CN112066950B - Multi-optical-axis parallel mapping camera single-center projection conversion method - Google Patents
Multi-optical-axis parallel mapping camera single-center projection conversion method Download PDFInfo
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Abstract
The invention discloses a single-center projection conversion method for a multi-optical-axis parallel surveying and mapping camera, which provides a conversion model from a multi-center projection image to a single-center projection image and a conversion error calculation formula, solves the problem that the conversion model of the multi-optical-axis parallel surveying and mapping camera cannot be accurately described by the conventional single-center projection conversion method, and realizes the core problem of a large-breadth aerial surveying camera by splicing optical-axis parallel multi-area arrays.
Description
Technical Field
The invention belongs to the technical field of aerial photogrammetry, and particularly relates to a single-center projection conversion method for a surveying and mapping camera with multiple parallel optical axes.
Background
The surveying and mapping method is widely applied to the fields of natural disaster emergency monitoring, land resource investigation, ecological environment monitoring, urban fine management and the like.
The large-format surveying camera is the future development direction of area array surveying equipment, large-format imaging is difficult to realize due to the limitation of the pixel scale of a single CCD or CMOS device, and the common solution is to adopt a multi-area array splicing technology, and the methods generally comprise inner view field splicing, outer view field splicing, inner and outer view field mixed splicing and the like. Generally, the inner view field is spliced by adopting a single lens, and single-center photogrammetry is adopted; the outer view field splicing generally adopts inclined photography, a main optical axis of each lens has a certain angle with the vertical direction, and an approximate single-center photogrammetric spliced image is obtained through data processing; the inner and outer fields of view are mixed and spliced to form a common lens in a linear arrangement, the height approximate to that of a single-center photogrammetry is realized through delayed simultaneous exposure, and the data processing method of the splicing method is relatively mature.
Under the limitation of the device scale and the limitation of a surveying and mapping equipment mounting platform, the splicing method has difficulty in further increasing the imaging breadth. The splicing of multiple lenses and multiple detectors with parallel main optical axes can realize the splicing integration of more imaging devices and realize the imaging with larger breadth. However, in the application of the multi-lens multi-detector splicing camera with parallel main optical axes in the surveying and mapping field, the single-center projection conversion process and the virtual single-center image generation method are very important to the imaging precision and the application of the camera.
Aiming at multi-lens multi-detector splicing surveying and mapping equipment with parallel main optical axes, the existing single-center projection conversion method cannot accurately describe a conversion model of a surveying and mapping camera with parallel multi-optical axes.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method overcomes the defects of the prior art, provides a single-center projection conversion method of the surveying and mapping camera with multiple parallel optical axes, solves the problem that the conventional single-center projection conversion method cannot accurately describe a conversion model of the surveying and mapping camera with multiple parallel optical axes, and realizes the core problem of a large-breadth aerial surveying camera through splicing of optical axis parallel multi-area arrays.
