5.2) camera light axial vector is calculated

Preferably, described step 5.1) comprising: obtain according to camera perspective projection principle:

$\tan \mathrm{\α}=\frac{(U_3-U_2)*{\mathrm{sin\θ}}_1*\sin ({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)}{(U_2-U_1)*{\mathrm{sin\θ}}_2-(U_3-U_2)*{\mathrm{sin\θ}}_1*cos({\mathrm{\θ}}_1+{\mathrm{\θ}}_2)}---\left(2\right)$

Wherein θ ₁, θ ₂be respectively photocentre O and subpoint p ₁, p ₂, p ₃between formed angle ∠ p ₁op ₂, ∠ p ₂op ₃, U ₁, U ₂, U ₃for subpoint p ₁, p ₂, p ₃pixel coordinate, without loss of generality, make U ₁<U ₂<U ₃;

Obtained by formula (1) and (2):

$U_0=U_1+\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}(U_3-U_1)---\left(3\right)$

$f=\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}*\tan \mathrm{\&alpha;}*(U_3-U_1)*dx---\left(4\right)$

Preferably, described step 5.2) comprise further: camera optical axis and straight line P ₁p ₃intersection point be Q, according to linear perspective projection theory, known therefore only demand invocation point Q coordinate.Point Q meets following constraint condition:

A) Q is put at straight line P ₁p ₃on;

B) according to the U tried to achieve in formula (3) ₀, utilize linear perspective projection theory, obtain ∠ QOP ₁, then put Q and meet equation: and ∠ QOP ₁=90 ° of-α;

By a) coordinate of a Q being expressed as:

Obtained by the formula that formula (5) is brought into b):

Arrangement above formula obtains the quadratic equation with one unknown about t:

at ²+bt+c＝0(6)

Wherein,

Solution formula (6): t=t ₁or t=t ₂, a P should be positioned at according to a Q ₁and P ₃between, the value obtaining t can be judged, then bring formula (5) into, obtain the coordinate Q=(xyz) of spatial point Q.

Then camera light axial vector for:

$\stackrel{\&RightArrow;}{Z_f}=Q-O---\left(7\right)$

Compared with prior art, the invention has the beneficial effects as follows:

The solving precision of imaging features point just can be ensured without the need to making precision target drone; Moving target mark is not needed in calibration process; Timing signal, do not require that camera target surface is parallel to target plane, camera attitude can be any.Meanwhile, the method utilizes vector method nominal light axial vector, replaces and demarcates rotation matrix, is more suitable for the vision measurement system resolving spatial point three-dimensional coordinate based on interspace analytic geometry theory.The method stated accuracy is high, calibration process flexible, is particularly useful for carrying out Fast Calibration to line-scan digital camera in harsh environments.

Accompanying drawing explanation

Fig. 1 is the schematic diagram according to line-scan digital camera scaling method of the present invention.

Fig. 2 is according to target figure of the present invention.

Fig. 3 is the simplified model figure according to line-scan digital camera scaling method of the present invention.

In figure, the implication of each mark is as follows:

In Fig. 1: 1 is total powerstation; 2 is target 1; 3 is target 2; 4 is target 3; O is camera photocentre; P ₁, P ₂, P ₃for the imaging features point in space; p ₁, p ₂, p ₃for P ₁, P ₂, P ₃corresponding perspective projection point.

In Fig. 2: O _t-x _ty _tz _tfor target co-ordinates system; A, P, B, C are camera fields of view plane 4 intersection points crossing with the vertical curve in target and skew lines, and wherein P is impact point.

In Fig. 3: O is camera photocentre; P ₁, P ₂, P ₃for the imaging features point of three in space; p ₁, p ₂, p ₃for corresponding perspective projection point; α, β are line and line segment p between photocentre O and subpoint ₁p ₃the angle formed; for the optical axis vector of camera; Under the prerequisite not considering lens distortion, optical axis vector is vertical with CCD target surface, and the intersection point of optical axis and CCD target surface is figure principal point q.

