CN110060303A - A kind of two step scaling methods of light-field camera - Google Patents
A kind of two step scaling methods of light-field camera Download PDFInfo
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Abstract
A kind of two step scaling methods of light-field camera, based on light-field camera imaging model, the first step realizes the calibration of main lens parameter using equivalent camera projection model by the characteristic point coordinate in the sub-aperture image of extraction center；The constraint relationship of second step combination light field parallax and Object Depth, fitting solve lenticule parameter, demarcate to obtain the physical parameter of light-field camera by two steps.The present invention is based on the image-forming principles of light-field camera, establish a kind of projection model that can degenerate to traditional camera, propose a kind of two more generally applicable step scaling methods in particular for non-focusing type light-field camera.Pass through the derivation to light-field camera imaging model, center sub-aperture image is equivalent to traditional camera image, to which classical Zhang Zhengyou plane reference method to be applied in light-field camera calibration, by deriving the constraint relationship of light field parallax and depth, the method that straight line fitting solves lenticule parameter is realized.
Description
Technical field
The present invention relates to camera calibration technology, it is related to the calibration based on non-focusing type light-field camera, for for based on light field
The three-dimensional imaging of camera provides technical parameter, is a kind of two step scaling methods of light-field camera.
Background technique
Traditional camera calibration algorithm is based on pin-hole model, first shooting scaling board image, scaling board, that is, each characteristic point
Spatial position all through in advance survey reference of reference plate, further according to characteristic point image coordinate and true three-dimension space coordinate projection
Mapping relations, solution obtain the inside and outside parameter of camera.And it is directed to the calibration of light-field camera, current main method is to establish and pass
The different light-field camera projection model of system model, describes projection mapping relationship using multilevel parametrization structure, then pass through bat
Take the photograph scaling board image calibration light-field camera parameter.But such method have the defects that it is certain, due to the projective module of light-field camera
Type is changed compared to the pin-hole model of traditional camera, and the calibration result of the above method is typically only capable to obtain light-field camera
Projection matrix, and the optical parameter with physical significance can not be solved, such as sub-aperture width, lenticule focal length.Needle at present
To light-field camera, there has been no scaling methods highly effective and versatile.
Summary of the invention
The problem to be solved in the present invention is: the existing scaling method for light-field camera establishes the projective module in light-field camera
On the basis of type, the projection matrix of light-field camera can only be obtained, can not solve to obtain the optical parameter with physical significance, Bu Nengman
Sufficient use demand.
The technical solution of the present invention is as follows: a kind of two step scaling methods of light-field camera, for non-focusing type light-field camera, with
Based on light-field camera projection model, each lenticule is considered as an equivalent pixel, traditional camera projection model is equivalent to
A kind of degeneration of light-field camera projection model is expressed, and recycle traditional calibration algorithm to be demarcated, including two steps: the first step mentions
The sub-aperture image of light-field camera is taken, the sub-aperture image for defining main lens optical center position is center sub-aperture image, by mentioning
The coordinate for taking the point in the sub-aperture image of center is considered as traditional camera image for center sub-aperture image is equivalent, by center sub-aperture
Diameter image demarcates the inside and outside parameter of main lens according to Zhang Zhengyou plane reference method, realizes the calibration of main lens parameter；Second step, by
Pass through the position coordinates of primary mirror head plane when the three-dimensional coordinate of any in space and the point are incident on light-field camera, it may be determined that should
Coordinate of the point in lenticule plane, in conjunction with the constraint relationship of light field parallax and Object Depth, fitting, which solves, obtains lenticule ginseng
Number, the light field parallax refer to object point P in the parallax of any two width adjacent sub-aperture image；It demarcates to obtain light-field camera by two steps
Physical parameter.
