CN112258584A - Lens distortion model considering distortion partitions such as depth of field dimension and space - Google Patents

Lens distortion model considering distortion partitions such as depth of field dimension and space Download PDF

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CN112258584A
CN112258584A CN202011111757.XA CN202011111757A CN112258584A CN 112258584 A CN112258584 A CN 112258584A CN 202011111757 A CN202011111757 A CN 202011111757A CN 112258584 A CN112258584 A CN 112258584A
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李肖
李伟
殷晓康
袁新安
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China University of Petroleum East China
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    • G06T7/80—Analysis of captured images to determine intrinsic or extrinsic camera parameters, i.e. camera calibration
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Abstract

The invention belongs to the technical field of computer vision measurement, and provides a lens distortion model considering distortion partitions such as depth of field dimension, space and the like. And introducing the depth of field dimension of lens imaging into the lens distortion model to form the depth of field distortion model. And (3) performing two-dimensional partition on the image plane by adopting an equal distortion partition criterion, and establishing an equal distortion partition model of an imaging distortion space. And fusing the depth of field distortion model and the spatial equal distortion partition model to form the lens distortion model considering the spatial equal distortion partition and the depth of field dimension. The lens distortion model disclosed by the invention enriches the construction theory of the lens distortion model and increases the applicability of the distortion model in the field depth space. In addition, the distortion of the lens is partitioned in the space dimension by adopting the equal distortion partition criterion, so that the problem of large distortion solving error caused by uneven distortion distribution is solved, and the lens distortion solving precision is improved. Meanwhile, the lens distortion model also has the advantages of simplicity and easiness in implementation.

Description

Lens distortion model considering distortion partitions such as depth of field dimension and space
Technical Field
The invention belongs to the technical field of computer vision measurement, and relates to a lens distortion model considering the field depth dimension, the spatial distortion and other distortion partitions.
Background
The vision measurement technology is a multidisciplinary crossing technology integrating computer science, advanced mathematics, signal processing and machine learning, and has become the leading edge and hotspot field of vision research by virtue of the advantages of high real-time performance, strong intuition, spatial universe measurement and high-precision perception. The camera and lens are two key components essential for visual imaging. Researches show that the lens distortion is related to an imaging depth of field space, and when close-range imaging parameters such as a small object distance and a short focal length are adopted to ensure the visual range and accuracy of visual measurement, the lens distortion is particularly serious and becomes a key factor for restricting the improvement of the measurement accuracy. In addition, each lens of the lens is an axisymmetric body, so that image distortion is circularly and symmetrically distributed. However, the distribution of the lens distortion has non-uniformity in the radial direction along the circle, and such distribution may extend into the depth of field range in the optical axis direction. Therefore, establishing a lens distortion model considering the depth of field dimension and the equal distortion partition has important significance for improving the vision measurement precision.
The patent number of konchang invented by great-connection-day-good electronics limited company is CN 201611210098 'high-precision camera calibration method based on mixed distortion model', invented the camera parameter calibration method considering various distortions, and the method utilizes the extracted sub-pixel information of the mark points on the template image to solve the imaging model parameters. Firstly, separating internal and external parameters from a homography matrix, and then, optimizing and solving the radial distortion coefficient and the eccentric distortion coefficient of the lens through an improved LM algorithm. Although the distortion parameter of the lens can be obtained by the method, the depth of field dimension of imaging and the unevenness of distortion distribution on the image are not considered, and the method has low resolution precision on the lens distortion. The invention discloses an improved method for solving intrinsic parameters, extrinsic parameters and distortion coefficients of a camera, which is invented by Liuxin sea and the like of Nanjing science and engineering university and has the patent number of CN 201710718981 'a method for calibrating a camera based on an improved distortion model'. First, the method solves for the approximate initial values of the intrinsic parameters from the camera model by means of the orthogonal properties of the matrix. Then, according to the constraint equation and the homography matrix, other parameters except distortion coefficients in the camera model are solved. And finally, combining Zhangzhen friend and Heikkila models, and optimizing and solving the distortion coefficient of the camera through an LM algorithm. The method disclosed by the invention only uses a group of distortion coefficients to express the distortion condition of the image, and does not incorporate the depth dimension of the imaged image and the image distortion partition into a lens distortion model.