The purpose of the invention is realized by the following technical scheme: a method of single-center projection conversion for a multi-axis parallel mapping camera, the method comprising the steps of:
the method comprises the following steps: the method comprises the steps that S camera units are arranged in a preset camera, the parameters of lenses in each camera unit are the same, and the main optical axes of the lenses are parallel; the camera has M multiplied by N focal plane components participating in splicing, the number of pixels of each focal plane component which are effectively spliced is M multiplied by N, and the size of a virtual focal plane at the focal plane of the lens of each camera unit is Mm multiplied by Nn; wherein M is the number of rows participating in splicing the focal plane assembly array, N is the number of columns participating in splicing the focal plane assembly array, M is the number of rows of the number of effective splicing pixels of each focal plane assembly, and N is the number of columns of the number of effective splicing pixels of each focal plane assembly;
establishing a focal plane coordinate system o of the lens of the ith camera unit by taking the virtual focal plane pixel center of the lens of the ith camera unit as a coordinate origin, taking the virtual focal plane pixel row direction as a u axis and taking the virtual focal plane pixel column direction as a v axis i -u i v i Wherein i =1,2, … S;
using the shooting station of the ith camera unit as the coordinate origin S i Establishing an image space coordinate system S of the ith camera unit according to a right-hand coordinate system by taking the pixel row direction of the parallel virtual focal plane as an x axis and the pixel column direction of the parallel virtual focal plane as a y axis i -x i y i z i Wherein i =1,2, … S;
step two: establishing a ground auxiliary coordinate system O-XYZ; wherein the camera station S of the 1 st camera unit 1 The vertical projection point on the ground is O point, and x of the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the X-axis of the ground auxiliary coordinate system and the y-axis of the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the y axis of the ground auxiliary coordinate system;
step three: obtaining a rotation matrix of each camera unit except the 1 st camera unit relative to the 1 st camera unit according to a line element of each camera unit except the 1 st camera unit relative to the 1 st camera unit and an angle element of each camera unit except the 1 st camera unit relative to the 1 st camera unit;
step four: with the image space coordinate system S of the 1 st camera unit 1 -x 1 y 1 z 1 And (3) as a virtual image space coordinate system, carrying out projection conversion on coordinate points of all camera units except the 1 st camera unit to the virtual image space coordinate system according to a mapping camera single-center projection conversion formula with multiple parallel optical axes to obtain a large-breadth virtual image with equivalent single-center projection.
In the above single-center projection conversion method for multi-optical-axis parallel mapping camera, in step three, a rotation matrix of the ith camera unit relative to the 1 st camera unit is obtained according to the line element of the ith camera unit relative to the 1 st camera unit and the angle element of the ith camera unit relative to the 1 st camera unit.
In the above single-center projection conversion method for a multi-axis parallel mapping camera, the rotation matrix of the ith camera unit relative to the 1 st camera unit is obtained by the following formula:
wherein, a i1 、a i2 、a i3 、b i1 、b i2 、b i3 、c i1 、c i2 And c i3 Are all coefficients in the rotation matrix of the i-th camera element relative to the 1 st camera element, Δ X i Is the abscissa, deltaY, of the camera station of the ith camera unit relative to the 1 st camera unit in the face auxiliary coordinate system O-XYZ i For the camera station of the ith camera unit, in the ground-assisted coordinate system O-XYZ, relative to the ordinate, Δ Z, of the 1 st camera unit i Is the vertical coordinate, phi, of the camera station of the ith camera unit relative to the 1 st camera unit in the ground auxiliary coordinate system O-XYZ i As image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 X axial rotation angle of, omega i For the image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Y-axis rotation angle of (k) i As image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Z-axis rotation angle.
In the foregoing method for converting single-center projection of a multi-optical-axis parallel surveying camera, in step four, the conversion formula of single-center projection of the multi-optical-axis parallel surveying camera is:
wherein x is 1 A virtual ideal imaging point a of the ground point A in the 1 st camera unit in the ground auxiliary coordinate system O-XYZ 1 Abscissa of (a), y 1 A virtual ideal imaging point a of the ground point A in the 1 st camera unit in the ground auxiliary coordinate system O-XYZ 1 H is the camera site S of the 1 st camera unit 1 Vertical coordinates in a ground auxiliary coordinate system O-XYZ; f. of 1 Is the principal distance of the 1 st camera unit, a i1 、a i2 、a i3 、b i1 、b i2 And b i3 Are all coefficients in the rotation matrix of the i-th camera element relative to the 1 st camera element, f i Is the principal distance, x, of the ith camera unit i0 Is the principal point abscissa, y, of the ith camera unit i0 Is the principal point ordinate of the i-th camera element.
The single-center projection conversion method of the mapping camera with the parallel multiple optical axes further comprises the following steps: and calculating the theoretical conversion error of the large-format virtual image of the equivalent single-center projection.
