CN103530852A - Method for correcting distortion of lens - Google Patents
Method for correcting distortion of lens Download PDFInfo
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- CN103530852A CN103530852A CN201310482910.3A CN201310482910A CN103530852A CN 103530852 A CN103530852 A CN 103530852A CN 201310482910 A CN201310482910 A CN 201310482910A CN 103530852 A CN103530852 A CN 103530852A
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Abstract
The invention discloses a method for correcting the distortion of a lens. The method is characterized in that the method comprises the following steps: providing a correcting image which is a rectangular grid chart, reading the correcting image by the to-be-corrected lens, producing a photo image of the correcting image, establishing a two-dimensional coordinate system in the photo image, establishing a two-dimensional coordinate system in the correcting image, selecting datum points from the photo image, calculating the radius of each datum point in the photo image, selecting datum points from the correcting image, calculating the radius of each datum point in the correcting image, obtaining correcting coefficients in a polynomial function fitting mode according to distortion quantity, obtaining the coordinate of any grid point in the photo image, calculating the radius of the grid point, obtaining the corrected theory radius of the grid point according to the correcting coefficients, and finally obtaining the corrected coordinate of the grid point. The tangential distortion and the radial distortion of the lens can be unified, so that the image distortion degree of the lens can be reduced to an utmost extent.
Description
Technical field
The present invention relates to a kind of bearing calibration, be specifically related to a kind of lens distortion calibration method.
Background technology
Generally can there is distortion to a certain degree in ordinary optical camera lens, concrete manifestation can be divided into two kinds of situations: pincushion distortion and barrel distortion in imaging.Due to the existence of distortion, when rectangle of alignment lens is taken, imaging is no longer rectangle, but shape as shown in Figure 1.What after the pincushion deformation that is pincushion having formed after the distortion of rectangular normal picture, normal picture as provided respectively in Fig. 1, normal picture distortion, form is barrel-shaped barrel-shaped deformation.In most situation, people's brain-capacity is carried out automatic calibration to it, substantially can not affect the perception of people to things, but for computing machine and a lot of software, this will cause the deviation of some data, is therefore necessary the image of distortion suitably to proofread and correct.
The method of existing compensating images distortion, if the applying date is the Chinese patent 98122712.0 on November 26th, 1998, is all first to read a correcting sheet, and this correcting sheet has the chequered with black and white striped of scheduled volume, and the exact position of black streaking is known.After correcting sheet reads, can obtain the chequered with black and white striped of corresponding scheduled volume, through judgement, can be calculated black streaking position.Then, calculate the interpolation of calculating location after the exact position of the chequered with black and white striped of this scheduled volume and image reading, obtain each reference point to variable.The amount of distortion of each reference point is deposited in storer and finishes the correcting sheet fetch program.While carrying out image reading, be stored in respectively being gone to variable in storer, the pattern distortion causing to revise optical system at every turn.
But there is certain problem in existing said method.First, what after its calculating black and white strip, obtain is the amount of distortion of several reference points, then corresponding image information is proofreaied and correct to variable according to these reference points.Therefore, this bearing calibration is not that each point of image is carried out to distortion correction, and the effect of this distortion correction is not very accurate, can not obtain complete satisfactory correcting image; Secondly, solve the problem of optical system distortion, the most basic approach is, a strict mathematical model is set up in generation to distortion, study on this basis the reason of its generation and find solution, prior art is not to adopt to set up a strict mathematical model and solve technical matters, therefore can not realize the accurate correction to the image of distortion.
Summary of the invention
For solving the deficiencies in the prior art, the object of the present invention is to provide a kind of lens distortion calibration method.