Disclosure of Invention
The invention provides a lens distortion model considering distortion partitions such as depth of field dimension, space and the like, and aims to overcome the defects of the prior art.
The technical scheme of the invention is as follows:
a lens distortion model considering distortion partitions such as depth of field dimension and space is characterized in that firstly, the depth of field dimension of lens imaging is introduced into the lens distortion model, and in the aspect of lens radial distortion, a relation between a radial distortion coefficient on any focusing plane in the depth of field and radial distortion conditions on two focusing planes in the depth of field space is established; in the aspect of lens eccentric distortion, establishing a relation between an eccentric distortion coefficient on any focusing plane in the depth of field and the eccentric distortion condition on a certain focusing plane in the depth of field space to form a lens depth of field distortion model; secondly, carrying out equal distortion zoning on image plane distortion, and carrying out zoning division on distortion in a depth space on a three-dimensional layer according to a camera model so as to establish an equal distortion zoning model of spatial distortion; finally, fusing the lens depth of field distortion model and the equal distortion partition model of the spatial distortion to form a lens distortion model considering the equal distortion partition of the spatial distortion and the depth of field dimension, thereby realizing the high-precision representation of the distortion in the depth of field range of the lens imaging; the lens distortion model considering distortion partitions such as depth of field dimension and space is specifically as follows:
(1) camera model and conventional distortion model
The linear pinhole model expresses a one-to-one mapping relation between a three-dimensional scene space and a two-dimensional image plane; let (u v) be a space point P (X)w Yw Zw) Undistorted image point coordinates (u v) and P (X) mapped on the image planew Yw Zw) Is expressed by formula (1) as:
Figure BDA0002728822140000021
wherein s' is a proportionality coefficient, K is an internal parameter matrix of the camera, and key parameters of the photosensitive element and the lens are quantitatively represented; the matrix M comprises a rotation matrix R and a translation matrix T, expresses the conversion relation between a camera coordinate system and a world coordinate system, and can calibrate an internal parameter matrix K including a camera focal length f by adopting a Zhang-Yong calibration method;
manufacturing and assembling errors of the lens may cause radial distortion and eccentric distortion, which are expressed by equation (2):
Figure BDA0002728822140000031
wherein the content of the first and second substances,
Figure BDA0002728822140000032
is the distorted coordinates of the image points; deltau、δvIs the distortion function of the imaging point in the image u and v directions; (u)0 v0) Is the center of the image;
Figure BDA0002728822140000033
is the distortion radius; k1、K2First and second order radial distortion coefficients, P, respectively1And P2First order and second order eccentric distortion coefficients, respectively;
(2) depth-of-field dependent distortion model
1) Depth-of-field dependent radial distortion model
Let delta r∞The radial distortion amount, δ r, at focusing distance at infinity-∞For the amount of radial distortion at focus distance minus infinity,
Figure BDA0002728822140000034
is a focal distanceIs s isnVertical magnification on the time-focus plane; a focus distance of snRadial distortion on time-focusing plane
Figure BDA0002728822140000035
Expressed by equation (3):
Figure BDA0002728822140000036
order to
Figure BDA0002728822140000037
Respectively represent the focus distance smAnd skRadial distortion on two pairs of focal planes; then the focus distance is s at this focal lengthnThe amount of radial distortion on the time-focus plane is expressed by equation (4):
Figure BDA0002728822140000038
wherein the content of the first and second substances,
Figure BDA0002728822140000039
then the focus distance is snThe radial distortion coefficient on the in-focus plane is expressed by equation (5):
Figure BDA00027288221400000310
wherein the content of the first and second substances,
Figure BDA00027288221400000311
is a focal distance of snThe ith radial distortion coefficient on the time focusing plane;
Figure BDA00027288221400000312
is a focal distance of smThe ith radial distortion coefficient on the time focusing plane;
Figure BDA00027288221400000313
