CN108876749A - A kind of lens distortion calibration method of robust - Google Patents
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Abstract
A kind of lens distortion calibration method of robust, proposes the method separating lens distortion from camera parameters and individually solving, step is：Feature extraction is carried out to gridiron pattern calibration object, first angle point Corner Detection is carried out using Shi-Tomasi operator, it is screened later according to the distinctive symmetrically feature big with variance of X-comers, finally uses sub-pix optimization algorithm, obtain the accurate subpixel coordinates of X-comers；Then camera imaging model and lens distortion model are established, the optimization object function about distortion parameter is obtained；Distortion parameter finally is solved using nonlinear optimization algorithm, is used for distortion correction.The experimental results showed that the present invention only needs the calculating that all main distortion parameters can be completed comprising tessellated calibration object picture, model is simple, and computational efficiency and stability are high, and application adaptability is good in industrial circle, and computational accuracy is suitable with conventional method.
Description
Technical field
The invention belongs to machine vision and digital image processing techniques field, are related to lens distortion calibration, are a kind of robust
Lens distortion calibration method.
Background technique
The main task of camera calibration is the property parameters such as the position of determining video camera, posture, is appointed with establishing in space
Meaning some corresponding relationship between its picture point after video camera imaging on the image plane.Where picture point on the plane of delineation
The space geometry position of the corresponding object point in position is directly related, and is determined by the geometrical model of video camera imaging.Pass through calibration
Obtained camera parameters can calculate the geological information of object in three-dimensional space.In computer vision field, learn both at home and abroad
Person is in the latest 20 years conducting in-depth research camera calibration technology, proposes the scaling method and work of a series of classics
Tool.Wherein, Tsai calibration algorithm is a kind of two step calibration algorithms based on radial constraint, and the algorithm of Zhang is based on plane reference
Object.Traditional scaling method is estimated inside and outside video camera using the pixel coordinate of calibration object characteristic point with the corresponding relationship of its world coordinates
Initial parameter values carry out nonlinear optimization together with distortion parameter later, obtain the optimal solution of all parameters.However, in video camera
Coupling between outer parameter and distortion parameter can make solution procedure unstable, or even be misexplained.In order to guarantee video camera
The stabilization of inside and outside parameter and the consistency of distortion parameter need to separate the solution of the two.
In terms of the independent solution of distortion parameter, the method for mainstream is roughly divided into method for measurement and non-method for measurement two at present
Class.Method for measurement needs the exact position of known features point in space, and in method for measurement, He Junji etc. is proposed based on friendship
Than aberration correction algorithm (He Junji, Zhang Guangjun, Yang Xian inscription lens distortion parameter calibration of the based on Cross ration invariability of invariance
Method [J] Chinese journal of scientific instrument, 2004,25 (5):597-599.), base of the Carlos Ricolfe-Viala in cross ratio invariability
Linear equation is added on plinth, obtains operation result (C Ricolfe-Viala, the A Sanchez- of more robust
Salmeron.Robust metric calibration of non-linear camera lens distortion[J]
.Pattern Recognition,2010,43(4):1688-1699.).Non- method for measurement then makes full use of perspective geometry constant
Amount, in these invariants, straight line has very strong measured capabilities to distortion, thus is widely adopted, method proposed by the present invention
Belong to non-method for measurement.
It is domestic about lens distortion calibration also many patent disclosures at present, Chinese patent application through retrieving
CN201410809482.5《The bearing calibration of fish eye images distortion》, standard testing waffle slab is obtained first in technical solution
Fish eye images and the fish eye images real image；Then the fish eye images obtained carry out distortion measurement, according to Polar Coordinate Model pair
Distortion factor is demarcated；Then be corrected according to calibration model, for guarantee correction accuracy, timing by central vision, in
Between visual field, peripheral field Stepwise calibration；Finally corresponding gray value is assigned to the pixel after spatial alternation with bilinear interpolation
To restore the gray value of origin-location.Chinese patent ZL200910185954.3《Distortion correction based on elliptic fisheye image
Method》, in the technical solution of the patent, first under camera coordinate system using paraboloid establish oval fish eye images at
As model, then the parameter of model is approximately demarcated using pixel coordinate system, finally using the model of foundation to obtaining
Fish-eye image carry out distortion correction.Provide a kind of distortion correction side based on elliptic fisheye image for 180 degree visual angle
Method, the fluoroscopy images after elliptic fisheye image correction can be obtained in the case where unknown camera parameters.