In the above single-center projection conversion method for a surveying and mapping camera with parallel multiple optical axes, the conversion error is as follows:
where Δ x is the conversion error of the abscissa, Δ y is the conversion error of the ordinate, H 0 Is the actual elevation of the ground point A, f 1 Is the principal distance of the 1 st camera unit, and H is the camera site S of the 1 st camera unit 1 Vertical coordinate, Δ X, in the ground-assisted coordinate system O-XYZ i Is the abscissa, deltaY, of the camera station of the ith camera unit in the ground auxiliary coordinate system O-XYZ relative to the 1 st camera unit i The camera station for the ith camera element is the ordinate of the 1 st camera element in the ground-assisted coordinate system O-XYZ.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a single-center projection conversion method of a surveying camera with multiple parallel optical axes, provides a conversion model from a multi-center projection image to a single-center projection image from a principle level, provides a conversion error calculation formula, solves the problem that the conversion model of the surveying camera with multiple parallel optical axes cannot be accurately described by the conventional single-center projection conversion method, and realizes the core problem of a large-breadth aerial surveying camera by splicing optical axis parallel multi-area arrays. And the approximate single-center projection image can be output according to the invention, the image output interface is the same as that of the existing single-center aerial survey camera, and the seamless butt joint with the existing aerial survey system processing software is realized.
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Various other advantages and benefits will become apparent to those of ordinary skill in the art upon reading the following detailed description of the preferred embodiments. The drawings are only for purposes of illustrating the preferred embodiments and are not to be construed as limiting the invention. Also, like reference numerals are used to refer to like parts throughout the drawings. In the drawings:
FIG. 1 is a schematic diagram of an image space coordinate system provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a ground-assisted coordinate system provided by an embodiment of the invention;
FIG. 3 is a schematic diagram of a multi-center to single-center projection transformation model provided by an embodiment of the invention;
fig. 4 is a schematic diagram of an imaging system provided by an embodiment of the invention.
Detailed Description
Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be embodied in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art. It should be noted that the embodiments and features of the embodiments of the present invention may be combined with each other without conflict. The present invention will be described in detail below with reference to the embodiments with reference to the attached drawings.
The embodiment provides a single-center projection conversion method of a mapping camera with multiple parallel optical axes, which comprises the following steps:
the method comprises the following steps: the method comprises the steps that S camera units are arranged in a preset camera, the parameters of lenses in each camera unit are the same, and the main optical axes of the lenses are parallel; the camera has M multiplied by N focal plane components participating in splicing, the number of pixels of each focal plane component which are effectively spliced is M multiplied by N, and the size of a virtual focal plane at the focal plane of the lens of each camera unit is Mm multiplied by Nn; wherein M is the number of rows participating in splicing the focal plane assembly array, N is the number of columns participating in splicing the focal plane assembly array, M is the number of rows of the number of effective splicing pixels of each focal plane assembly, and N is the number of columns of the number of effective splicing pixels of each focal plane assembly;
establishing a focal plane coordinate system o of the lens of the ith camera unit by taking the virtual focal plane pixel center of the lens of the ith camera unit as a coordinate origin, taking the virtual focal plane pixel row direction as a u axis and taking the virtual focal plane pixel column direction as a v axis i -u i v i Wherein i =1,2, … S;
using the shooting station of the ith camera unit as the coordinate origin S i Establishing an image space coordinate system S of the ith camera unit according to a right-hand coordinate system by taking the pixel row direction of the parallel virtual focal plane as an x axis and the pixel row direction of the parallel virtual focal plane as a y axis i -x i y i z i Wherein i =1,2, … S;
step two: establishing a ground auxiliary coordinate system O-XYZ; wherein the camera station S of the 1 st camera unit 1 The vertical projection point on the ground is O point, and x of the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the X-axis of the ground auxiliary coordinate system and the y-axis of the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the y axis of the ground auxiliary coordinate system; as shown in fig. 2.
Step three: obtaining a rotation matrix of each camera unit except the 1 st camera unit relative to the 1 st camera unit according to a line element of each camera unit except the 1 st camera unit relative to the 1 st camera unit and an angle element of each camera unit except the 1 st camera unit relative to the 1 st camera unit;
step four: using the image space coordinate system S of the lens of the 1 st camera unit 1 -x 1 y 1 z 1 And (3) as a virtual image space coordinate system, carrying out projection conversion on coordinate points of all camera units except the 1 st camera unit to the virtual image space coordinate system according to a mapping camera single-center projection conversion formula with multiple parallel optical axes to obtain a large-breadth virtual image with equivalent single-center projection.