In order to realize above-mentioned target, the present invention adopts following technical scheme:
A method, is characterized in that, comprises the steps:
Step 1 a: correcting image is provided, described correcting image is a rectangle net trrellis diagram, in described rectangle net trrellis diagram, be provided with many transverse grid lines and many longitudinal network rulings, the cross one another point of crossing of transverse grid line and longitudinal network ruling forms a lattice point, between lattice point, is uniformly distributed;
Step 2: read described correcting image with camera lens to be corrected, produce the photographs of described correcting image, on described photographs, there are many horizontal netting twines and many longitudinal netting twines, laterally netting twine and longitudinally a lattice point of netting twine cross one another point of crossing formation, every horizontal netting twine is unique corresponding to a transverse grid line, and every longitudinal netting twine is unique corresponding to a longitudinal network ruling;
Step 3: in photographs, choose the horizontal netting twine of distortion degree minimum as transverse axis X, choose longitudinal netting twine of distortion degree minimum as longitudinal axis Y, transverse axis X and longitudinal axis Y are intersected to the lattice point P forming mutually and set up two-dimensional coordinate system as initial point;
Step 4: in correcting image, choose the transverse grid line corresponding with transverse axis X as transverse axis x, choose the longitudinal network ruling corresponding with longitudinal axis Y as longitudinal axis y, choosing transverse axis x and longitudinal axis y mutually intersects the lattice point p forming and sets up two-dimensional coordinate system as initial point, transverse axis x is consistent with the direction of transverse axis X, and longitudinal axis y is consistent with the direction of longitudinal axis Y;
Step 5: in photographs, choose i+1 lattice point P, Q
1, Q
2, Q
3... Q
ias reference point, obtain arbitrary lattice point Q
kcoordinate (X
k, Y
k), calculate lattice point Q
kradius R to lattice point P
k, k, i is positive integer, k≤i < j;
Step 6: in correcting image, choose i+1 lattice point p, q
1, q
2, q
3... q
ias reference point, obtain arbitrary lattice point q
kcoordinate (x
k, y
k), calculate lattice point q
kradius r to lattice point p
k, lattice point q
kwith lattice point Q
kmutually corresponding, k, i is positive integer, k≤i < j;
Step 7: according to amount of distortion (R
k, r
k), by the mode of Polynomial curve-fit, obtain correction coefficient K
0, K
1, K
2... K
n, n is natural number;
Step 8: for any one the lattice point Q in photographs
m, obtain its coordinate (X
m, Y
m), calculate it to the radius R of lattice point P
m, according to correction coefficient K
0, K
1, K
2... K
n, obtain lattice point Q
mtheoretical radius L after correction
m, L
m=K
n* (R
m)
n+ K
n-1* (R
m)
n-1+ ... + K
2* (R
m)
2+ K
1* R
m+ K
0, m is positive integer;
Step 9: obtain lattice point Q
mcoordinate (A after correction
m, B
m), A
m=X
m* L
m/ R
m, B
m=Y
m* L
m/ R
m.
A kind of aforesaid lens distortion calibration method, is characterized in that, in described correcting image, the horizontal spacing of described rectangle net trrellis diagram and longitudinal pitch equate.
Usefulness of the present invention is: the present invention can realize the tangential distortion of camera lens and radial distortion are unified, thereby reduces to greatest extent the degree of lens image distortion.
Accompanying drawing explanation
The contrast schematic diagram of normal picture and fault image when Fig. 1 is a lens distortion of the present invention;
Fig. 2 is a structural representation of preferably implementing of correcting image of the present invention;
Fig. 3 is a structural representation of preferably implementing of photographs of the present invention;
Fig. 4 is the schematic diagram of the present invention's selection reference point in photographs;
Fig. 5 is the schematic diagram of the present invention's selection reference point in correcting image;
Fig. 6 is step schematic diagram of the present invention.
The implication of Reference numeral in figure:
1, transverse grid line, 2, longitudinal network ruling, 3, lattice point, 4, horizontal netting twine, 5, longitudinal netting twine, 6, lattice point.
Embodiment
Below in conjunction with the drawings and specific embodiments, the present invention is done to concrete introduction.
The principle of the invention is first to have set up a mathematical model, can sample and integrate by the part point to image, thereby obtain the check point of each point, convenient simply again, and the whole employing of the present invention is diagonal line correction method, therefore can realize the tangential distortion of camera lens and radial distortion are unified, thereby reduce to greatest extent the degree that lens image distorts.