Embodiment

Below in conjunction with accompanying drawing, further describe the present invention, but the scope do not limited the present invention in any way.

The concrete implementation process of the present invention is as follows:

First design and make target, then the inside and outside parameter of calibration line array camera, parameter comprises: figure principal point U ₀, focal distance f and camera optical axis vector

One, the operating process of line-scan digital camera demarcation

(1) design and make target.By analysis and experiment, the final design of target as shown in Figure 2, finally makes 3 identical targets.

(2) be third party's instrument with total powerstation, set up world coordinate system.

(3) the coordinate O=(XYZ) of total station survey camera photocentre O in world coordinate system is utilized.

(4) 3 targets are placed in the field range of camera, the suitable distance and each target is separated by.

(5) take the image of respective point on each target with linear array CCD camera, obtain the pixel coordinate of respective point.Then, by the Special Targets target calculation method made, impact point P is obtained ₁, P ₂, P ₃world coordinates.Utilize 4 common point coordinates of each target under total station survey world coordinate system, obtain the rotation matrix R between target co-ordinates system and world coordinate system _iwith translation vector T _i.The world coordinates that can obtain three imaging features points is P _wi=r _i* P _ti+t _i, wherein P _tifor the coordinate in target co-ordinates system, (i=1,2,3).

(6) world coordinates calibration for cameras focal distance f, the figure principal point U of three coplanar imaging features points is utilized ₀with camera light axial vector

Two, the concrete calibration process of line-scan digital camera

1. design and make target

Demarcate in target at existing line-scan digital camera, mostly utilize parallel lines and oblique line to form target line, facilitate the use cross ratio invariability theorem or letter than constant theorem.And in the document utilizing cross ratio invariability theorem, whether the relative position relation that current nobody proposes three parallel lines can have an impact to result of calculation.But find in the process of actual experiment, if do not make accurate target, the relative position relation of three parallel lines can have a huge impact result of calculation.By error analysis, shown that the optimum position of three parallel lines should be the centre that straight line is positioned at target, all the other two lay respectively at the high order end of target and the conclusion of low order end.In order to improve the solving precision of target point further, the slope of skew lines can be made to be 1, therefore final design plane target drone as shown in Figure 2.In the case, even if the position of three parallel lines exists certain error in target manufacturing process, but it is very little to solve the impact of generation to the coordinate of target point.Set up target co-ordinates system as shown in Figure 2, the Y of three parallel lines _tcoordinate is known, if line-scan digital camera view plane and three parallel lines and oblique line intersect at A, B, C point and P point respectively, corresponding pixel coordinate is U _a, U _b, U _c, U _p.Then utilize cross ratio invariability theorem can obtain the coordinate of P point in target co-ordinates system:

$Y_p=\frac{Y_a*k_1-Y_b*k_2}{k_1-k_2};$

Wherein, k ₁=(Y _b-Y _c) (U _a-U _c) (U _b-U _p);

k ₂＝(Y _a-Y _c)(U _b-U _c)(U _a-U _p)。

By Y _pvalue substitutes into the equation of skew lines, X _p.Therefore the three-dimensional coordinate P of imaging features point P under target co-ordinates system on target is obtained _t=(X _p, Y _p, 0).

2. set up world coordinate system

The total powerstation model used in experiment is ZT80XR+, and measuring accuracy is 2mm, and is third party's instrument with total powerstation, sets up world coordinate system.

3. measure the coordinate of camera photocentre

Utilize the mechanical dimension of CCD camera, and by the photocentre coordinate O=(XYZ) of total powerstation determination camera;