is a focal distance of skThe ith radial distortion coefficient on the time focusing plane; thus, if the radial distortion coefficients at 2 focal planes within the depth of field are known, the arbitrary focal distance s is obtained from equation (5)nRadial distortion coefficient on focusing plane
Figure BDA00027288221400000314
2) Depth-of-field dependent off-center distortion model
Let the focusing distance be snThe eccentric distortion coefficient on the time-focusing plane is
Figure BDA00027288221400000315
A focus distance of smThe eccentric distortion coefficient on the time-focusing plane is
Figure BDA00027288221400000316
According to the Conrady model, the model,
Figure BDA00027288221400000317
and
Figure BDA00027288221400000318
the relationship between them is expressed by the formula (6):
Figure BDA0002728822140000041
wherein the content of the first and second substances,
Figure BDA0002728822140000042
and
Figure BDA0002728822140000043
respectively, are a focus distance smAnd snA principal imaging distance; as can be seen from the equation for a thin prism,
Figure BDA0002728822140000044
integrating the two formulas into formula (6) yields formula (7))：
Figure BDA0002728822140000045
(3) Lens distortion space equal distortion partition model
With equal distortion partition as a criterion, firstly carrying out two-dimensional partition on distortion on an image, and then expanding the two-dimensional partition condition to the three-dimensional depth of field range of lens imaging, thereby realizing spatial equal distortion partition of lens distortion, and the specific steps are as follows:
a) two-dimensional partition with equal distortion
Recording a distortion curve describing the relationship between the distortion radius of the image and the magnitude of the distortion as L; the maximum distortion of the whole image is deltamaxThe number of image distortion divisions is na(ii) a Then, the distortion amount of the image distortion section is equally divided into
Figure BDA0002728822140000046
Combining the distortion curve L, the partition range of each partition on the image plane can be solved;
b) three-dimensional partition with equal distortion
Then, extending the distortion two-dimensional partition condition to a three-dimensional depth-of-field space; from the camera model, the coordinate relationship of two spatial points is expressed by equation (8):
Figure BDA0002728822140000047
wherein, Pm(xm ym zm) And Pk(xk yk zk) Two spatial points; (x 'y') is a two-dimensional image point of two space points in mm projected on an image plane through the imaging model; then for partition radius x'2+y′2＝r′2：
Figure BDA0002728822140000048
Finishing to obtain f.rm＝r′·zmAnd zm·rk＝zk·rm；zmAnd zkIs the mth (Π)m) And kth (Π)k) The focal distance, r, of the focal planemAnd rkThe radius of the partition on the corresponding two focusing planes; let sm＝zmAnd sk＝zk(ii) a Then, pi for the focusing planemThe g 'range of (a) is [ (g' -1) · rm g′·rm]Partition of, focusing plane pikAnd pinHas a corresponding partition range of [ (g' -1) ·(s)k·rm/sm)g′·(sk·rm/sm)]And [ (g' -1) ·(s)n·rm/sm)g′·(sn·rm/sm)]；
(4) Lens distortion model considering distortion partition such as depth of field dimension and space
After the field depth distortion partition is completed, the distortion space partition condition is contained in a field depth distortion model, and the focus distance in the field depth is snThe calculation steps of the distortion partition range and the distortion coefficient on the time focal plane are as follows:
1) to focusing plane pim(focal distance is s)m) The distortion of the upper part is subjected to equal distortion partition, and the ith radial distortion coefficient and the ith eccentric distortion coefficient under the g' th partition are calculated and recorded as
Figure BDA0002728822140000051
And
Figure BDA0002728822140000052
2) with focusing plane pim(focal distance is s)m) Calculating the pi of the focusing plane based on the upper distortion zonek(object distance is s)k) Upper distortion partition condition and simultaneously calculating focusing plane pikThe ith radial distortion coefficient of the upper g' th partition, noted
Figure BDA0002728822140000053
3) With focusing plane pim(focal distance is s)m) Calculating the pi of the focusing plane based on the upper distortion zonen(focal distance is s)n) The distorted partition condition of (1); then, focusing plane ΠnRadial distortion coefficient of g' th sub-area
Figure BDA0002728822140000054
And coefficient of eccentric distortion
Figure BDA0002728822140000055
Can be expressed by the formula (10):
Figure BDA0002728822140000056
"show the expansion equation (10):
Figure BDA0002728822140000057
"display
Therefore, a lens distortion model considering distortion partitions such as depth of field dimension and space is established.