Although above-mentioned technical proposal can be in the barrel distortion of correction image in various degree, there are model complexity, meters
Calculation amount is big, the not high problem of practicability, it is therefore desirable to design that a kind of model is simple, calculation amount is small, the stronger camera lens of robustness is abnormal
Become bearing calibration.
Summary of the invention
The problem to be solved in the present invention is：The generally existing distortion of camera lens, and inside and outside ginseng in traditional camera scaling method
Number couple distortion factor is caused to be difficult to solve with existing between lens distortion, the independent solution scheme presence of existing distortion parameter
Model is complicated, computationally intensive, the not high problem of practicability.
The technical scheme is that：A kind of lens distortion calibration method of robust, includes the following steps：
1) using gridiron pattern as calibration object, with needing the camera of distortion correction to take pictures, it is ensured that calibration gridiron pattern is as far as possible
Full of the visual field, the X-comers of sub-pix dimension accuracy are extracted as correction foundation；
2) imaging model of camera and the distortion model of camera lens are established, by the gridiron pattern of the sub-pix dimension accuracy extracted
Angle point brings model into, determines optimization object function：
3) to the resulting optimization object function of step 2), distortion parameter solution is carried out using nonlinear optimization algorithm；
4) distortion parameter that step 3) is calculated is brought into distortion model, carries out distortion correction to picture.
It is preferred that step 1) extracts sub-pixel X-comers, it is divided into three steps：
1.1) the angle point collection in resulting entire image of taking pictures is obtained using Shi-Tomasi Corner Detection Algorithm；
1.2) obtained angle point collection is screened using SV operator, obtains X-comers；
1.3) refinement X-comers use inner product of vectors theory, i.e. two mutually orthogonal vectors to sub-pixel precision
The theoretical sub-pix refinement for carrying out X-comers that inner product is zero, the q that sets up an office is sub-pix angle point to be asked, and p is one in q neighborhood
It is a, vector pq is obtained, gradient direction G in the picture at point p is calculatedxp、Gyp, obtain unit along its gradient direction to
Measure Gp, the calculation formula of gradient direction θ is：
Gxp=I (x-1, y+1)+2I (x, y+1)+I (x+1, y+1)-I (x-1, y-1) -2I (x+1, y-1)-I (x+1, y-1)
Gyp=I (x-1, y-1)+2I (x-1, y)+I (x-1, y+1)-I (x+1, y-1) -2I (x+1, y)-I (x+1, y+1)
G in above formulaxp、GypIt is X at point p respectively, the gradient value of Y-direction, I (x, y) indicates that coordinate is (x, y) in image
The gray value of pixel；
No matter p where, pqG in sub-pix angle point neighborhood to be askedpIt is zero.Several are chosen in q neighbors around
Point pi, seek its gradient direction vector GpiWith vector qpiInner product, obtain optimization object function：
The coordinate q for the smallest q of F that sends as an envoy to is calculated using least square method optimizationn, by qnIt is repeated the above process as q, until
Reach target sub-pixel precision or the number of iterations reaches the upper limit；Accurate sub-pixel X-comers are extracted, after being
Distortion correction provide nominal data.
Camera imaging model is established described in step 2) is：
An object point P (X in spacew,Yw,Zw) obtain corresponding to picture point p (u, v) in picture by video camera imaging, this process
Undergo coordinate transform three times：
(1) world coordinate system Ow-XwYwZwTo camera coordinate system Oc-XcYcZcTransformation：The rigid body translation of three-dimensional space,
It is characterized with spin matrix R and translation vector t；
(2) camera coordinate system Oc-XcYcZcTo imaging plane physical coordinates system xOpThe transformation of y：Projective transformation, by internal reference
Matrix number M characterization；
(3) imaging plane physical coordinates system xOpTransformation of the y to pixel coordinate system uOv：Principal point offset amount；
Coordinate system transformation relationship is：
P (X in above formulaw,Yw,Zw) be space in a certain object point coordinate, p (u, v) be obtained through video camera imaging image seat
The corresponding coordinate of point in mark system, f are the focal lengths of camera lens, and dx, dy are respectively X, and the pixel equivalent of Y-direction, M is camera internal reference square
Battle array.