4. obtain the world coordinates of impact point on target

The line-scan digital camera scaling method that the present invention proposes needs the world coordinates of three target points in known spatial, although also three points can be solved on a target, but be evenly distributed in the field range of camera to make target point, the dirigibility of target size and raising camera calibration can be reduced simultaneously, therefore made three identical targets, each target has solved an impact point.As shown in Figure 1, make three targets are evenly placed in the field range of line-scan digital camera, and target is maintained a certain distance.Take the image of respective point on each target with linear array CCD camera, obtain the pixel coordinate of respective point, the method in recycling 1 obtains three impact points at respective target co-ordinates system O _ti-X _tiy _tiz _tiin target co-ordinates P _ti=(X _pi, Y _pi, 0) and (i=1,2,3).Then utilize 4 common point coordinates of each target under total station survey world coordinate system, obtain the rotation matrix R between target co-ordinates system and world coordinate system _iwith translation vector T _i.The world coordinates that then finally can obtain three imaging features points is:

P _wi＝R _i*P _ti+T _i(i＝1,2,3)

5. calculate the inside and outside parameter of line-scan digital camera

The inside and outside parameter of line-scan digital camera comprises: camera focus f, figure principal point U ₀with camera light axial vector

1) camera focus f and figure principal point U ₀calculating

According to camera perspective projection principle, obtained by Fig. 3:

$\tan \mathrm{\&alpha;}=\frac{(U_3-U_2)*{\mathrm{sin\&theta;}}_1*\sin ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{(U_2-U_1)*{\mathrm{sin\&theta;}}_2-(U_3-U_2)*{\mathrm{sin\&theta;}}_1*cos({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}---\left(2\right)$

Wherein θ ₁, θ ₂be respectively photocentre O and subpoint p ₁, p ₂, p ₃between formed angle ∠ p ₁op ₂, ∠ p ₂op ₃, U ₁, U ₂, U ₃for subpoint p ₁, p ₂, p ₃pixel coordinate, without loss of generality, make U ₁<U ₂<U ₃.

Obtained by formula (1) and (2):

$U_0=U_1+\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}(U_3-U_1)---\left(3\right)$

$f=\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}*\tan \mathrm{\&alpha;}*(U_3-U_1)*dx---\left(4\right)$

2) line-scan digital camera optical axis vector calculating

According to linear perspective projection theory, known therefore only demand invocation point Q coordinate.

Point Q meets following constraint condition:

A () some Q is at straight line P ₁p ₃on;

B () is according to ∠ QOP ₁=90 ° of-α, can obtain

The coordinate of a Q can be expressed as by (a):

Formula (5) is brought into (b) to obtain:

Arrange above formula, the quadratic equation with one unknown about t can be obtained:

at ²+bt+c＝0(6)

Wherein,

Solution formula (6): t=t ₁or t=t ₂, a P should be positioned at according to a Q ₁and P ₃between, the value obtaining t can be judged.Then bring formula (5) into, obtain the coordinate Q=(xyz) of spatial point Q.

Then camera light axial vector for:

$\stackrel{\&RightArrow;}{Z_f}=Q-O---\left(7\right)$

Three, the calibration result of line-scan digital camera

The method proposed by the present invention completes the calibration experiment of line-scan digital camera.Camera model is DALSAPiranhaHS-S0-12k40, and image resolution ratio is 12000 × 256, and pixel dimension is 5.2 μm, and lens focus is 47mm, only extracts the pixel value of the 128th row, camera is equivalent to line-scan digital camera during actual experiment.The total powerstation model used in experiment is ZT80XR+, and measuring accuracy is 2mm, and is world coordinate system with total station instrument coordinate.According to the acquisition principle of described target point, the parameter calculating three imaging features points is as shown in table 1.

The parameter of table 1. three target points

According to the mechanical dimension of camera, the photocentre coordinate calculating line-scan digital camera is:

O _c＝(1.45684,-0.883207,-0.159201)

Utilize the scaling method that the present invention proposes, the parameter calculating line-scan digital camera is as shown in table 2.

The calibration result of table 2. camera parameter

Above-described embodiment, the just one of the present invention's more preferably embodiment, the change that those skilled in the art carries out within the scope of technical solution of the present invention and replacing all should be included in protection scope of the present invention.