Specifically, in the first step, each focal plane pixel is renamed. The size of the virtual focal plane at the lens focal plane in each camera unit is Mm N, as in FIG. 1, the focal plane at row A and column B, where point P (i, j) is renamed to P ((A-1) m + i, (B-1) n + j).
Establishing a focal plane coordinate system o by taking the center of a virtual focal plane pixel as a coordinate origin, the row direction of the virtual focal plane pixel as a u axis and the row direction of the virtual focal plane pixel as a v axis i -u i v i Where i =1,2, … S.
Using camera station as coordinate origin S i Establishing an image space coordinate system S according to a right-hand coordinate system, wherein the x axis is parallel to the pixel row direction of the virtual focal plane and the y axis is parallel to the pixel row direction of the virtual focal plane i -x i y i z i Where i =1,2, … S.
Second, the pickup station of the 1 st camera unit is S 1 O point is S 1 And (3) projecting in a ground auxiliary coordinate system, establishing a virtual ground auxiliary coordinate system by taking O as an origin, wherein a X, Y axis is parallel to x and y axes of an image space coordinate system, and establishing a ground auxiliary coordinate system projection O-XYZ according to a right-hand coordinate system.
And thirdly, the internal orientation element comprises a principal point, a principal distance and a distortion parameter. Measuring the interior orientation element in each camera unit, the principal point being (x) i0 ,y i0 ) Main pitch f i And a distortion parameter, wherein i =1,2, … S.
Fourthly, measuring relative exterior orientation elements in each camera unit, wherein the relative exterior orientation elements in each camera unit comprise relative exteriorAn azimuth element and an outer azimuth element. The line element of each camera unit with respect to the 1 st camera unit is (Δ X) i ,ΔY i ，ΔZ i ) Angle element phi of each camera unit with respect to the 1 st camera unit i 、ω i 、κ i The corresponding rotation matrix is R i Defined as:
wherein i =2,3, … S. a is i1 、a i2 、a i3 、b i1 、b i2 、b i3 、c i1 、c i2 And c i3 Are all coefficients in the rotation matrix of the i-th camera element relative to the 1 st camera element, Δ X i Is the abscissa, deltaY, of the camera station of the ith camera unit in the ground auxiliary coordinate system O-XYZ relative to the 1 st camera unit i For the camera station of the ith camera unit, in the ground-assisted coordinate system O-XYZ, relative to the ordinate, Δ Z, of the 1 st camera unit i Is the vertical coordinate, phi, of the camera station of the ith camera unit relative to the 1 st camera unit in the ground auxiliary coordinate system O-XYZ i As image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 X axial rotation angle, ω i For the image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Y-axis rotation angle of (k) i As image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Z-axis rotation angle.