Lens distortion model described in step 2) is illustrated from the picture point (x for having distortiond,yd) arrive ideal undistorted picture point
(xu,yu) mapping u：
u：(xd, yd)→(xu, yu)
Its mathematic(al) representation is：
xu=xd+δx
yu=yd+δy
In above formula(cx,cy) sat for the pixel of center of distortion
Mark, k1,k2... it is coefficient of radial distortion, p1,p2For tangential distortion coefficient.
Further, optimization object function is specially in step 2)：If a width reference object image extracts L row M column feature
Point, every a line have NlA characteristic point, it is each to show NmA characteristic point investigates two neighboring characteristic point PiAnd Pi+1The vector of compositionWherein Pi(xu,yu), i=1,2,3... be ideal image point, thus constructs sequence vector, and two neighboring vector is taken to do multiplication cross
Operation simultaneously calculates its mould, obtains following formula, the as function of distortion parameter：
In above formulaIt is X in three-dimensional system of coordinate respectively, Y, the unit vector in Z-direction,
The optimization object function for establishing distortion parameter is estimated using this distortion, and is distorted and joined with nonlinear optimization search finding
Number k1, k2, p1, p2, cx, cy, the optimization object function of foundation be in sequence vector the mould of adjacent vector apposition and function：
Above formula adds up after summing respectively to the vector of every a line and each column, obtains the optimization aim letter for calculating distortion parameter
Number.
In step 3), using LM nonlinear optimization algorithm, i.e. damped least square method optimizes optimization object function
It solves, optimization object function is made to reach the distortion parameter of global minima, the camera lens that as model finally solves distort
Parameter.
The invention proposes a kind of lens distortion calibration method of robust, propose it is a kind of by lens distortion from camera parameters
In separate the algorithm individually solved, based on " straight line in three-dimensional space by following the camera projection of perspective model, in phase
It is still straight line in machine plane " this basic Consensus.To orthoscopic image, outside the collinear vectors that any two characteristic point is constituted on straight line
Product module should be zero.Distortion parameter is solved using nonlinear optimization method.The present invention is based on classical camera calibration models, propose new
Distortion model and method for solving, efficiently solve that conventional lenses distortion parameter solving model is complicated, computationally intensive, poor robustness
The problem of, the distortion parameter of camera lens can be simply and efficiently solved, the purpose of camera distortion correction is completed.
System designed by the invention has following remarkable result compared with existing well-known technique：
(1) the lens distortion calibration method of a kind of robust of the invention, derived from traditional camera based on X-comers
Scaling method, algorithm is mature, and the X-comers coordinate precision of extraction is good, and not by the interference of environmental background, robustness is good；
(2) the lens distortion calibration method of a kind of robust of the invention, based on " straight line in three-dimensional space is by following
The camera of perceived model projects, and is still straight line in camera plane " this basic Consensus, establish distortion model objective function, principle
Simply, the solution of distortion parameter can be only completed with a calibration maps, correction efficiency and stability are high, and calculation amount is small；
(3) the lens distortion calibration method of a kind of robust of the invention is carried out abnormal using LM Nonlinear Least-Square Algorithm
The Optimization Solution of variable element, is verified by largely testing, and has the advantages that high robust, Computationally efficient.
Detailed description of the invention
Fig. 1 is the flow chart of the method for the present invention.
Fig. 2 is the gridiron pattern calibration maps that the embodiment of the present invention uses.
Fig. 3 is extraction effect figure of the embodiment of the present invention to X-comers.
Fig. 4 is the comparison diagram that the embodiment of the present invention optimizes and is not optimised to center of distortion in distortion parameter.
(a)~(c) in Fig. 5 is of the invention to go distortion effect contrast figure.
Fig. 6 is the schematic diagram assessed using the method for least square fitting straight line the solution of the present invention.
Specific embodiment
It is stranded to solve to exist between inside and outside parameter and lens distortion in traditional cameras scaling method to couple and cause to solve
Difficult problem, the invention proposes a kind of lens distortion calibration methods of robust, and main flow is referring to Fig. 1, below by tool
Body embodiment illustrates the solution of the present invention.