First step calibration specifically:
1) acquire scaling board image, fixed light-field camera, using light-field camera to the same scaling board of different angle into
Row shooting；
2) four-dimensional field information is decoded from the original image that light-field camera acquires, and extracts sub-aperture image, is decoded
Journey includes: micro- picture centre extraction, micro- image slant correction, micro- image segmentation and colour correction, and micro- image refers to that light passes through
Cross after a lenticule at picture, the four-dimensional light field L (s, t, x, y) decoded is converted to sub-aperture image by following formula:
Wherein (s, t) indicates coordinate of the light Jing Guo main lens plane, characterizes directional information, and (x, y) indicates that light is incident
The coordinate of lenticule plane, characterizes location information, and I (x, y) indicates the lenticule at (x, y) in (s0,t0) arrive (s0+Δs,t0
Light integral in+Δ t) pore diameter range；
3) each lenticule is considered as an equivalent pixel, the pixel coordinate of center sub-aperture image is considered as traditional camera
The image pixel coordinates of projection model, equivalent pixel width are considered as pixel physical size, and centering center subaperture image is according to just
The inside and outside parameter of friendly plane reference method calibration main lens.
It is preferred that the calibration plate surface at least has 4 white circular patterns, more pairs of calibration accuracies of circle
Promotion is bigger, and the white circular center of circle is arranged according to horizontal, vertical direction, and the spacing between the adjacent center of circle is equal.
Second step calibration specifically:
4) it calculates light field parallax all sub-aperture images of extraction are calculated its characteristic point coordinate, then sit characteristic point
Being marked in pole figure indicates, since the corresponding different picture points of the same characteristic point of object space are in straight line in pole figure, passes through
The method of straight line fitting determines the corresponding pole figure straight line of each characteristic point, to calculate its light field parallax；
5) characteristic point depth is obtained, according to parameter matrix M outside first step main lens obtained by calibrating2, for each spy
Coordinate p of the sign point under world coordinate systemw=(xw,yw,zw), its coordinate (x under camera coordinates system can be obtainedc,yc,zc)
=pc=M2pw, zcThe as depth of this feature point；
6) fitting solves lenticule parameter, and for each characteristic point, step 4) 5) has calculated separately out its light field parallax
With depth, there are the constraint relationships shown in following formula:
Wherein, hmFor object distance, h 'mFor image distance, Δ x is object point P in the parallax of any two width adjacent sub-aperture image, and d is phase
Adjacent lenticule center spacing, q are pixel wide, and D is sub-aperture width, and b is lenticule focal length, accordingly by least square fitting
Method calibrating parameters b, D and hmValue, complete lenticule parameter calibration.
It is preferred that carrying out nonlinear optimization to two steps parameter obtained by calibrating: using Levenberg-
Marquardt algorithm carries out nonlinear optimization, and optimization aim is so that the re-projection error of characteristic point is minimum, and the parameter of optimization is
All physical parameters of light-field camera main lens and lenticule.
In view of the problems of the existing technology, the present invention is based on the image-forming principles of light-field camera, and establishing one kind can degenerate
To the projection model of traditional camera, a kind of two more generally applicable step calibration sides are proposed in particular for non-focusing type light-field camera
Method.By the derivation to light-field camera imaging model, center sub-aperture image is equivalent to traditional camera image, thus by classical
Zhang Zhengyou plane reference method is applied in light-field camera calibration, by deriving the constraint relationship of light field parallax and depth, is realized straight
The method that line fitting solves lenticule parameter, thus solves and obtains the optical parameter with physical significance.
Detailed description of the invention
Fig. 1 is light-field camera projection model, and it (c) is lenticule that (a), which is whole projection model, (b) indicates image coordinate system,
Plane coordinate system.
Fig. 2 is the similarity transformation relationship in projection model of the present invention, and (a) is the linear relationship schematic diagram of D and q, (b) is s
With the linear relationship schematic diagram of u.
Fig. 3 is the equivalent projection model degenerated in the present invention.
The case where Fig. 4 is re-projection error model in the present invention, and (a) shows traditional camera, (b) shows light-field camera
The case where.
Fig. 5 is to demarcate algorithm flow chart in the present invention.
Fig. 6 is circle scaling board in the present invention.
Fig. 7 is the positional relationship of light-field camera and scaling board in the present invention.
Fig. 8 be in the present invention re-projection error as a result, (a) is initial value as a result, (b) being result after nonlinear optimization.
Specific embodiment
The present invention provides a kind of two step scaling methods based on non-agglomerated type light-field camera, this method uses light-field camera
The scaling board of different angle is shot, by extracting center sub-aperture image, demarcates main lens parameter first.Further according to light
The constraint relationship of field parallax and depth, fitting obtains lenticule parameter, to complete the calibration of light-field camera.The present invention can use
In providing technical parameter for the three-dimensional imaging based on light-field camera, it is suitable for the numerous areas such as industrial detection, medicine detection.