Shown in Fig. 6, a kind of lens distortion calibration method of the present invention, comprises the steps:
Step 1 a: correcting image is provided, as shown in Figure 3, described correcting image is a rectangle net trrellis diagram, in described rectangle net trrellis diagram, be provided with many transverse grid lines 1 and many longitudinal network rulings 2, the cross one another point of crossing of transverse grid line 1 and longitudinal network ruling 2 forms a lattice point 3, between lattice point 3, is uniformly distributed;
Correcting image in the present invention adopts as standard picture, and it is used for reading with camera lens to be corrected the photographs producing thereafter and compares, so is rectangle net trrellis diagram in correcting image.Each grid of known rectangle net trrellis diagram is rectangle, and grid is intersected and is separated by transverse grid line 1 and longitudinal network ruling 2, and the point of crossing of transverse grid line 1 and longitudinal network ruling 2 is the so-called lattice point of the present invention.And because every transverse grid line 1 and every longitudinal network ruling 2 intersect mutually, therefore in correcting image, there are a plurality of grids.Lattice point in the present invention is extremely important in whole bearing calibration, because by photographs and correcting image contrast, can clearly find, in photographs, be also present in the lattice point of equal number in correcting image, even because the reason of distortion, in photographs the position of lattice point 6 with in correcting image, compare the movement that position has occurred, but each lattice point in photographs remains the lattice point that can obtain in correcting image corresponding thereto.
Step 2: read described correcting image with camera lens to be corrected, produce the photographs of described correcting image, as shown in Figure 3, on described photographs, there are many horizontal netting twines 4 and many longitudinal netting twines 5, laterally netting twine 4 and longitudinally a lattice point of netting twine 5 cross one another point of crossing formation, every horizontal netting twine 4 is unique corresponding to a transverse grid line 1, and every longitudinal netting twine 5 is unique corresponding to a longitudinal network ruling 2.
In Fig. 3, in order to make photographs of the present invention more clear, the present invention has omitted some horizontal netting twines 4 and longitudinal netting twine 5 in Fig. 3, only shown each lattice point, but those skilled in the art should be understood that, on photographs, there are many horizontal netting twines 4 and many longitudinal netting twines 5, laterally netting twine 4 and longitudinally a lattice point of netting twine 5 cross one another point of crossing formation.In addition, the horizontal netting twine 4 of here every is unique corresponding to a transverse grid line 1, and every longitudinal netting twine 5 is unique corresponding to a longitudinal network ruling 2.Therefore, each lattice point in photographs all can unique each lattice point corresponding to showing in image.Horizontal netting twine 4 of the present invention refers to the same with transverse grid line 1, and the bearing of trend of line is horizontal, and similarly, longitudinally the bearing of trend of the line of netting twine 5 is longitudinally, the same with longitudinal network ruling 2.This point, as well known to those skilled in the art.In the present invention, need to the lattice point in photographs, horizontal netting twine 4, longitudinal netting twine 5 is mutually corresponding with the lattice point, transverse grid line 1, the longitudinal network ruling 2 that show image respectively, but the present invention do not limit the lattice point that makes, laterally netting twine 4, longitudinally netting twine 5 respectively with the lattice point, transverse grid line 1, longitudinal network ruling 2 that show image corresponding mode mutually, such as it can be undertaken by modes such as algorithm identified, can certainly obtain by artificial cognition mode.