1) first using gridiron pattern as calibration object, calibration paper printed in advance is fitted in smooth plane completely
On, with needing the camera of distortion correction to take pictures, it is ensured that calibration gridiron pattern is full of the visual field as far as possible, and picture captured by camera is as schemed
Shown in 2, the X-comers of sub-pix dimension accuracy are extracted as correction foundation；
Gridiron pattern be classical camera calibration method in the calibration object that is widely used, it is conllinear coplanar using X-comers
The characteristics of feature carries out the calculating of camera calibration parameter and distortion parameter, has structure simple, and angle point easily extracts.About gridiron pattern
Angle point grid, the present invention are proposed using sub-pixel X-comers detection algorithm of the Shi-Tomasi in conjunction with SV operator, originally
The effect for inventing the sub-pixel angle point extracted is as shown in Figure 3；
X-comers extraction process includes following three steps：
(1) the angle point collection in entire image is obtained using Shi-Tomasi Corner Detection Algorithm, algorithm basic thought is to make
The sliding on any direction is carried out on the image with a fixed window, compares and slides preceding and sliding latter two situation, in window
Pixel grey scale variation degree suffer from larger grey scale change if there is the sliding on any direction, then we can recognize
For there are angle points in the window.When [u, v], which occurs, for window moves, i.e., v pixel is moved in the mobile u pixel in the direction x, the direction y,
Portray sliding front and back window in pixel gray level variation E formula be：
[u, v] is the offset of window in formula, and (x, y) is pixel coordinate position corresponding in window, window have it is much,
Just there are multiple positions, I (x, y) is gray value of the image at (x, y).In order to facilitate calculating, E is carried out using Taylor series expansion
It is approximate：
Then available：WhereinIx, IyFor point
The gradient value in the direction the x at (x, y), y, calculation formula are：
Ix=I (x-1, y+1)+2I (x, y+1)+I (x+1, y+1)-I (x-1, y-1) -2I (x+1, y-1)-I (x+1, y-1)
Iy=I (x-1, y-1)+2I (x-1, y)+I (x-1, y+1)-I (x+1, y-1) -2I (x+1, y)-I (x+1, y+1) meter
Calculate the eigenvalue λ of matrix M1And λ2, to obtain the evaluation function R=min (λ of Shi-Tomasi algorithm1,λ2), it is set when R is greater than
When fixed threshold value, then point (x, y) is judged to angle point, is recorded；
(2) obtained angle point collection is screened using SV operator, SV operator can be found in《A kind of new gridiron pattern image angle
Point detection algorithm》(Liu Yangcheng, Zhu Feng,《Journal of Image and Graphics》In May, 2006, the 5th phase of volume 11).In the present invention, on
One step is using the angle point that the angle point that Shi-Tomasi algorithm obtains is in general sense, wherein may be comprising not being much chessboard
The interference angle point of lattice angle point, therefore the present invention uses SV operator according to the particularity of X-comers, carries out angle point screening.Because
Gridiron pattern is that square identical by size, chequered with black and white is constituted, therefore has good symmetry, about X-comers center
Symmetrical pixel gray value all relatively, and other gray values of non-X-comers about the symmetrical pixel of central point
Then there is larger difference.Therefore present invention firstly provides the symmetric operator S in SV operator, and each Shi-Tomasi angle point is concentrated
Angle point I (x, y), the 5x5 window centered on the point is denoted as W, define symmetric operator response be window W in about
The mean value of the gray scale difference absolute value of (x, y) symmetrical every a pair of of pixel, formula are：
N is the number of pixel in window W, and for X-comers, symmetric operator response S is smaller；And for other angles
Point, S are bigger.S reflects the spatial symmetry of the distribution of the wicket pixel grey scale centered on the point.However it is only calculated by symmetrical
Sub- S can't filter out X-comers well, because of flat site in the picture, the response of S also can be smaller.Cause
The invention proposes the variance operator V in SV operator for this, since the variation of black and white block is obvious near X-comers, therefore can set
The gray variance value near variance operator V calculating angle point in wicket is counted, to react the violent journey of gray-value variation around angle point
Degree.The calculation formula of variance operator V is：
N is the number of pixel in window W,It is the average value of all pixels gray scale in window W, I (x+p, y+q) refers to I
(x, y) is each pixel in center 5x5 window W.For the pixel of flat site, the response V of variance operator is smaller, and
The variance V of X-comers is then larger.In summary symmetric operator S and variance operator V, the present invention combine the two, propose SV
Operator, for selecting the angle point that symmetry is good and variance is big, the calculation formula of SV operator is：
SV (x, y)=k*V (x, y)-S (x, y)
K is adjustment parameter, and for value range usually in 0.1-0.5, SV value is greater than given threshold value SVminAngle point i.e. recognized
To be X-comers.
