CN109754431A - Light-field camera scaling method based on self-polar triangle - Google Patents
Light-field camera scaling method based on self-polar triangle Download PDFInfo
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Abstract
The present invention provides a kind of light-field camera scaling method based on self-polar triangle establishes light-field camera caliberating device and method based on self-polar triangle for the limited excessive and not high accuracy disadvantage of current light-field camera calibration.Design the scaling board with parameter distinction and self-polar triangle characteristic, pass through the scaling board of rotation scaling board or mobile light-field camera shooting in different positions, and determine the homography of world point and picture point, the outer parameter under linear initialization calculating light-field camera intrinsic parameter and corresponding posture is carried out using the characteristic of self-polar triangle and absolute conic, distortion model and cost function are finally established, iteration acquires optimal solution.The present invention can it is more flexible, accurately solve light-field camera internal reference and outer ginseng.
Description
Technical field
The present invention relates to computer vision, computer camera shooting is learned and optical engineering field, and in particular to a kind of mark of camera
Cover half type and method.
Background technique
The rise of optical field imaging theory is a big important innovation in computer camera field, it breaches tradition imaging skill
Various limitations of art.Light-field camera reduces the loss of photographing information by the position and angle information of light in record space,
Have in fields such as estimation of Depth, refocusing, three-dimensional reconstructions and is widely applied.The processing of field information is built upon in later period application
On the basis of camera parameter calibration, accurate calibration result is to the promotion of later image resolution ratio and the improvement meaning of image quality
It is great.
There are three types of common calibration plate modes, i.e. point, line and conic section at present.Existing method usually utilizes tessellated
The line feature of angle point or scaling board demarcates light-field camera.However due to influence of noise, sub-aperture image and lenticule
The image quality of image limits, it is difficult to carry out accurate angle point grid and Line feature.Camera is being carried out using conic section
Calibration aspect, Quan et al. propose the invariance that two concentric circles are total to self-polar triangle, and Kim et al. is to by concentric circles
It carries out algebraical sum geometrical constraint and restores the center of circle and circular points respectively.However in the studies above, the reconstruction of the center of circle and the hachure that disappears is usual
It is carried out separately.Huang et al. studies the characteristic of the total self-polar triangle of concentric circles, and proposes one kind and estimate
Count the method singly answered.However this method only accounts for the estimation of camera internal reference, can not solve the outer parameter of camera.
Summary of the invention
For overcome the deficiencies in the prior art, the present invention provides a kind of light-field camera parameter calibration device and method, it is intended to
It is more flexible, accurately solve light-field camera internal reference and outer ginseng.
The technical solution adopted by the present invention to solve the technical problems the following steps are included:
The scaling board that S1, design are made of oval and circle combination, makes it have parameter distinction and self-polar triangle
Feature；TPP coordinate system is established, the collected light of light-field camera is described, then establishes the inside and outside moduli of light-field camera
Type and projection model；
S2, according to calibration Slab self-polar triangle characteristic and absolute conic characteristic, establish scaling board plane
On point and its sub-aperture image in homography H between picture point and solve, then acquire light-field camera intrinsic parameter and
Outer parameter；
S3, the Distortion Vector k for introducing four parametersd=(k1,k2,k3,k4), establish distortion modelDeviation existing between practical light and imaging model describing mode is corrected, wherein(x, y) is that the point on scaling board passes through internal reference (ki,kj) and the outer non-distortion point for joining projection, k1And k2It is light field
The adjustment factor that conventional radial distorts in camera, k3And k4It is for the coefficient that distortion is introduced caused by light-field camera viewpoint switch；
To the circle or ellipse C on scaling boardw,nIt is projected according to projection formula and distortion formula, subpointIt should be
Cw,nSub-aperture image CiOn, that is, meetSampson error cost function is established according to this relationshipSearching enables cost function reach the smallest parameter i.e.
For optimal solution.
The scaling board includes concentric ellipse and circle combination, and concentric circles and model of ellipse have altogether from polarity triangle
Shape, elliptical major and minor axis ensure that parameter distinction.
The step S2 is located at o=(x to the center of circle0,y0) at concentric circles C1With oval C2, according to altogether from polarity triangle
Shape relationship is learntThree feature vectors be respectively the center of circle (x0,y0,0)T, circular points (1,0,0)T、(0,1,0)T；In son
In subaperture image, the hachure that disappears is rebuild using circular points, finds orthogonal direction u on hachure disappearinga、ubConstruct equation groupTo rebuild the image of absolute conicIt is rightCholesky is carried out to decompose to obtain intrinsic parameter (ku,kv,
u0,v0)；Internal reference (ki,kj) and outer parameter (r1,r2, t) and pass through three feature vector ekWith its sub-aperture imageProjection close
SystemIt solves, k=1,2,3；Outer parameter r3According to the orthogonality r of spin matrix3=r1×r2It asks
Solution.