Step 3: in photographs, as shown in Figure 3, choose the horizontal netting twine 4 of distortion degree minimum as transverse axis X, choose longitudinal netting twine 5 of distortion degree minimum as longitudinal axis Y, transverse axis X and longitudinal axis Y are intersected to the lattice point P forming mutually and as initial point, set up two-dimensional coordinate system.In this step, those skilled in the art all should be clear, and the horizontal netting twine 4 in photographs and longitudinally netting twine 5 have all produced distortion, and in photographs, different horizontal netting twines 4 is different with the distortion degree of longitudinal netting twine 5.Based on camera lens principle, there is a horizontal netting twine 4, it is in almost not distortion of longitudinal direction, and the distortion degree of longitudinal direction is minimum.Also have a longitudinal netting twine 5, it is in almost not distortion of horizontal direction, and the distortion degree of horizontal direction is minimum.Therefore, can be respectively as transverse axis X and longitudinal axis Y.The lattice point P obtaining like this can determine it is amount of distortion minimum in all lattice points of photographs, in engineering, can not assert and distorts.Arrange is like this to guarantee the precision adjusted in engineering.The present invention do not limit how to choose distortion degree minimum horizontal netting twine 4 as transverse axis X, how to choose longitudinal netting twine 5 of distortion degree minimum as longitudinal axis Y.In general, can adopt recognizer to realize by manually judging from the instruments such as ruler or the means such as visual, certainly also not getting rid of.But the present invention must get the horizontal netting twine 4 of distortion degree minimum as transverse axis X, choose longitudinal netting twine 5 of distortion degree minimum as longitudinal axis Y, can not select other horizontal netting twines 4 or longitudinal netting twine 5 to carry out.Its objective is that lattice point P sets up coordinate system as initial point, if and adopt other modes to set up coordinate system, the initial point of choosing is not just lattice point P, the step of carrying out again below the present invention just there will be very large deviation, can not realize principle of the present invention, by the part point to image, sample and integrate, thereby obtaining the check point of each point.
Step 4: in correcting image, choose the transverse grid line 1 corresponding with transverse axis X as transverse axis x, choose the longitudinal network ruling 2 corresponding with longitudinal axis Y as longitudinal axis y, choosing transverse axis x and longitudinal axis y mutually intersects the lattice point p forming and sets up two-dimensional coordinate system as initial point, transverse axis x is consistent with the direction of transverse axis X, and longitudinal axis y is consistent with the direction of longitudinal axis Y.
This step and step 2 are similar, and it is all to set up coordinate system, as shown in Figure 2.This step should guarantee that transverse axis x is consistent with the direction of transverse axis X, longitudinal axis y is consistent with the direction of longitudinal axis Y, that is to say, in setting up coordinate system, the direction of transverse axis x should be consistent with the direction of transverse axis X, and the direction of longitudinal axis y should be consistent with the direction of longitudinal axis Y.It is in order to make it possible to finally calculate the departure of any one lattice point that object is set like this.
Step 5: in photographs, choose i+1 lattice point P, Q
1, Q
2, Q
3... Q
ias reference point, obtain arbitrary lattice point Q
kcoordinate (X
k, Y
k), calculate lattice point Q
kradius R to lattice point P
k, k, i is positive integer, k≤i < j.The present invention does not limit the number of reference point, and as preferably, reference point is 5-15 and is advisable.Reference point number selects multiple spot, can improve the degree of accuracy of correction coefficient.
The object of this step is in order to set up in photographs after coordinate system, chooses a plurality ofly as reference point, and these reference points will be for obtaining correction coefficient.By these reference points, finally realize and proofread and correct any one lattice point.In this step, finally obtain each reference point to the radius of lattice point P.
Now, illustrate, as shown in Figure 4, choose lattice point Q
1, Q
2, Q
3, Q
4, Q
5, Q
6, Q
1coordinate is (76,67), represents Q in figure with alphabetical A
2coordinate is (143,141), represents Q in figure with letter b
3coordinate is (214,207), represents Q in figure by letter C
4coordinate is (275,272), represents Q in figure with alphabetical D
5coordinate is (338,336), represents Q in figure with letter e
6coordinate is (391,393), in figure, with alphabetical F, represents, origin (0,0), represents with O in figure.Now can obtain R
1=101.3, R
2=200.8, R
3=297.7, R
4=386.8, R
5=476.6, R
6=554.4.Certainly, now lattice point P is 0 to the radius of lattice point P, is defined as R
0=0.
In this step, reference point choose a certain quadrant that is not limited in two-dimensional coordinate system, also not limiting all reference points must be in same quadrant, selection reference point is all positioned at some quadrants in practice certainly.