The present invention is considered as an equivalent pixel based on light-field camera projection model, each lenticule, by traditional phase
Machine projection model, i.e. pin hole projection model are equivalent to a kind of degeneration expression of light-field camera projection model, utilize on this basis
Traditional calibration algorithm demarcates light-field camera, including two steps:
The first step extracts the sub-aperture image of light-field camera, centered on the sub-aperture image for defining main lens optical center position
Sub-aperture image is considered as traditional phase for center sub-aperture image is equivalent by extracting the coordinate of the point in center sub-aperture image
Machine image is demarcated the inside and outside parameter of main lens by center sub-aperture image according to Zhang Zhengyou plane reference method, realizes main lens ginseng
Several calibration.
1) acquire scaling board image, fixed light-field camera, using light-field camera to the same scaling board of different angle into
Row shooting；The calibration plate surface at least has 4 white circular patterns, and the promotion of more pairs of calibration accuracies of circle is bigger, and
The white circular center of circle is arranged according to horizontal, vertical direction, and the spacing between the adjacent center of circle is equal.
2) four-dimensional field information is decoded from the original image that light-field camera acquires, and extracts sub-aperture image, is decoded
Journey includes: micro- picture centre extraction, micro- image slant correction, micro- image segmentation and colour correction, and micro- image refers to light by one
After a lenticule at picture, such as a circle in Fig. 1 (b), 4 circles are 4 micro- images.Decode obtain four-dimensional light field L (s,
T, x, y), sub-aperture image is converted to by following formula:
Wherein (s, t) indicates coordinate of the light Jing Guo main lens plane, characterizes directional information, and (x, y) indicates that light is incident
The coordinate of lenticule plane, characterizes location information, and I (x, y) indicates the lenticule at (x, y) in (s0,t0) arrive (s0+Δs,t0
Light integral in+Δ t) pore diameter range；
3) each lenticule is considered as an equivalent pixel, the pixel coordinate of center sub-aperture image is considered as traditional camera
The image pixel coordinates of projection model, equivalent pixel width are considered as pixel physical size, and centering center subaperture image is according to just
The inside and outside parameter of friendly plane reference method calibration main lens.
Second step, by primary mirror head plane when being incident on light-field camera by the three-dimensional coordinate of any in space and the point
Position coordinates, it may be determined that coordinate of this in lenticule plane, in conjunction with the constraint relationship of light field parallax and Object Depth, fitting
Solution obtains lenticule parameter, and the light field parallax refers to object point P in the parallax of any two width adjacent sub-aperture image；By two steps
Calibration obtains the physical parameter of light-field camera.
4) it calculates light field parallax all sub-aperture images of extraction are calculated its characteristic point coordinate, then sit characteristic point
Being marked in pole figure indicates, since the corresponding different picture points of the same characteristic point of object space are in straight line in pole figure, passes through
The method of straight line fitting determines the corresponding pole figure straight line of each characteristic point, to calculate its light field parallax.
5) characteristic point depth is obtained, according to parameter matrix M outside first step main lens obtained by calibrating2, for each spy
Coordinate p of the sign point under world coordinate systemw=(xw,yw,zw), its coordinate (x under camera coordinates system can be obtainedc,yc,zc)
=pc=M2pw, zcThe as depth of this feature point.
6) fitting solves lenticule parameter, and for each characteristic point, step 4) 5) has calculated separately out its light field parallax
With depth, there are the constraint relationships shown in following formula:
Wherein, hmFor object distance, h 'mFor image distance, Δ x is object point P in the parallax of any two width adjacent sub-aperture image, and d is phase
Adjacent lenticule center spacing, q are pixel wide, and D is sub-aperture width, and b is lenticule focal length, accordingly by least square fitting
Method calibrating parameters b, D and hmValue, complete lenticule parameter calibration.
In order to improve calibration accuracy, it is preferred that, nonlinear optimization is carried out to two steps parameter obtained by calibrating: being adopted
Nonlinear optimization is carried out with Levenberg-Marquardt algorithm, optimization aim is the re-projection error minimum so that characteristic point,
The parameter of optimization is all physical parameters of light-field camera main lens and lenticule.