The method has the advantages that the influence of imaging depth of field on lens distortion is considered, the radial distortion coefficient and the eccentric distortion coefficient on any focusing plane in the depth of field range can be calculated through the distortion conditions on two focusing planes in the depth of field, and the description capability of the distortion model on the depth of field distortion is enhanced. In addition, the distortion of the lens in the depth of field space is divided on a three-dimensional layer, so that the expression of the lens distortion model on the imaging distortion in the depth of field is more accurate. In addition, the lens depth distortion model provided by the invention is simple and convenient to operate in practical application.
Drawings
Fig. 1 is a schematic view of a lens distortion model construction considering distortion partitions such as depth of field dimension and space.
Fig. 2 is a flow chart of lens distortion model construction considering distortion partitions such as depth of field dimension and space.
Detailed Description
The following describes the embodiments of the present invention in detail with reference to the technical solutions and the accompanying drawings 1 and 2.
Fig. 1 is a schematic view of a lens distortion model construction considering distortion partitions such as depth of field dimension and space. Fig. 2 is a flow chart of lens distortion model construction considering distortion partitions such as depth of field dimension and space.
The invention relates to a lens distortion model considering distortion partitions such as depth of field dimension, space and the like. Firstly, the imaging depth dimension is considered, the focusing distance, the radial distortion coefficient and the eccentric distortion coefficient on the focusing plane are introduced, and the relationship between the radial distortion coefficient on any focusing plane of the depth of field and the distortion conditions on two focusing planes in the depth of field is established. Meanwhile, a relation between the eccentric distortion coefficient of any focusing plane of the depth of field and the eccentric distortion condition of a certain pair of focusing planes in the depth of field is established, and a depth of field distortion model containing the radial distortion coefficient and the eccentric distortion coefficient is formed. Secondly, two-dimensional partition is carried out on image distortion by taking the equal distortion as a criterion, and on the basis, the two-dimensional partition condition is expanded into a depth of field space by means of a camera imaging model, so that a lens distortion space equal distortion partition model is formed. And finally, fusing the depth of field distortion model with a lens distortion space equal distortion partition model to form the lens distortion model considering the depth of field dimension, the space equal distortion partition. The selected camera imaging resolution is 2560 pixels × 2560 pixels, and the implementation is described in detail below:
1. camera model and conventional distortion model
And (3) respectively programming a camera model and a traditional distortion model in a program by referring to a formula (1) and a formula (2), and solving the internal parameters of the camera model by adopting a Zhang Zhengyou calibration method to obtain f which is 18.2 mm.
2. Depth-of-field dependent distortion model
1) Depth-of-field dependent radial distortion model
Generalizing the conclusion of the formula (3) by the focusing distance smAnd skRadial distortion in time two pairs of focal planes
Figure BDA0002728822140000061
And
Figure BDA0002728822140000062
according to the formula (4), the focusing distance s is calculatednRadial distortion on time-focusing plane
Figure BDA0002728822140000071
On the basis, according to the formula (2), the focusing distance s is obtained by calculating the formula (5)nRadial distortion factor in the in-focus plane
Figure BDA0002728822140000072
On the basis of the above, a depth-of-field-dependent radial distortion model is programmed.
2) Depth-of-field dependent off-center distortion model
According to the focusing distance of smThe eccentric distortion coefficient on the time-focusing plane is
Figure BDA0002728822140000073
Calculating the focus distance s by the formula (6) and the formula (7)nThe eccentric distortion coefficient on the time-focusing plane is
Figure BDA0002728822140000074
On the basis of the above, the off-center distortion model relating to the depth of field is programmed.