The step S3 is iterated optimization by Levenberg-Marquardt algorithm, acquires and enables cost function most
Small parameter value.
The beneficial effects of the present invention are: for the limited excessive and not high accuracy disadvantage of current light-field camera calibration,
Establish light-field camera caliberating device and method based on self-polar triangle.Design has parameter distinction and from polarity triangle
The scaling board of shape characteristic by the scaling board of rotation scaling board or mobile light-field camera shooting in different positions, and determines generation
The homography of boundary point and picture point carries out linear initialization calculating using the characteristic of self-polar triangle and absolute conic
Outer parameter under light-field camera intrinsic parameter and corresponding posture, finally establishes distortion model and cost function, and iteration acquires optimal solution.
Scaling board design of the invention is more succinct flexible.Gridiron pattern compared to traditional scaling board designs, the present invention
Scaling board used only contains several conic section combinations, simplest situation lower needs one group of concentric circle and ellipse.
Method of the invention is more accurate and stablizes.Traditional scaling method relies on angle point grid, angle point grid error pair
Calibration result has larger impact.The present invention only needs to carry out conic fitting to the set of point, is missed by individual angle point grids
Difference influence is small, has higher accuracy and robustness.
The method scope of application of the invention is wider.Since the present invention is demarcated using conic section, the extraction accuracy of point is wanted
Ask low, thus cause due to being influenced environment etc. image quality is not good enough, point position not enough clearly stand good.
Methodological function of the invention is more perfect.Camera can only be solved compared to round scaling method is contained only in scaling board
The scaling method that the design of elliptical major and minor axis has parameter distinction is utilized in the present invention, so that of the invention in the case where internal reference
Intrinsic parameter can be not only solved, the outer parameter of light-field camera can be equally solved.
The distortion model that the present invention establishes is more comprehensively.The distortion model of two traditional coefficients only considers that traditional radial direction is abnormal
Become, distortion model proposed by the present invention is also contemplated due to the different caused distortion of light-field camera viewpoint, so that light description is more
Close to practical drop shadow effect.
The invention also provides a kind of practical cost functions.Traditional cost function need established according to re-projection error
Want the corresponding relationship of the point on known calibration plate and picture point, cost function of the invention according to the geometry of conic section and point about
Shu Jianli does not need harsh corresponding relationship, more practical under real scene.
Detailed description of the invention
Fig. 1 is scaling board design diagram.
Fig. 2 is double parallel plane coordinate system system.
Fig. 3 is the flow chart of the method for the present invention.
Specific embodiment
Present invention will be further explained below with reference to the attached drawings and examples, and the present invention includes but are not limited to following implementations
Example.
The present invention proposes a kind of scaling method based on self-polar triangle, calculate light-field camera internal reference and outer ginseng.It is main
Wanting link includes: that scaling board designs and based on double parallel areal model (Two-parallel-plane Model, TPP) coordinate
Projective transformation that system is established is distorted in light-field camera internal reference and the solution joined outside, nonlinear optimization in linear initialization
The foundation of model and cost function and the method for solving of optimal solution.The method comprises the steps of:
S1, scaling board design and establish projective transformation based on TPP coordinate system.
S1.1, according to demand, the scaling board that design is made of oval and circle combination make it have parameter distinction and certainly
Polar triangle feature.
One selection is to be combined using concentric ellipse and circle, or the more complicated model comprising this combination.With one heart
Round and model of ellipse has total self-polar triangle, and elliptical major and minor axis ensure that parameter distinction.
S1.2, TPP coordinate system is established, the collected light of light-field camera is described, light-field camera is then established
Inside and outside moduli type and projection model.
S2, linear initialization
According to the self-polar triangle characteristic and absolute conic characteristic of calibration Slab, establish in scaling board plane
Homography H in point and its sub-aperture image between picture point is simultaneously solved, then acquire light-field camera intrinsic parameter and outer ginseng
Number.