The present invention is further described with reference to the accompanying drawings and embodiments.
Fig. 1 is the projection model of light-field camera.Fig. 1 (a) is whole projection model, with main lens optical center OcFor origin, with
Optical axis is ZcAxis establishes camera coordinates system Oc-XcYcZc, the point O of lenticule plane is passed through with optical axis respectively0, that optical axis passes through imaging is flat
The point O in face1For origin, lenticule plane coordinate system O is established0-XmYmWith image coordinate system O1-XpYp, it is single that (i, j), which is with pixel,
The coordinate of the image coordinate system of position, is the pixel coordinate under whole picture original image, identical, (u, v) is defined with conventional two-dimensional image
It is the coordinate in micro- image as unit of pixel, is that light-field camera is peculiar, (u0,v0) be uv coordinate system center point coordinate, (x,
Y) it is coordinate in lenticule plane coordinate system as unit of the spacing of contiguous microlens center, as shown in Fig. 1 (c).Point P is in the world
Coordinate (x under coordinate systemw,yw,zw), corresponding to camera coordinates system is (xc,yc,zc), correspond to the point coordinate of main lens plane
For (s, t), optical axis passes through the point O of lenticule plane0Coordinate under (x, y) coordinate system is (x0,y0)。
Fig. 2 is the similarity transformation relationship in light-field camera projection model.Shown in Fig. 1 (a) (s, t), (u, v) and (x, y) is equal
Respectively one plane coordinate system of characterization, only consider one of dimension of each two-dimensional surface to get to (s, u, x) dimension and
(t, v, y) dimension for convenience of explanation only analyzes (s, u, x) dimension, and (t, v, y) dimension is similar therewith.
The linear relationship chart and lenticule focal length b of (a) sub-aperture width D and pixel wide q according to fig. 2, You Tuzhong's
Geometrical relationship is available:
The linear relationship chart of the coordinate u of coordinate s in (b) main lens plane and imaging plane according to fig. 2, for main lens
There is the transformation relation such as following formula (2) in the coordinate s in plane:
Fig. 3 is the equivalent projection model degenerated, i.e., each lenticule is considered as an equivalent pixel.Object point P in analysis chart 3
Projection process, can be obtained according to geometrical relationship:
Wherein hmFor object distance, h 'mFor image distance, f is focal length, xmIndicate coordinate of the subpoint in equivalent pixel plane, xcTable
Show coordinate of the subpoint on primary mirror head plane.Formula (3) is rewritable are as follows:
It can be seen that the three-dimensional coordinate of any in given space, and its pass through the position of primary mirror head plane when being incident on camera
Coordinate s is set, its coordinate in lenticule plane can be uniquely determined.Knowing s according to formula (2), there are one-to-one relationships with u.This
Invention defines main lens optical center position, that is, takes s=u=0, and the sub-aperture image of t=v=0 is center sub-aperture image.
According to formula (4), u is enabledl、ul+1Respectively indicate the coordinate that index value under u coordinate system is l, l+1, sl=D (ul-u0)、
sl+1=D (ul+1-u0),Coordinate of the corresponding subpoint in equivalent pixel plane is respectively indicated, i.e. lenticule is flat
Coordinate under areal coordinate system (x, y), obtains:
Formula (5) up and down subtract each other by two formulas, and abbreviation obtains:
According to Gauss formula and enableThen formula (6) is rewritable are as follows:
And Δ x is parallax of the object point P in any two width adjacent sub-aperture image, Δ x is referred to as light field and regarded by the present invention
Difference.
It obtains shown in world coordinate system and camera coordinates system transformation relation such as formula (7)
Wherein R, t are respectively spin matrix and translation vector.Camera coordinates system to lenticule coordinate system transformation relation such as
Shown in formula (9):
Shown in coordinate conversion relation such as formula (10) under lenticule coordinate system:
Convolution (8) (9) (10),
When taking center sub-aperture image (s=0, t=0), formula (11) is turned to:
As it can be seen that the pixel that the image pixel coordinates in conventional pinhole projection model have been replaced by center sub-aperture image is sat
Mark, pixel physical size have been replaced by equivalent pixel width.There are similitudes on projection model for the two, therefore, available
Center sub-aperture image demarcates the inside and outside parameter of main lens by Zhang Zhengyou calibration algorithm.