3. Equal distortion partition of lens distortion space
With equal distortion partition as a criterion, firstly carrying out two-dimensional partition on distortion on an image, and then expanding the two-dimensional partition condition to the three-dimensional depth of field range of lens imaging, thereby realizing spatial equal distortion partition of lens distortion, and the specific steps are as follows:
1) two-dimensional partition with equal distortion
Solving the distortion curve L of the whole image with the image distortion radius as an independent variable and the distortion magnitude as a dependent variable, and calculating the whole image distortion radius 1810 pixels by the resolution of the image of 2560 pixels multiplied by 2560 pixelsMaximum distortion, Δ, of sheet imagemaxSet the number of partitions of an image to n, 39.2 pixelsaEqual distortion amount of the image distortion partition is 2
Figure BDA0002728822140000075
A pixel. Combining the distortion curve L of the whole image, the partition ranges of the 2 partitions on the solved image plane are [0 pixel 1152 pixel]And [1152 pixel 1810 pixel]。
2) Three-dimensional partition with equal distortion
And then, extending the distorted two-dimensional zoning condition to a three-dimensional depth space. Setting the focus distance to sm400mm and skCalculating a focusing plane Π in mm according to equations (8) and (9) at 500mmmAnd pikUpper partition range. Focusing plane pimThe range of the upper 2 subareas is respectively [0mm 224mm]And [224mm 276mm]Focusing plane pikThe two partition ranges of the upper partition and the lower partition are respectively [0mm 280mm ]]And [280mm 345mm]。
4. Lens depth of field distortion model based on equal distortion quantity partitions
After the field depth distortion partition is completed, the distortion space partition condition is contained in a field depth distortion model, and the focus distance in the field depth is snThe calculation steps of the distortion partition range and the distortion coefficient on the focal plane when the focal plane is 450mm are as follows:
1) to focusing plane pim(focal distance is s)m400mm) is equally divided into equal distortion segments, where g' is na2. Respective order coefficients of radial distortion and eccentric distortion on the first and second partitions are calculated. The first two-order radial distortion coefficients of the first subarea obtained by calculation are respectively
Figure BDA0002728822140000081
And
Figure BDA0002728822140000082
Figure BDA0002728822140000083
before the first partition obtained by calculationThe two-order eccentricity distortion coefficients are respectively
Figure BDA0002728822140000084
And
Figure BDA0002728822140000085
the first two-order radial distortion coefficients of the second partition are respectively obtained by calculation
Figure BDA0002728822140000086
And
Figure BDA0002728822140000087
the first two-order eccentricity distortion coefficients of the second subarea are calculated respectively as
Figure BDA0002728822140000088
Figure BDA0002728822140000089
And
Figure BDA00027288221400000810
2) with focusing plane pim(focal distance is s)m500mm) as a reference, calculating the pi of the focusing planek(focal distance is s)k500mm) of the first and second partitions of the radial distortion. The first two-order radial distortion coefficients of the first subarea obtained by calculation are respectively
Figure BDA00027288221400000811
And
Figure BDA00027288221400000812
Figure BDA00027288221400000813
the first two-order radial distortion coefficients of the second partition are respectively
Figure BDA00027288221400000814
And
Figure BDA00027288221400000815
Figure BDA00027288221400000816
3) with focusing plane pim(focal distance is s)m) Calculating the pi of the focusing plane by using the formula (8) and the formula (9) based on the upper distortion zonen(focal distance is s)n450mm), the focal plane Π is calculated by equation (10) and equation (11)nAbove (object distance is s)n450mm) distortion zone the order coefficients of radial distortion and eccentric distortion on the first zone and the second zone. The first two-step radial distortion coefficient of the first partition is
Figure BDA00027288221400000817
And
Figure BDA00027288221400000818
the first two-step eccentric distortion coefficient of the first partition is
Figure BDA00027288221400000819
Figure BDA00027288221400000820
And
Figure BDA00027288221400000821
the first two-order radial distortion coefficient of the second partition is
Figure BDA00027288221400000822
And
Figure BDA00027288221400000823
the first two-order eccentricity distortion coefficient of the second partition is
Figure BDA00027288221400000824
And
Figure BDA00027288221400000825
Figure BDA00027288221400000826
at this time, a radial distortion coefficient and an eccentric distortion coefficient on any focusing plane are calculated by using a lens distortion model considering distortion partitions such as depth of field dimension, space and the like.
The invention relates to a lens distortion model considering distortion partitions such as depth of field dimension, space and the like. Firstly, the influence of the imaging depth of field on the lens distortion is considered, the focusing distance and the distortion condition on the focusing surface are introduced in the process of establishing the distortion model, and the adaptability of the distortion model in the depth of field direction is improved. In addition, distortion in a depth of field space is finely divided on a three-dimensional level through an equal distortion criterion, so that distortion solving of the lens in the depth of field is more accurate. In addition, the distortion model provided by the invention also has the advantages of simplicity and convenience in implementation.