Substantially step is to be located at o=(x to the center of circle0,y0) at concentric circles C1With oval C2, according to total self-polar triangle
Known to relationshipThree feature vectors be respectively the center of circle (x0,y0,0)T, circular points (1,0,0)T、(0,1,0)T.In sub-aperture
In diameter image, the hachure that disappears is rebuild using circular points.By the right angle characteristic of round self-polar triangle, disappear found on hachure it is orthogonal
Direction ua、ubConstruct equation groupTo rebuild the image of absolute conicIt is rightCarry out Cholesky decomposition
Obtain intrinsic parameter (ku,kv,u0,v0).Internal reference (ki,kj) and outer parameter (r1,r2, t) and three feature vector e can be passed throughk(k=1,
2,3) with its sub-aperture imageProjection relationIt solves.Outside
Parameter r3According to the orthogonality r of spin matrix3=r1×r2It solves.
S3, nonlinear optimization
Outer ginseng under the internal reference and each posture of the light-field camera obtained as above arrived is a coarse solution, without specific
Physical significance, select reasonable cost function to all parameters carry out nonlinear optimization.
S3.1, distortion model is introduced
Due to the optical characteristics of lens and the mismachining tolerance of lenticule, deposited between practical light and imaging model describing mode
In certain deviation, therefore introduces distortion model and corrected.The present invention considers the radial distortion of the light-field camera plane of delineation, introduces four
The Distortion Vector k of parameterd=(k1,k2,k3,k4), establish distortion model:
Wherein(x, y) is that the point on scaling board passes through internal reference (ki,kj) and the outer non-distortion point for joining projection,
k1And k2It is the adjustment factor that conventional radial distorts in light-field camera, k3And k4It is for abnormal caused by light-field camera viewpoint switch
Become the coefficient introduced.
S3.2, cost function is established, is iterated and seeks optimal solution
According to perspective geometry relationship establish can with the cost function of characterising parameter error, the present invention on scaling board circle or
Person's ellipse Cw,nIt is projected according to projection formula and distortion formula, subpointIt should be in Cw,nSub-aperture image CiOn, i.e., it is full
FootSampson error cost function is established according to this relationshipSearching enables cost function reach the smallest parameter i.e.
For optimal solution.
One selection is that optimization can be iterated by Levenberg-Marquardt algorithm, acquires and enables cost function
The smallest parameter value.
As shown in figure 3, the light-field camera parameter calibration method that the embodiment of the present invention proposes, comprising the following steps:
S1, scaling board design and establish projective transformation based on TPP coordinate system.
S1.1, according to demand designs the scaling board with parameter distinction and self-polar triangle feature
The scaling board that the present invention designs is made of concentric circle and ellipse, as shown in Figure 1.Known concentric circles and ellipse have and
Only one is total to self-polar triangle and is right angled triangle.The three sides of a triangle are located at elliptical long axis, short axle
And line at infinity, and one of vertex is located at the center point.
Assuming that there is the center of circle to be located at o=(x0,y0) at concentric circles C1With oval C2, C1Radius be r, C2Long axis and short axle
Respectively a, b then have:
Known C1And C2One and only one total self-polar triangle, that is, have three pairs of copolar point-polar curve relationships, it is assumed that point x with
Straight line l is one pair of them pole and polar curve, i.e. l=C1X and l=λ C2X then has
Wherein x is C1And C2Copolar point,Feature vector be exactly x in formula 2 solution.It can obtain:
λ1、λ2And λ3It isThree characteristic values, e1、e2And e3It is corresponding feature vector, can be weighed according to formula 3
Build concentric circles and elliptical self-polar triangle altogether.e1、e2The direction of the straight line where elliptical long axis and short axle is respectively represented,
Also the intersection point of itself and line at infinity, e are represented3It is then the round and elliptical public center of circle.Three different characteristic values ensure that outer ginseng
Ga s safety degree when number solves.
S1.2, TPP coordinate system is established, the collected light of light-field camera is described, and then establish light-field camera
Inside and outside moduli type and projection model.
The present invention is described the collected light of light-field camera using TPP model, and the specific method is as follows: defining one
TPP coordinate system, as shown in Fig. 2, viewpoint plane is located at Z=0, the plane of delineation is located at Z=f, in practical applications frequently with
Simplified TPP model, that is, unitization f=1.A piece light of light-field camera record is expressed as p=(i, j, u, v), wherein (i, j)
It is the serial number of viewpoint, (u, v) is the pixel coordinate under the viewpoint in sub-aperture image.Light field L that light-field camera is recorded (i,
J, u, v) a homogeneous decoding matrix can be passed throughIt is converted into the light field L (s, t, x, y) of physical unit,
Wherein (ki,kj,ku,kv,u0,v0) be light-field camera internal reference, (ki,kj)、(ku,kv) it is that corresponding viewpoint is flat respectively
The scale factor of s, t axis on face and the x on the plane of delineation, y-axis, (- u0/ku,-v0/kv) indicate that the principal point of sub-aperture image is inclined
It moves.