The fifth step is to use the image space coordinate system S of the 1 st camera unit 1 -x 1 y 1 z 1 Mapping camera units according to multiple parallel optical axes for a virtual image space coordinate systemThe central projection conversion formula performs projection conversion on coordinate points of all the camera units except the 1 st camera unit to a virtual image space coordinate system to obtain a large-format virtual image projected by an equivalent single center. The derivation process of the conversion formula (6) of the single-center projection of the mapping camera with multiple parallel optical axes is as follows:
as shown in FIG. 3, assume the 1 st camera unit' S photosite S in the ground-aided coordinate system O-XYZ 1 The coordinate is S 1 (0, H) wherein H is S 1 Vertical coordinates in a ground auxiliary coordinate system O-XYZ;
the line element from the fourth step ith camera unit to the 1 st camera unit is (Δ X) i ,ΔY i ,ΔZ i ) Easy to obtain the shooting point S of the ith camera unit in the ground auxiliary coordinate system O-XYZ i The coordinate is S i (ΔX i ,ΔY i ,H+ΔZ i )；
Ground point A (X, Y, 0) in the ground auxiliary coordinate system O-XYZ, which is the imaging point a in the i-th camera unit i (x i ,y i ,-f i ) Virtual imaging point a in the 1 st camera unit 1 (x 1 ,y 1 ,-f 1 )。
Shooting station S of ith camera unit in ground auxiliary coordinate system O-XYZ i And in the ground auxiliary coordinate system O-XYZ, the ground point A (X, Y, 0) is imaged in the ith camera unit in a space coordinate system S i -x i y i z i Middle real imaging point a i And a ground point A in the ground auxiliary coordinate system O-XYZ, wherein the three points are collinear and are represented by a collinear equation:
x i is a i Abscissa, y, of the imaged point i Is a i Ordinate, x, of the imaging point i0 Is the principal point abscissa, y, of the ith camera unit i0 Is the principal point ordinate, f, of the i-th camera unit i Is the principal distance of the ith camera element,
is a rotation matrix in the formula (1),
is a transition matrix.
It is possible to obtain a solution of,
shooting station S of the 1 st camera unit in the ground auxiliary coordinate system O-XYZ 1 And an ideal imaging point a of the ground point A (X, Y, 0) in the 1 st camera unit in the ground auxiliary coordinate system O-XYZ 1 The ground point A in the ground auxiliary coordinate system O-XYZ is collinear, and the collinear equation is as follows:
x 1 is a 1 Abscissa, y, of the imaged point 1 Is a 1 Ordinate of imaging point, f 1 Is the principal distance of the camera 1.
The formula (4) with the person formula (5) has
And the formula (6) is a single-center projection conversion formula of the mapping camera with multiple parallel optical axes.
And sixthly, correcting the ground hypothesis as a plane by a formula (6) in order to realize the splicing construction of the virtual image approximate to the single center. The fluctuation of the actual ground surface can cause the theoretical error of splicing in the conversion, as shown in FIG. 3, the actual elevation of the point A is assumed to be H 0 Relative H and H-H in actual engineering implementation 0 Δ Z i Very small, let H + Δ Z i ≈H，H-H 0 +ΔZ i ≈H-H 0 Can obtain the productError is as follows
In the embodiment of the single-center projection conversion method of the multi-optical-axis parallel mapping camera, optical axes of 4 lenses corresponding to an imaging system are parallel, each lens corresponds to one group of focal planes, namely 2 x 2 focal plane components participate in splicing, the effective splicing pixel number of each focal plane component is 5120 x 5120, and the total effective splicing pixel number after splicing is 2 x 5120 x 2 x 5120. The method comprises the following specific steps:
first, the pixels at each focal plane are renamed. The size of the virtual focal plane at each lens focal plane is 2 × 5120 × 2 × 5120, as in FIG. 4, the focal plane at row 2 and column 2, with point P (i, j) renamed to P ((2-1) × 5120+ i, (2-1) × 5120+ j).
Establishing a focal plane coordinate system o by taking the center of a focal plane pixel as a coordinate origin and the pixel arrangement directions as u and v axes respectively i -u i v i Where i =1,2, ….
Using camera station as coordinate origin S i The pixel arrangement directions are respectively x-axis and y-axis, and an image space coordinate system S is established according to a right-hand coordinate system i -x i y i z i Where i =1,2, ….
In the second step, the O point is S 1 And (3) projecting in a ground auxiliary coordinate system, establishing a virtual ground auxiliary coordinate system by taking O as an origin, wherein a X, Y axis is parallel to an x axis and a y axis of an image space coordinate system, and establishing a ground auxiliary coordinate system projection O-XYZ according to a right-hand coordinate system.
Thirdly, measuring the internal orientation elements of each camera, wherein the principal point is (x) i0 ,y i0 ) Main distance f i And a distortion parameter, wherein i =1,2, ….