(3) X-comers are refined to sub-pixel precision using sub-pix angle point thinning method.Since Shi-Tomasi is calculated
The angle point that method detection and SV operator screen is whole pixel corner, there is a problem of that precision is inadequate for distortion correction.This hair
The theoretical sub-pix refinement for carrying out angle point bright theoretical using inner product of vectors, i.e. that two mutually orthogonal inner product of vectors are zero.By
It is to be made of the intersection of two edges of regions, therefore the q that sets up an office is sub-pix angle point to be asked in angle point, p is some in q neighborhood
Point calculates the gradient direction G at point p to obtain vector pqxpAnd Gyp, obtain the unit vector G along its gradient directionp, ladder
Degree direction θ calculation formula be：
Gxp=I (x-1, y+1)+2I (x, y+1)+I (x+1, y+1)-I (x-1, y-1) -2I (x+1, y-1)-I (x+1, y-1)
Gyp=I (x-1, y-1)+2I (x-1, y)+I (x-1, y+1)-I (x+1, y-1) -2I (x+1, y)-I (x+1, y+1)
When point p is located at region inner flat region, gradient 0, gradient direction vector GpIt also is zero, therefore vector pq
With GpInner product be zero；When point p is located at edges of regions, gradient is not zero, but its gradient direction GpIt is vertical with vector pq, at this time
Pq and GpInner product be also zero.So no matter p wherein, pqGpIt is zero.Therefore the chess that the present invention is screened in SV operator
Several points p is chosen in disk lattice angle point q neighbors aroundi, seek its gradient direction vector GpiWith vector qpiInner product, optimized
Objective function：
The coordinate q for the smallest q of F that sends as an envoy to is calculated using least square method optimizationn, by qnIt is repeated the above process as q, until
Reach target sub-pixel precision or the number of iterations reaches the upper limit.
2) imaging model of camera and the distortion model of camera lens are established, by the gridiron pattern of the sub-pix dimension accuracy extracted
Angle point brings model into, determines final optimization pass objective function；
Camera imaging model is established, camera imaging model includes linear model and nonlinear model, and nonlinear model adds
Compensation and amendment to camera lens distortion are entered.If not considering to distort, linear model is widely used in camera calibration, also
That is pin-hole model.Pin-hole model is slightly varied, so as to be located at lens ipsilateral to get to more meeting reality for object and its imaging
Border situation.
In this camera model, an object point P (X in spacew,Yw,Zw) obtain corresponding in picture by video camera imaging
Picture point p (u, v), this process need to undergo coordinate transform three times：
(1) world coordinate system Ow-XwYwZwTo camera coordinate system Oc-XcYcZcTransformation：The rigid body translation of three-dimensional space,
It is characterized with spin matrix R and translation vector t.
(2) camera coordinate system Oc-XcYcZcTo imaging plane physical coordinates system xOpThe transformation of y：Projective transformation, by internal reference
Matrix number M characterization.
(3) imaging plane physical coordinates system xOpTransformation of the y to pixel coordinate system uOv：Principal point offset amount.
Coordinate system transformation relationship is：
P (X in above formulaw,Yw,Zw) be space in a certain object point coordinate, p (u, v) be obtained through video camera imaging image seat
The corresponding coordinate of point in mark system, f are the focal lengths of camera lens, and dx, dy are respectively X, and the pixel equivalent of Y-direction, M is camera internal reference square
Battle array.
Establish lens distortion model, the image acquired in pin-hole model video camera and ideal model imaging between there is
Error, this error are shown on the position of picture point, generally this error are referred to as the nonlinear distortion of camera lens.It takes the photograph
Camera lens distortion mainly includes radial distortion and centrifugal distortion.It is radial that radial distortion generates actual image point and ideal image point
Displacement, main reason is the wrap-around error of lens.The origin cause of formation of centrifugal distortion is then that lens axis and camera optical axis be not coaxial.