A point X according to light-field camera projection model, in spacec=(X, Y, Z)TWith the pixel (x, y) on the plane of delineation
Matching, then meet
Additionally, it is contemplated that the point X in world coordinateswWith the point X that is corresponding to it in camera coordinates systemc, with spin matrix R=
(r1,r2,r3) ∈ SO (3) and translation matrixTo describe the pass between world coordinate system and camera coordinates system
, then there is X in systemc=RXw+ t, [R | t] the i.e. outer ginseng of light-field camera.
S2, linear initialization
According to the self-polar triangle characteristic of calibration Slab, picture in the point on stencil plane and its sub-aperture image is established
Point between homography H and solve, then acquire the intrinsic parameter of light-field camera and an initial linear solution of outer parameter.
In conjunction with formula 4,5, the pixel (u, v) on sub-aperture image can be retouched with the relationship between corresponding three-dimensional space point
It states are as follows:
It wherein indicates differing the equivalence in a scale factor, tst=(s, t, 0)T,(s,t)T=Kij(i,j)T。
Point on plane at infinity projects on sub-aperture image, and corresponding plane homography isFor
Absolute conic Ω on plane at infinity∞, enableFor Ω∞Projection on sub-aperture image, thenIf figure
As upper two o'clock ua、ubTwo vertical directions are respectively corresponded, then are met
Assuming that scaling board plane is Z in world coordinatesw=0 plane, for the conic section on scaling board, formula 6 can
With simplification are as follows:
HijIndicate the plane shock wave of (i, j) viewpoint.Assuming thatWithConcentric circles and ellipse are respectively indicated in viewpoint (i, j)
Sub-aperture image, then have
Wherein C1And C2In the form under world coordinate system as described in formula 1.
WithIt is similar matrix, characteristic value having the same, corresponding feature vector meets:
According to formula 3, the sub-aperture image of total self-polar triangle can be reconstructed and disappear hachure and the center of circle.
A known circle has numerous self-polar triangle and is all right angled triangle, using any two from polarity three
It is angular to bring following formula into:
Wherein ua、ubIt is the point to disappear on hachure, the direction of straight line where also representing two right-angle sides of self-polar triangle.By
Formula 11 can calculate the image of absolute conic ΩOnceIt is known that can decompose to obtain by Cholesky interior
Parameter (ku,kv,u0,v0).Other intrinsic parameters of light-field camera and outer parameter can also be found out in the following manner:
r3=r1×r2 (15)
Wherein | | | | indicate L2Norm,It is obtained by formula 11,WithIt is respectivelyWithMinimal characteristic
Value, τ indicate scale factor.(x0,y0) it is the center of circle under world coordinate system.WithIt isIn (i, j) viewpoint
Feature vector, respectively correspond the e under world coordinate system1、e2And e3And eigenvalue λ1、λ2And λ3。
S3, nonlinear optimization
S3.1, distortion model is introduced
Due to the optical characteristics of lens and the mismachining tolerance of lenticule, light inevitably generates distortion.It examines herein
Consider the radial distortion of the light-field camera plane of delineation:
Wherein(x, y) is that the point on scaling board passes through internal reference (ki,kj) and the outer non-distortion point for joining projection,
k1And k2It is the adjustment factor that conventional radial distorts in light-field camera, k3And k4It is for abnormal caused by light-field camera viewpoint switch
Become the coefficient introduced.In short, the Distortion Vector of light-field camera is kd=(k1,k2,k3,k4)。
S3.2, cost function is established, is iterated and seeks optimal solution
Nonlinear optimization is carried out to initial linear solution by establishing suitable cost function.It can be according to Sampson error
Establish cost function:
Wherein Cw,nIt is the conic section under world coordinate system described in formula 1,It is Cw,nOn point it is public according to projection
The projection of formula 4,5 and distortion formula 16.P and kdRespectively represent internal reference and Distortion Vector, RpAnd tpIt is the outer ginseng of each posture.This
The Jacobian matrix of cost function be it is sparse, can be optimized by Levenberg-Marquardt algorithm, so that generation
The smallest parameter value of valence function is exactly the optimal solution of the problem.