Further, the present invention is advanced optimized for the calibration of light-field camera.Fig. 4 is re-projection error model
Schematic diagram.In traditional camera, as shown in Fig. 4 (a), a characteristic point is only corresponded to as a point in plane, ideal point and sight
Euclidean distance between measuring point is defined as re-projection errorAnd in light-field camera, a characteristic point is corresponding as flat
Multiple points on face, therefore there are multiple re-projection errors, i.e.,The target of present invention design nonlinear optimization
Function is as follows:
Wherein k is distortion parameter, Nu×NvFor the sub-aperture image number that a width light field image decodes, ncFor scaling board
On characteristic point quantity, M be shoot different angle scaling board quantity.Optimization aim is so that sub-aperture under all shooting angle
The re-projection error of the feature point for calibration of image is minimum.Wherein world coordinates (the x of each feature point for calibrationw,yw,zw) pass through formula
(11) it is transformed into image coordinate (xreprojected,yreprojected), with (ximage,yimage) indicate this feature point in sub-aperture image
In pixel coordinate, then the re-projection error of this feature point are as follows: E=(xreprojected-ximage)2+(yreprojected-yimage)2。
Fig. 5 is the entire flow figure of scaling method of the present invention.First with the scaling board figure of light-field camera shooting different angle
Picture then decodes original image and extracts sub-aperture image, recycles sub-aperture image in center according to Zhang Zhengyou plane reference method mark
Determine main lens parameter, is then fitted according to the constraint relationship of light field parallax and depth and solves remaining physical parameter, finally carried out non-
Linear optimization is to improve precision.
Fig. 6 is one embodiment of scaling board of the present invention, it is shown that circle scaling board image.Scaling board picture on surface is 64
It is arranged in strict accordance with horizontal, vertical direction, the equal standard round of distance of center circle, characteristic point is the center of circle of each circle.The adjacent center of circle
Between spacing be 30mm ± 5 μm to demarcate any round heart of plate surface as origin be x with scaling board planewywPlane, with vertical
In scaling board in-plane be zwAxis constructs world coordinate system, and the world coordinates of available 64 characteristic points is to camera mark
It is fixed.
Embodiment: it is tested with the second generation light-field camera Lytro Illum that Lytro company, the U.S. produces, camera sequence
Row number are as follows: B5152200720, this camera can decode from every width light field original image and obtain 15 × 15 width sub-aperture images,
Every width sub-aperture image resolution ratio is 625 × 434, and contiguous microlens center spacing is d=0.01732mm, pixel wide q=
0.0014mm, shoots the scaling board image of 13 angles altogether, and the position spectrum of light-field camera and scaling board is as shown in Figure 7.Calibration
Obtained physical parameter is as shown in the table:
Fig. 8 is the re-projection error result of the present embodiment, it is seen then that when not carrying out nonlinear optimization, re-projection error exists
Within 0.008mm, after nonlinear optimization, re-projection error is within 0.005mm, and it is attached to be mostly focused on 0.002mm
Closely, the RMS value of re-projection error is 0.0017mm after optimization.
Claims (5)
1. a kind of two step scaling methods of light-field camera are projected it is characterized in that being directed to non-focusing type light-field camera with light-field camera
Based on model, each lenticule is considered as an equivalent pixel, traditional camera projection model is equivalent to light-field camera projection
A kind of degeneration of model is expressed, and recycle traditional calibration algorithm to be demarcated, including two steps: the first step extracts light-field camera
Sub-aperture image, the sub-aperture image for defining main lens optical center position is center sub-aperture image, by extracting center sub-aperture
The coordinate of point in image is considered as traditional camera image for center sub-aperture image is equivalent, by center sub-aperture image according to
The inside and outside parameter of positive friend's plane reference method calibration main lens, realizes the calibration of main lens parameter；Second step, by a bit in space
Pass through the position coordinates of primary mirror head plane when three-dimensional coordinate and the point are incident on light-field camera, it may be determined that the point is flat in lenticule
Coordinate on face, in conjunction with the constraint relationship of light field parallax and Object Depth, fitting, which solves, obtains lenticule parameter, the light field view
Difference refers to object point P in the parallax of any two width adjacent sub-aperture image；It demarcates to obtain the physical parameter of light-field camera by two steps.