The nonlinear distortion model of camera lens is illustrated from the picture point (x for having distortiond,yd) arrive ideal undistorted picture point (xu,yu)
Map u：
u：(xd, yd)→(xu, yu)
Its mathematic(al) representation is：
xu=xd+δx
yu=ya+δy
In above formula(cx,cy) sat for the pixel of center of distortion
Mark, the usually coordinate of image center, k1,k2For coefficient of radial distortion, p1,p2For tangential distortion coefficient.It is answered in real system
In, second order coefficient of radial distortion just can usually meet the required precision of system, so the coefficient of radial distortion of higher order does not have to
It discusses again.
Building calculates the optimization object function of distortion parameter, if camera lens does not distort, straight line passes through in space
It is still straight line on as plane after the projection of pin-hole model camera.According to geometric knowledge, if two collinear vectors, they
Apposition should be null vector.Therefore, the vector constituted for any two points on straight line, due to conllinear, the mould of apposition is zero.?
For in this meaning, the mould of collinear vectors apposition, which can be used as distortion, to be estimated.Assuming that a width reference object image extracts L row M column
Characteristic point, every a line have NlA characteristic point, it is each to show NmA characteristic point.Investigate two neighboring characteristic point PiAnd Pi+1Constitute to
AmountWherein Pi(xu,yu), i=1,2,3... is ideal image point.To the sequence vector constructed in this way, take two neighboring
Vector does multiplication cross operation and calculates its mould, obtains following formula, the as function of distortion parameter：
In above formulaIt is X in three-dimensional system of coordinate respectively, Y, the unit vector in Z-direction.
The optimization object function for establishing distortion parameter is estimated using this distortion, and is distorted and joined with nonlinear optimization search finding
Number.Set objective function as in sequence vector the mould of adjacent vector apposition and function：
Above formula adds up after summing respectively to the vector of every a line and each column, obtains the optimization aim letter for calculating distortion parameter
Number, Outer Product of Vectors calculate simply, and calculation amount is small, therefore majorized function can submit the effect of the method for the present invention using Outer Product of Vectors
Rate.k1,k2,p1,p2For coefficient of radial distortion and tangential distortion coefficient, cx, cyFor the coordinate of center of distortion, make objective function F most
Small k1, k2, p1, p2, cx, cySeek to the distortion parameter solved.
3) to the resulting objective function of step 2), distortion parameter solution is carried out using nonlinear optimization algorithm；
4) distortion parameter that step 3) is calculated is brought into distortion model, carries out distortion correction to picture, and assess
Distortion correction effect.
The CB-200GE camera of JAI company, the 5mm camera lens of Computar company are selected in experiment.With different positions and pose to calibration
Object has taken 14 pictures, and picture size is 1624 pixels × 1236 pixels.Distortion parameter is calculated to this 14 picture respectively, it is excellent
Change mode is divided into optimization center of distortion and is not optimised two kinds of center of distortion, and result is as shown in Figure 4.Fig. 4 shows distortion parameter,
What is indicated is to optimize center of distortion and be not optimised under the two ways of center of distortion, four be calculated distortion parameter k1, k2,
The comparison of p1, p2, we compare discovery, center of distortion c in an experimentx, cyVariation is very small afterwards before optimization, to finally going
The influence of the effect of distortion can be ignored, therefore subsequent experiment has been all made of and has not optimized center of distortion, and picture centre is straight
It connects and brings objective function into as center of distortion and solve other 4 parameters.In Fig. 4, (a) first order radial distortion coefficient k1, (b) single order
Coefficient of radial distortion k2, (c) centrifugal distortion coefficient p1, (d) centrifugal distortion coefficient claps p2, optimizing the mode of center of distortion, refer to will be abnormal
Change center is optimized with distortion factor together as unknown quantity, i.e., F formula has 6 variables；It is not optimised the mode of center of distortion then
Center of distortion is set as center picture, only distortion factor is optimized, i.e., F formula there are 4 variables.