Claims (4)
1. a kind of light-field camera scaling method based on self-polar triangle, it is characterised in that include the following steps:
The scaling board that S1, design are made of oval and circle combination, makes it have parameter distinction and self-polar triangle feature；
TPP coordinate system is established, the collected light of light-field camera is described, then establishes the inside and outside moduli type and throwing of light-field camera
Shadow model；
S2, according to calibration Slab self-polar triangle characteristic and absolute conic characteristic, establish in scaling board plane
Homography H in point and its sub-aperture image between picture point is simultaneously solved, then acquire light-field camera intrinsic parameter and outer ginseng
Number；
S3, the Distortion Vector k for introducing four parametersd=(k1,k2,k3,k4), establish distortion model
Deviation existing between practical light and imaging model describing mode is corrected, wherein(x, y) is calibration
Point on plate passes through internal reference (ki,kj) and the outer non-distortion point for joining projection, k1And k2It is the tune that conventional radial distorts in light-field camera
Save coefficient, k3And k4It is for the coefficient that distortion is introduced caused by light-field camera viewpoint switch；
To the circle or ellipse C on scaling boardw,nIt is projected according to projection formula and distortion formula, subpointIt should be in Cw,n
Sub-aperture image CiOn, that is, meetSampson error cost function is established according to this relationshipSearching enables cost function reach the smallest parameter i.e.
For optimal solution.
2. the light-field camera scaling method according to claim 1 based on self-polar triangle, it is characterised in that: described
Scaling board includes concentric ellipse and circle combination, and concentric circles and model of ellipse have self-polar triangle altogether, elliptical major and minor axis
It ensure that parameter distinction.
3. the light-field camera scaling method according to claim 1 based on self-polar triangle, it is characterised in that: described
Step S2 is located at o=(x to the center of circle0,y0) at concentric circles C1With oval C2, learnt according to total self-polar triangle relationship
Three feature vectors be respectively the center of circle (x0,y0,0)T, circular points (1,0,0)T、(0,1,0)T；In sub-aperture image, utilize
Circular points rebuild the hachure that disappears, and orthogonal direction u is found on hachure disappearinga、ubConstruct equation groupTo rebuild absolute two
The image of secondary curveIt is rightCholesky is carried out to decompose to obtain intrinsic parameter (ku,kv,u0,v0)；Internal reference (ki,kj) and outer parameter
(r1,r2, t) and pass through three feature vector ekWith its sub-aperture imageProjection relationIt asks
Solution, k=1,2,3；Outer parameter r3According to the orthogonality r of spin matrix3=r1×r2It solves.
4. the light-field camera scaling method according to claim 1 based on self-polar triangle, it is characterised in that: described
Step S3 is iterated optimization by Levenberg-Marquardt algorithm, acquires and enables the smallest parameter value of cost function.
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Cited By (4)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN110298890A (en) * | 2019-06-24 | 2019-10-01 | 西北工业大学 | A kind of light-field camera scaling method based on Planck parametrization |
| CN110310338A (en) * | 2019-06-24 | 2019-10-08 | 西北工业大学 | A kind of light-field camera scaling method based on multicenter projection model |
| CN110310337A (en) * | 2019-06-24 | 2019-10-08 | 西北工业大学 | A kind of more view optical field imaging system population parameter estimation methods based on light field fundamental matrix |
| CN110322514A (en) * | 2019-06-24 | 2019-10-11 | 西北工业大学 | A kind of light-field camera method for parameter estimation based on multicenter projection model |
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2018
- 2018-12-20 CN CN201811560397.4A patent/CN109754431A/en active Pending
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| QI ZHANG等: "《Common Self-polar Triangle of Concentric Conics for Light Field Camera Calibration》", 《ACCV 2018》 * |
Cited By (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110298890A (en) * | 2019-06-24 | 2019-10-01 | 西北工业大学 | A kind of light-field camera scaling method based on Planck parametrization |
| CN110310338A (en) * | 2019-06-24 | 2019-10-08 | 西北工业大学 | A kind of light-field camera scaling method based on multicenter projection model |
| CN110310337A (en) * | 2019-06-24 | 2019-10-08 | 西北工业大学 | A kind of more view optical field imaging system population parameter estimation methods based on light field fundamental matrix |
| CN110322514A (en) * | 2019-06-24 | 2019-10-11 | 西北工业大学 | A kind of light-field camera method for parameter estimation based on multicenter projection model |
| CN110322514B (en) * | 2019-06-24 | 2022-05-03 | 西北工业大学 | Light field camera parameter estimation method based on multi-center projection model |
| CN110310338B (en) * | 2019-06-24 | 2022-09-06 | 西北工业大学 | Light field camera calibration method based on multi-center projection model |
| CN110298890B (en) * | 2019-06-24 | 2022-09-06 | 西北工业大学 | Light field camera calibration method based on Planck parameterization |
| CN110310337B (en) * | 2019-06-24 | 2022-09-06 | 西北工业大学 | Multi-view light field imaging system full-parameter estimation method based on light field fundamental matrix |
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Application publication date: 20190514 |