Step 6: in correcting image, choose i+1 lattice point p, q
1, q
2, q
3... q
ias reference point, obtain arbitrary lattice point q
kcoordinate (x
k, y
k), calculate lattice point q
kradius r to lattice point p
k, lattice point q
kwith lattice point Q
kmutually corresponding, k, i is positive integer, k≤i < j.
Seemingly, it is also finally will obtain each reference point to the radius r of lattice point p for this step and previous step comparing class
k.And the reference point in this step all will with photographs in the mutual unique correspondence of reference point.Continue to illustrate, in correcting image as shown in Figure 5, find out with Fig. 4 in lattice point Q
1, Q
2, Q
3, Q
4, Q
5, Q
5the lattice point that difference is corresponding, i.e. q
1, q
2, q
3, q
4, q
5, q
6, q
1coordinate is (74,74), represents q in figure with alphabetical a
2coordinate is (148,148), represents q in figure with alphabetical b
3coordinate is (222,222), represents q in figure with alphabetical c
4coordinate is (296,296), represents q in figure with alphabetical d
5coordinate is (370,370), represents q in figure with alphabetical e
6coordinate is (444,444), in figure, with alphabetical f, represents, origin (0,0), represents with o in figure.Now can obtain r
1=104.7, r
2=209.3, r
3=314, r
4=418.6, r
5=523.3, r
6=627.9.Certainly, now lattice point p is 0 to the radius of lattice point p, is defined as r
0=0.
Step 7: according to amount of distortion (R
k, r
k), by the mode of Polynomial curve-fit, obtain correction coefficient K
0, K
1, K
2... K
n, n is natural number.Here adopting the reason of Polynomial curve-fit to be that all functions can represent with polynomial expression, is a reasonable mode so carry out matching with polynomial function.Continue to illustrate, according to coordinate (101.3,104.7), (200.8,209.3), (297.7,314), (386.8,418.6), and (476.6,523.3), (554.4,627.9), add (R
0, r
0), i.e. (0,0), obtains setting up a polynomial functional relation, finds out the funtcional relationship between R and r.
0=K
n×0
n+K
n-1×0
n-1+…+K
2×0
2+K
1×0+K
0
104.7=K
n×101.3
n+K
n-1×101.3
n-1+…+K
2×101.3
2+K
1×101.3+K
0
209.3=K
n×200.8
n+K
n-1×200.8
n-1+…+K
2×200.8
2+K
1×200.8+K
0
314=K
n×297.7
n+K
n-1×297.7
n-1+…+K
2×297.7
2+K
1×297.7+K
0
418.6=K
n×386.8
n+K
n-1×386.8
n-1+…+K
2×386.8
2+K
1×386.8+K
0
523.3=K
n×476.6
n+K
n-1×476.6
n-1+…+K
2×476.6
2+K
1×476.6+K
0
627.9=K
n×554.4
n+K
n-1×554.4
n-1+…+K
2×554.4
2+K
1×554.4+K
0
We can carry out matching with excel instrument, OriginPro, find out optimal polynomial number of times and each coefficient.By above-mentioned matching, the present invention can realize the tangential distortion of camera lens and radial distortion are unified, thereby reduces to greatest extent the degree of lens image distortion.
Step 8: for any one the lattice point Q in photographs
m, obtain its coordinate (X
m, Y
m), calculate it to the radius R of lattice point P
m, according to correction coefficient K
0, K
1, K
2... K
n, obtain lattice point Q
mtheoretical radius L after correction
m, L
m=K
n* (R
m)
n+ K
n-1* (R
m)
n-1+ ... + K
2* (R
m)
2+ K
1* R
m+ K
0, m is positive integer.As by above-mentioned 7 groups of polynomial relations, with excel matching optimal function out, should be finally: L
m=4E-07R
m 3-6E-05R
m 2+ 1.0388R
m-0.1472.
Step 9: obtain lattice point Q
mcoordinate (A after correction
m, B
m), A
m=X
m* L
m/ R
m, B
m=Y
m* L
m/ R
m.