It is not difficult to find out that, regardless of whether optimization center of distortion, the solution of coefficient of radial distortion is all sufficiently stable, and changes from Fig. 4
Change optimal way can directly result in centrifugal distortion coefficient and vary widely.From the point of view of the origin cause of formation that both distort, this is easy
Understand.Radial distortion is the wrap-around error due to lens and generates, unrelated with the position of center of distortion.And centrifugal distortion be by
It is not coaxial with camera optical axis in lens axis and generate, characterize the relative positional relationship between two planes.Different Optimization side
Formula causes center of distortion position different so that the offset between optical center and image center changes, so as to cause from
Corresponding variation occurs for heart distortion factor.The quantity of variable in non-linear objective function can be reduced without optimizing center of distortion,
Its convergence rate is set to become faster, it is as a result more stable.Therefore, the present invention, which uses, sets center of distortion as the mode of center picture, benefit
Distortion parameter is calculated with the method for the present invention and corrected implementation such as Fig. 5, Fig. 5 show that three groups are removed distortion effect picture, figure
Middle left side is in the presence of the image of distortion, and right part of flg is the later image that distorts.Using least squares line fitting algorithm to abnormal
Become the X-comers that correction front and back is extracted and carry out straight line fitting, be corrected assessment, calculates the effect picture that point arrives straight line variation
As shown in fig. 6, the smaller proof distortion removal effect of deviation is better.
A kind of lens distortion calibration method of robust, belongs to machine vision and Digital Image Processing described in above-described embodiment
Technical field.The present invention mainly proposes a kind of algorithm separating lens distortion from camera parameters and individually solving, base
In " straight line in three-dimensional space is projected by following the camera of perspective model, is still straight line in camera plane ", this is substantially total
Know.To orthoscopic image, the outer product module of the collinear vectors that any two characteristic point is constituted on straight line should be zero.Utilize nonlinear optimization side
Method solves distortion parameter.Its step is：Calibration object feature extraction is carried out to image, feature extraction is carried out to gridiron pattern calibration object, first
Angle point Corner Detection is carried out using Shi-Tomasi operator, later according to the distinctive symmetrically feature big with variance of X-comers
It is screened, finally uses sub-pix optimization algorithm, obtain the accurate subpixel coordinates of X-comers；Then establish camera at
As model and lens distortion model, projected based on the 3 d-line in world coordinate system by following the camera of perspective model,
It is still the criterion of straight line on the image that camera imaging plane is formed, establishes the optimization object function about distortion parameter；Last benefit
Distortion parameter is solved with nonlinear optimization algorithm.The experimental results showed that the present invention only needs the picture comprising calibration object
The calculating of all main distortion parameters is completed, model is simple, and computational efficiency and stability are high, the application adaptability in industrial circle
It is good, and computational accuracy is suitable with conventional method.
Schematically the present invention and embodiments thereof are described above, description is not limiting, institute in attached drawing
What is shown is also one of embodiments of the present invention, and actual structure is not limited to this.So if the common skill of this field
Art personnel are enlightened by it, without departing from the spirit of the invention, are not inventively designed and the technical solution
Similar frame mode and embodiment, are within the scope of protection of the invention.
Claims (6)
1. a kind of lens distortion calibration method of robust, it is characterized in that including the following steps：
1) using gridiron pattern as calibration object, with needing the camera of distortion correction to take pictures, it is ensured that calibration gridiron pattern is full of as far as possible
The X-comers of sub-pix dimension accuracy are extracted as correction foundation in the visual field；
2) imaging model of camera and the distortion model of camera lens are established, by the X-comers of the sub-pix dimension accuracy extracted
It brings model into, determines optimization object function：
3) to the resulting optimization object function of step 2), distortion parameter solution is carried out using nonlinear optimization algorithm；
4) distortion parameter that step 3) is calculated is brought into distortion model, carries out distortion correction to picture.