Claims (1)

1. A lens distortion model considering distortion partitions such as depth of field dimension and space is characterized in that firstly, the depth of field dimension of lens imaging is introduced into the lens distortion model, and in the aspect of lens radial distortion, a relation between a radial distortion coefficient on any focusing plane in the depth of field and radial distortion conditions on two focusing planes in the depth of field space is established; in the aspect of lens eccentric distortion, establishing a relation between an eccentric distortion coefficient on any focusing plane in the depth of field and the eccentric distortion condition on a certain focusing plane in the depth of field space to form a lens depth of field distortion model; secondly, carrying out equal distortion zoning on image plane distortion, and carrying out zoning division on distortion in a depth space on a three-dimensional layer according to a camera model so as to establish an equal distortion zoning model of spatial distortion; finally, fusing the lens depth of field distortion model and the equal distortion partition model of the spatial distortion to form a lens distortion model considering the equal distortion partition of the spatial distortion and the depth of field dimension, thereby realizing the high-precision representation of the distortion in the depth of field range of the lens imaging; the lens distortion model considering distortion partitions such as depth of field dimension and space is specifically as follows:
(1) camera model and conventional distortion model
The linear pinhole model expresses a one-to-one mapping relation between a three-dimensional scene space and a two-dimensional image plane; let (u v) be a space point P (X)w Yw Zw) Undistorted image point coordinates (u v) and P (X) mapped on the image planew Yw Zw) Is expressed by formula (1) as:
Figure FDA0002728822130000011
wherein s' is a proportionality coefficient, K is an internal parameter matrix of the camera, and key parameters of the photosensitive element and the lens are quantitatively represented; the matrix M comprises a rotation matrix R and a translation matrix T, expresses the conversion relation between a camera coordinate system and a world coordinate system, and can calibrate an internal parameter matrix K including a camera focal length f by adopting a Zhang-Yong calibration method;
manufacturing and assembling errors of the lens may cause radial distortion and eccentric distortion, which are expressed by equation (2):
Figure FDA0002728822130000012
wherein the content of the first and second substances,
Figure FDA0002728822130000013
is the distorted coordinates of the image points; deltau、δvIs the distortion function of the imaging point in the image u and v directions; (u)0 v0) Is the center of the image;
Figure FDA0002728822130000014
is the distortion radius; k1、K2First and second order radial distortion coefficients, P, respectively1And P2First order and second order eccentric distortion coefficients, respectively;
(2) depth-of-field dependent distortion model
1) Depth-of-field dependent radial distortion model
Let delta r∞The radial distortion amount, δ r, at focusing distance at infinity-∞For the amount of radial distortion at focus distance minus infinity,
Figure FDA0002728822130000021
is a focal distance of snVertical magnification on the time-focus plane; a focus distance of snRadial distortion on time-focusing plane
Figure FDA0002728822130000022
Expressed by equation (3):
Figure FDA0002728822130000023
order to
Figure FDA0002728822130000024
Respectively represent the focus distance smAnd skRadial distortion on two pairs of focal planes; then the focus distance is s at this focal lengthnThe amount of radial distortion on the time-focus plane is expressed by equation (4):
Figure FDA0002728822130000025
wherein the content of the first and second substances,
Figure FDA0002728822130000026
then the focus distance is snThe radial distortion coefficient on the in-focus plane is expressed by equation (5):
Figure FDA0002728822130000027
wherein the content of the first and second substances,
Figure FDA0002728822130000028
is a focal distance of snThe ith radial distortion coefficient on the time focusing plane;
Figure FDA0002728822130000029
is a focal distance of smThe ith radial distortion coefficient on the time focusing plane;
Figure FDA00027288221300000210
is a focal distance of skThe ith radial distortion coefficient on the time focusing plane; thus, if the radial distortion coefficients at 2 focal planes within the depth of field are known, the arbitrary focal distance s is obtained from equation (5)nRadial distortion coefficient on focusing plane