Correcting image provided by the invention, can be that horizontal spacing and the longitudinal pitch of rectangle net trrellis diagram equates, but equally distributed grid chart.The horizontal spacing here refers to two spacing between adjacent transverse grid line 1, longitudinal pitch refers to two spacing between adjacent longitudinal network ruling 2, certainly horizontal spacing and the longitudinal pitch of rectangle net trrellis diagram also can be unequal, but lattice point must be uniformly distributed.Horizontal spacing and longitudinal pitch can not wait, but horizontal spacing is uniformly, and longitudinal pitch must be also that lattice point is equally distributed uniformly, and setting can realize know-why of the present invention like this.
More than show and described ultimate principle of the present invention, principal character and advantage.The technician of the industry should understand, and above-described embodiment does not limit the present invention in any form, and all employings are equal to replaces or technical scheme that the mode of equivalent transformation obtains, all drops in protection scope of the present invention.
Claims (2)
1. a lens distortion calibration method, is characterized in that, comprises the steps:
Step 1 a: correcting image is provided, described correcting image is a rectangle net trrellis diagram, in described rectangle net trrellis diagram, be provided with many transverse grid lines and many longitudinal network rulings, the cross one another point of crossing of transverse grid line and longitudinal network ruling forms a lattice point, between lattice point, is uniformly distributed;
Step 2: read described correcting image with camera lens to be corrected, produce the photographs of described correcting image, on described photographs, there are many horizontal netting twines and many longitudinal netting twines, laterally netting twine and longitudinally a lattice point of netting twine cross one another point of crossing formation, every horizontal netting twine is unique corresponding to a transverse grid line, and every longitudinal netting twine is unique corresponding to a longitudinal network ruling;
Step 3: in photographs, choose the horizontal netting twine of distortion degree minimum as transverse axis X, choose longitudinal netting twine of distortion degree minimum as longitudinal axis Y, transverse axis X and longitudinal axis Y are intersected to the lattice point P forming mutually and set up two-dimensional coordinate system as initial point;
Step 4: in correcting image, choose the transverse grid line corresponding with transverse axis X as transverse axis x, choose the longitudinal network ruling corresponding with longitudinal axis Y as longitudinal axis y, choosing transverse axis x and longitudinal axis y mutually intersects the lattice point p forming and sets up two-dimensional coordinate system as initial point, transverse axis x is consistent with the direction of transverse axis X, and longitudinal axis y is consistent with the direction of longitudinal axis Y;
Step 5: in photographs, choose i+1 lattice point P, Q
1, Q
2, Q
3... Q
ias reference point, obtain arbitrary lattice point Q
kcoordinate (X
k, Y
k), calculate lattice point Q
kradius R to lattice point P
k, k, i is positive integer, k≤i < j;
Step 6: in correcting image, choose i+1 lattice point p, q
1, q
2, q
3... q
ias reference point, obtain arbitrary lattice point q
kcoordinate (x
k, y
k), calculate lattice point q
kradius r to lattice point p
k, lattice point q
kwith lattice point Q
kmutually corresponding, k, i is positive integer, k≤i < j;
Step 7: according to amount of distortion (R
k, r
k), by the mode of Polynomial curve-fit, obtain correction coefficient K
0, K
1, K
2... K
n, n is natural number;
Step 8: for any one the lattice point Q in photographs
m, obtain its coordinate (X
m, Y
m), calculate it to the radius R of lattice point P
m, according to correction coefficient K
0, K
1, K
2... K
n, obtain lattice point Q
mtheoretical radius L after correction
m, L
m=K
n* (R
m)
n+ K
n-1* (R
m)
n-1+ ... + K
2* (R
m)
2+ K
1* R
m+ K
0, m is positive integer;
Step 9: obtain lattice point Q
mcoordinate (A after correction
m, B
m), A
m=X
m* L
m/ R
m, B
m=Y
m* L
m/ R
m.
2. a kind of lens distortion calibration method according to claim 1, is characterized in that, in described correcting image, the horizontal spacing of described rectangle net trrellis diagram and longitudinal pitch equate.
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