2. the lens distortion calibration method of a kind of robust according to claim 1, it is characterized in that step 1) extracts sub-pix
Grade X-comers, are divided into three steps：
1.1) the angle point collection in resulting entire image of taking pictures is obtained using Shi-Tomasi Corner Detection Algorithm；
1.2) obtained angle point collection is screened using SV operator, obtains X-comers；
1.3) refinement X-comers use inner product of vectors theory, i.e. two mutually orthogonal inner product of vectors to sub-pixel precision
The theoretical sub-pix refinement for carrying out X-comers for being zero, the q that sets up an office is sub-pix angle point to be asked, and p is one in q neighborhood
Point obtains vector pq, calculates gradient direction G in the picture at point pxp、Gyp, obtain the unit vector along its gradient direction
Gp, the calculation formula of gradient direction θ is：
Gxp=I (x-1, y+1)+2I (x, y+1)+I (x+1, y+1)-I (x-1, y-1) -2I (x+1, y-1)-I (x+1, y-1)
Gyp=I (x-1, y-1)+2I (x-1, y)+I (x-1, y+1)-I (x+1, y-1) -2I (x+1, y)-I (x+1, y+1)
G in above formulaxp、GypIt is X at point p respectively, the gradient value of Y-direction, I (x, y) indicates that coordinate in image is the pixel of (x, y)
Gray value；
No matter p where, pqG in sub-pix angle point neighborhood to be askedpIt is zero, therefore chooses several points in q neighbors around
pi, seek its gradient direction vector GpiWith vector qpiInner product, obtain optimization object function：
The coordinate q for the smallest q of F that sends as an envoy to is calculated using least square method optimizationn, by qnIt is repeated the above process as q, until reaching
Target sub-pixel precision or the number of iterations reach the upper limit；Accurate sub-pixel X-comers are extracted, it is abnormal after being
Become correction and nominal data is provided.
3. the lens distortion calibration method of a kind of robust according to claim 1, it is characterized in that foundation described in step 2)
Camera imaging model is：
An object point P (X in spacew,Yw,Zw) obtain corresponding to picture point p (u, v) in picture by camera imaging, this process experience three
Secondary coordinate transform：
(1) world coordinate system Ow-XwYwZwTo camera coordinates system Oc-XcYcZcTransformation：The rigid body translation of three-dimensional space, with rotation
Matrix R and translation vector T characterization；
(2) camera coordinates system Oc-XcYcZcTo imaging plane physical coordinates system xOpThe transformation of y：Projective transformation, by Intrinsic Matrix M
Characterization；
(3) imaging plane physical coordinates system xOpTransformation of the y to pixel coordinate system uOv：Principal point offset amount；
Coordinate system transformation relationship is：
P (X in above formulaw,Yw,Zw) be space in a certain object point coordinate, p (u, v) is to obtain image coordinate system through video camera imaging
In the corresponding coordinate of point, f is the focal length of camera lens, and dx, dy are respectively X, and the pixel equivalent of Y-direction, M is camera internal reference matrix.
4. the lens distortion calibration method of a kind of robust according to claim 1, it is characterized in that camera lens described in step 2)
Distortion model is illustrated from the picture point (x for having distortiond,yd) arrive ideal undistorted picture point (xu,yu) mapping u：
u：(xd, yd)→(xu, yu)
Its mathematic(al) representation is：
xu=xd+δx
yu=yd+δy
In above formula(cx,cy) be center of distortion pixel coordinate,
k1,k2... it is coefficient of radial distortion, p1,p2For tangential distortion coefficient.
5. the lens distortion calibration method of a kind of robust according to claim 1, it is characterized in that optimization aim in step 2)
Function is specially：If a width reference object image extracts L row M column characteristic point, every a line has NlA characteristic point, it is each to show NmIt is a
Characteristic point investigates two neighboring characteristic point PiAnd Pi+1The vector of compositionWherein Pi(xu,yu), i=1,2,3... is reason
Imagine point, thus constructs sequence vector, take two neighboring vector to do multiplication cross operation and calculate its mould, obtain following formula, as distort
The function of parameter：
In above formulaIt is X in three-dimensional system of coordinate respectively, Y, the unit vector in Z-direction,
Estimated using this distortion and establish the optimization object function of distortion parameter, and with nonlinear optimization search finding distortion parameter k1,
k2, p1, p2, cx, cy, the optimization object function of foundation be in sequence vector the mould of adjacent vector apposition and function：
Above formula adds up after summing respectively to the vector of every a line and each column, obtains the optimization object function for calculating distortion parameter.
6. a kind of lens distortion calibration method of robust according to claim 1, it is characterized in that in step 3), it is non-using LM
Linear optimization algorithm, i.e. damped least square method optimize optimization object function, and optimization object function is made to reach complete
The camera lens distortion parameter that the smallest distortion parameter of office, as model finally solve.
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