And fourthly, measuring the relative external orientation elements of each camera, wherein the relative external orientation elements of each camera comprise relative external orientation angle elements and external orientation line elements. The line element of each camera unit with respect to the 1 st camera unit is (Δ X) i ,ΔY i ,ΔZ i ) Angle element phi of each camera unit with respect to the 1 st camera unit i 、ω i 、κ i To is aligned withThe corresponding rotation matrix is R i Defined as:
wherein i =2,3, ….
Fifthly, the image space coordinate system of the 1 st camera unit is a virtual image space coordinate system, and other camera units derive the formula converted from the 1 st camera unit. Assume that the pickup station S is, as in FIG. 3 1 (0, H), from the second step, S i (ΔX i ,ΔY i ,H+ΔZ i ) A ground point A (X, Y, 0) which is an imaging point a in the i-th camera unit i (x i ,y i ,-f i ) Virtual imaging point a in the 1 st camera unit 1 (x 1 ,y 1 ,-f 1 )。
S i A, A are collinear, and the collinearity equation is as follows:
wherein
Is a transition matrix.
It is possible to obtain,
S 1 、a 1 a collinearity, from collinearity equation:
obtaining the single-center projection conversion formula of the surveying and mapping camera with parallel multiple optical axes by using the two formulas
The single-center projection conversion formula of the surveying and mapping camera with the parallel multiple optical axes is a single-center projection conversion formula of the surveying and mapping camera with the parallel multiple optical axes. Single-center projection conversion and final projection transformation of multi-optical-axis parallel mapping camera to virtual image plane S 1 -x 1 y 1 And generating a large-format virtual image of the equivalent single-center projection through splicing conversion in the standard.
And sixthly, in order to realize splicing and construct a virtual image approximate to a single center, a mapping camera single-center projection conversion formula with multiple parallel optical axes corrects the ground by assuming the ground as a plane. The actual ground undulation will cause errors in the stitching in the transition, as shown in FIG. 3, assuming that the actual elevation at point A is H 0 Relative H and H-H in actual engineering implementation 0 Δ Z i Very small, order H + Δ Z i ≈H，H-H 0 +ΔZ i ≈H-H 0 The available error is
The main optical axis parallel mapping system is a novel mapping imaging system, the embodiment provides a single-center projection conversion method for a mapping camera with multiple parallel optical axes, a conversion model from multiple projection images to a single-center projection image is given from a principle level, a conversion error calculation formula is given, the problem that the conversion model of the mapping camera with multiple parallel optical axes cannot be accurately described by the existing single-center projection conversion method is solved, and the core problem of a large-breadth aerial mapping camera is realized by splicing multiple parallel optical axes. The invention can output approximate single-center projection images, has the same interface with the output images of the existing single-center aerial survey camera, and realizes seamless connection with the processing software of the existing aerial survey system.
Although the present invention has been described with reference to the preferred embodiments, it is not intended to limit the present invention, and those skilled in the art can make variations and modifications of the present invention without departing from the spirit and scope of the present invention by using the methods and technical contents disclosed above.