Figure FDA00027288221300000211
2) Depth-of-field dependent off-center distortion model
Let the focusing distance be snThe eccentric distortion coefficient on the time-focusing plane is
Figure FDA00027288221300000212
A focus distance of smThe eccentric distortion coefficient on the time-focusing plane is
Figure FDA00027288221300000213
According to the Conrady model, the model,
Figure FDA00027288221300000214
and
Figure FDA00027288221300000215
the relationship between them is expressed by the formula (6):
Figure FDA00027288221300000216
wherein the content of the first and second substances,
Figure FDA00027288221300000217
and
Figure FDA00027288221300000218
respectively, are a focus distance smAnd snA principal imaging distance; as can be seen from the equation for a thin prism,
Figure FDA00027288221300000219
integrating the two equations into equation (6) yields equation (7):
Figure FDA0002728822130000031
(3) lens distortion space equal distortion partition model
With equal distortion partition as a criterion, firstly carrying out two-dimensional partition on distortion on an image, and then expanding the two-dimensional partition condition to the three-dimensional depth of field range of lens imaging, thereby realizing spatial equal distortion partition of lens distortion, and the specific steps are as follows:
a) two-dimensional partition with equal distortion
Recording a distortion curve describing the relationship between the distortion radius of the image and the magnitude of the distortion as L; the maximum distortion of the whole image is deltamaxThe number of image distortion divisions is na(ii) a Then, the distortion amount of the image distortion section is equally divided into
Figure FDA0002728822130000032
Combining the distortion curve L, the partition range of each partition on the image plane can be solved;
b) three-dimensional partition with equal distortion
Then, extending the distortion two-dimensional partition condition to a three-dimensional depth-of-field space; from the camera model, the coordinate relationship of two spatial points is expressed by equation (8):
Figure FDA0002728822130000033
wherein, Pm(xm ym zm) And Pk(xk yk zk) Two spatial points; (x 'y') is a two-dimensional image point of two space points in mm projected on an image plane through the imaging model; then for partition radius x'2+y′2＝r′2：
Figure FDA0002728822130000034
Finishing to obtain f.rm＝r′·zmAnd zm·rk＝zk·rm；zmAnd zkIs the mth (Π)m) And kth (Π)k) The focal distance, r, of the focal planemAnd rkThe radius of the partition on the corresponding two focusing planes; let sm＝zmAnd sk＝zk(ii) a Then, pi for the focusing planemThe g 'range of (a) is [ (g' -1) · rm g′·rm]Partition of, focusing plane pikAnd pinHas a corresponding partition range of [ (g' -1) ·(s)k·rm/sm) g′·(sk·rm/sm)]And [ (g' -1) ·(s)n·rm/sm) g′·(sn·rm/sm)]；
(4) Lens distortion model considering distortion partition such as depth of field dimension and space
After the field depth distortion partition is completed, the distortion space partition condition is contained in a field depth distortion model, and the focus distance in the field depth is snThe calculation steps of the distortion partition range and the distortion coefficient on the time focal plane are as follows:
1) to focusing plane pimThe distortion of the upper part is divided into equal distortion partitions, and the focusing distance is smAnd calculating the ith radial distortion coefficient and ith eccentric distortion coefficient under the g' th subarea and recording the coefficients
Figure FDA0002728822130000041
And
Figure FDA0002728822130000042
2) with focusing plane pimWith the upper distortion zone as a reference and the focusing distance as smCalculating the focusing plane pikUpper distortion zone case with object distance skAnd simultaneously calculating the focusing plane pikThe ith radial distortion coefficient of the upper g' th partition, noted
Figure FDA0002728822130000043
3) With focusing plane pimWith the upper distortion zone as a reference and the focusing distance as smCalculating the focusing plane pinUpper distortion zone case, focal distance sn(ii) a Then, focusing plane ΠnRadial distortion coefficient of g' th sub-area
Figure FDA0002728822130000044
And coefficient of eccentric distortion
Figure FDA0002728822130000045
Expressed by equation (10):
Figure FDA0002728822130000046
the following equation (10) is developed:
Figure FDA0002728822130000047
therefore, a lens distortion model considering distortion partitions such as depth of field dimension and space is established.
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