Claims (8)

1., based on a line-scan digital camera scaling method for interspace analytic geometry, it is characterized in that, comprise the following steps:

1) world coordinate system is set up;

2) coordinate of photocentre O in world coordinate system of described line-scan digital camera is measured

O＝(XYZ)；

3) make and lay the plane target drone of demarcation;

4) take the image of respective point on each target with described line-scan digital camera, obtain the pixel coordinate of respective point; Then, by the calculation method of the plane target drone of making, impact point P is obtained ₁, P ₂, P ₃world coordinates;

5) described 3 calibration for cameras focal distance f, figure principal point U is utilized ₀with camera light axial vector

2. method according to claim 1, is characterized in that, described world coordinate system is set up by third party's instrument.

3. method according to claim 2, is characterized in that, described third party's instrument is total powerstation.

4. method according to claim 1 and 2, is characterized in that, in step 2) in, utilize the mechanical dimension of described line-scan digital camera, by total powerstation determination camera photocentre coordinate O=(XYZ).

5. method according to claim 1 and 2, is characterized in that, in step 3) in, make 3 plane target drones equally, and be placed in described line-scan digital camera within sweep of the eye; Each plane target drone comprises three parallel lines and a skew lines, and the straight line of described three parallel lines is positioned at the centre of target, all the other two high order end and the low order ends laying respectively at target; The slope of described skew lines is 1; Each plane target drone solves the world coordinates of an impact point, altogether P ₁, P ₂, P ₃the world coordinates of three impact points.

6. method according to claim 1 and 2, is characterized in that, in step 5) in, described demarcation content comprises further:

5.1) focal distance f and figure principal point U is calculated ₀;

5.2) camera light axial vector is calculated

7. method according to claim 6, is characterized in that, described step 5.1) comprising:

Obtain according to camera perspective projection principle:

$\tan \mathrm{\&alpha;}=\frac{(U_3-U_2)*{\mathrm{sin\&theta;}}_1*\sin ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{(U_2-U_1)*{\mathrm{sin\&theta;}}_2-(U_3-U_2)*{\mathrm{sin\&theta;}}_1*\cos ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}---\left(2\right)$

Wherein θ ₁, θ ₂be respectively photocentre O and subpoint p ₁, p ₂, p ₃between formed angle ∠ p ₁op ₂, ∠ p ₂op ₃, U ₁, U ₂, U ₃for subpoint p ₁, p ₂, p ₃pixel coordinate, without loss of generality, make U ₁<U ₂<U ₃;

Obtained by formula (1) and (2):

$U_0=U_1+\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}(U_3-U_1)---\left(3\right)$

$f=\frac{\tan \mathrm{\&alpha;}+\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}{({\tan }^2\mathrm{\&alpha;}+1)*\tan ({\mathrm{\&theta;}}_1+{\mathrm{\&theta;}}_2)}*\tan \mathrm{\&alpha;}*(U_3-U_1)*dx---\left(4\right).$

8. method according to claim 7, is characterized in that, described step 5.2) comprise further: camera optical axis and straight line P ₁p ₃intersection point be Q, according to linear perspective projection theory, known therefore only demand invocation point Q coordinate; Point Q meets following constraint condition:

A) Q is put at straight line P ₁p ₃on;

B) according to the U tried to achieve in formula (3) ₀, utilize linear perspective projection theory, obtain ∠ QOP ₁, then put Q and meet equation: and ∠ QOP ₁=90 ° of-α;

By a) coordinate of a Q being expressed as:

Obtained by the formula that formula (5) is brought into b):

Arrangement above formula obtains the quadratic equation with one unknown about t:

at ²+bt+c＝0(6)

Wherein,

$c=|\stackrel{\&RightArrow;}{{\mathrm{OP}}_1}{|}^4*{\cos }^2\mathrm{\&alpha;}.$

Solution formula (6): t=t ₁or t=t ₂, a P should be positioned at according to a Q ₁and P ₃between, the value obtaining t can be judged, then bring formula (5) into, obtain the coordinate Q=(xyz) of spatial point Q;

Then camera light axial vector for:

$\stackrel{\&RightArrow;}{Z_f}=Q-O---\left(7\right).$