2. two step scaling methods of a kind of light-field camera according to claim 1, it is characterized in that the first step is demarcated specifically:
1) scaling board image is acquired, fixed light-field camera is clapped using same scaling board of the light-field camera to different angle
It takes the photograph；
2) four-dimensional field information is decoded from the original image that light-field camera acquires, and extracts sub-aperture image, decoding process packet
Include: micro- picture centre extraction, micro- image slant correction, micro- image segmentation and colour correction, micro- image refer to light by one
After a lenticule at picture, the four-dimensional light field L (s, t, x, y) decoded is converted to sub-aperture image by following formula:
Wherein (s, t) indicates coordinate of the light Jing Guo main lens plane, characterizes directional information, and (x, y) indicates that light is incident micro-
The coordinate of mirror plane, characterizes location information, and I (x, y) indicates the lenticule at (x, y) in (s0,t0) arrive (s0+Δs,t0+Δ
T) the light integral in pore diameter range；
3) each lenticule is considered as an equivalent pixel, the pixel coordinate of center sub-aperture image is considered as traditional camera projection
The image pixel coordinates of model, equivalent pixel width are considered as pixel physical size, and centering center subaperture image is flat according to Zhang Zhengyou
The inside and outside parameter of face standardization calibration main lens.
3. two step scaling methods of a kind of light-field camera according to claim 2, it is characterized in that the calibration plate surface is extremely
There are 4 white circular patterns less, the promotion of more pairs of calibration accuracies of circle is bigger, and the white circular center of circle is according to horizontal, vertical
Direction arranges, and the spacing between the adjacent center of circle is equal.
4. two step scaling methods of a kind of light-field camera according to claim 2 or 3, it is characterized in that second step calibration is specific
Are as follows:
4) it calculates light field parallax all sub-aperture images of extraction are calculated its characteristic point coordinate, then characteristic point coordinate exists
It is indicated in pole figure, since the corresponding different picture points of the same characteristic point of object space are in straight line in pole figure, passes through straight line
The method of fitting determines the corresponding pole figure straight line of each characteristic point, to calculate its light field parallax；
5) characteristic point depth is obtained, according to parameter matrix M outside first step main lens obtained by calibrating2, exist for each characteristic point
Coordinate p under world coordinate systemw=(xw,yw,zw), its coordinate (x under camera coordinates system can be obtainedc,yc,zc)=pc=
M2pw, zcThe as depth of this feature point；
6) fitting solves lenticule parameter, and for each characteristic point, step 4) 5) has calculated separately out its light field parallax and depth
Degree, there are the constraint relationships shown in following formula:
Wherein, hmFor object distance, h 'mFor image distance, Δ x is parallax of the object point P in any two width adjacent sub-aperture image, and d is adjacent micro-
Lens centre spacing, q are pixel wide, and D is sub-aperture width, and b is lenticule focal length, accordingly by the side of least square fitting
Method calibrating parameters b, D and hmValue, complete lenticule parameter calibration.
5. two step scaling methods of a kind of light-field camera according to claim 1, it is characterized in that obtained by calibrating to two steps
Parameter carries out nonlinear optimization: carrying out nonlinear optimization using Levenberg-Marquardt algorithm, optimization aim is so that special
The re-projection error for levying point is minimum, and the parameter of optimization is all physical parameters of light-field camera main lens and lenticule.
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| CN114964032A (en) * | 2022-05-18 | 2022-08-30 | 北京理工大学 | Blind hole depth measuring method and device based on machine vision |
| CN115032756A (en) * | 2022-06-07 | 2022-09-09 | 北京拙河科技有限公司 | Micro-lens array positioning method and system of light field camera |
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| CN116630443A (en) * | 2023-07-24 | 2023-08-22 | 长春工程学院 | Augmented reality system calibration method based on four-dimensional dynamic light field |
| CN116630443B (en) * | 2023-07-24 | 2023-10-03 | 长春工程学院 | Augmented reality system calibration method based on four-dimensional dynamic light field |
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