Claims (1)
1. A method for converting single-center projection of a multi-optical-axis parallel mapping camera, the method comprising the steps of:
the method comprises the following steps: the method comprises the steps that S camera units are arranged in a preset camera, the parameters of lenses in each camera unit are the same, and the main optical axes of the lenses are parallel; the camera has M multiplied by N focal plane components for splicing, the effective splicing pixel number of each focal plane component is M multiplied by N, and the size of a virtual focal plane at the lens focal plane of each camera unit is Mm multiplied by Nn; wherein M is the number of rows participating in splicing the focal plane assembly array, N is the number of columns participating in splicing the focal plane assembly array, M is the number of rows of the number of effective splicing pixels of each focal plane assembly, and N is the number of columns of the number of effective splicing pixels of each focal plane assembly;
establishing a focal plane coordinate system o of the lens of the ith camera unit by taking the virtual focal plane pixel center of the lens of the ith camera unit as a coordinate origin, taking the virtual focal plane pixel row direction as a u axis and taking the virtual focal plane pixel column direction as a v axis i -u i v i Wherein i =1,2, … S;
taking the camera station of the ith camera unit as a coordinate origin S i Establishing an image space coordinate system S of the ith camera unit according to a right-hand coordinate system by taking the pixel row direction of the parallel virtual focal plane as an x axis and the pixel column direction of the parallel virtual focal plane as a y axis i -x i y i z i Wherein i =1,2, … S;
step two: establishing a ground auxiliary coordinate system O-XYZ; wherein the camera station S of the 1 st camera unit 1 The vertical projection point on the ground is O point, and x of the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the X axis of the ground auxiliary coordinate systemY in the image space coordinate system of the 1 st camera unit 1 The axis parallel to the axis is the y axis of the ground auxiliary coordinate system;
step three: obtaining a rotation matrix of each camera unit except the 1 st camera unit relative to the 1 st camera unit according to a line element of each camera unit except the 1 st camera unit relative to the 1 st camera unit and an angle element of each camera unit except the 1 st camera unit relative to the 1 st camera unit;
step four: with the image space coordinate system S of the 1 st camera unit 1 -x 1 y 1 z 1 For a virtual image space coordinate system, carrying out projection conversion on coordinate points of all camera units except the 1 st camera unit to the virtual image space coordinate system according to a mapping camera single-center projection conversion formula with multiple parallel optical axes to obtain a large-breadth virtual image with equivalent single-center projection;
in step three, a rotation matrix of the ith camera unit relative to the 1 st camera unit is obtained according to the line element of the ith camera unit relative to the 1 st camera unit and the angle element of the ith camera unit relative to the 1 st camera unit;
the rotation matrix of the ith camera element relative to the 1 st camera element is obtained by the following formula:
wherein, a i1 、a i2 、a i3 、b i1 、b i2 、b i3 、c i1 、c i2 And c i3 Are all coefficients in the rotation matrix of the ith camera element relative to the 1 st camera element i As image space coordinate system S of the ith camera unit i -x i y i z i Relative to the image space coordinate system S of the 1 st camera unit 1 -x 1 y 1 z 1 X axial rotation angle of, omega i For the image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Y-axis rotation angle of (k) i For the image space coordinate system S of the ith camera unit i -x i y i z i Image space coordinate system S relative to the 1 st camera unit 1 -x 1 y 1 z 1 Z-axis rotation angle of (c);
in step four, the conversion formula of the single-center projection of the mapping camera with parallel multiple optical axes is as follows:
wherein x is 1 A virtual ideal imaging point a of the 1 st camera unit for the ground point A in the ground auxiliary coordinate system O-XYZ 1 Abscissa of (a), y 1 A virtual ideal imaging point a of the 1 st camera unit for the ground point A in the ground auxiliary coordinate system O-XYZ 1 H is the camera site S of the 1 st camera unit 1 Vertical coordinates in a ground auxiliary coordinate system O-XYZ; f. of 1 Is the principal distance of the 1 st camera unit, a i1 、a i2 、a i3 、b i1 、b i2 And b i3 Are all coefficients in the rotation matrix of the i-th camera element relative to the 1 st camera element, f i Is the principal distance, x, of the ith camera unit i0 Is the principal point abscissa, y, of the ith camera unit i0 Is the principal point ordinate of the ith camera unit;
calculating a theoretical conversion error existing in a large-format virtual image of the equivalent single-center projection;
the theoretical conversion error is:
where Δ x is the conversion error of the abscissa, Δ y is the conversion error of the ordinate, H 0 Is the actual elevation of the ground point A, f 1 Is the principal distance of the 1 st camera unit, and H is the camera site S of the 1 st camera unit 1 On the groundVertical coordinate, Δ X, in an auxiliary coordinate system O-XYZ i Is the abscissa, deltaY, of the camera station of the ith camera unit in the ground auxiliary coordinate system O-XYZ relative to the 1 st camera unit i The camera station for the ith camera unit is the ordinate of the 1 st camera unit in the ground-assisted coordinate system O-XYZ.
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