CN109903227A - Full-view image joining method based on camera geometry site - Google Patents
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Abstract
The present invention provides a kind of full-view image joining method based on camera geometry site, and the method comprising the steps of 1, and assembling multicamera system is simultaneously demarcated, and the multicamera system is made of multiple cameras；Step 2, panoramic coordinates system is established, the outer ginseng between each camera and panoramic coordinates system is obtained；Step 3, distortion rectification is carried out to original distorted image, acquisition meets image after the correction of object point-optical center-picture point three point on a straight line；The region that partly overlaps between the image of adjacent cameras shooting is removed, and the image of duplicate removal poststack is mapped on panorama spherical surface；Step 4, panorama development of a sphere is obtained into spliced full-view image.The method of the present invention improves the splicing efficiency of full-view image, can splice on real-time level and obtain full-view image.
Description
Technical field
This method belongs to photogrammetric and computer vision field, is related to shooting camera the mark of inside and outside parameter when being imaged
Fixed and panorama mapping model foundation, can not need to calculate wait spell between image sequence transformation matrix or according to image from
Body feature obtains full-view image under the premise of finding optimal splicing line, greatly improves splicing speed.
Background technique
Full-view image is due to being capable of providing 360 degree of comprehensive scene information and in streetscape map, digital city, mobile survey
The fields such as amount are widely used, therefore the full-view image for how quickly and accurately obtaining different scenes is particularly important.Tradition
Method be usually pass through one or more camera shooting between any two with certain degree of overlapping image sequence, then pass through
Characteristic matching between overlapping region calculates the transformation matrix between image, realizes image sequence two finally by this transformation matrix
Splicing between two, obtains full-view image.This joining method based on characteristics of image need to every group of image to be spliced into
Row feature extraction and matching, splicing is computationally intensive, speed is slow.In addition, if textural characteristics in overlapping region between adjacent image
Deficient or overlapping region is smaller, is easy to cause between feature extraction or image that it fails to match, is unable to complete splicing.Another kind is common
Method be best splicing line between detecting image in overlapping region, multiple image is inlayed and obtains panoramic picture together.This
Kind method regards an energy-optimised problem as best splicing line is detected, and passes through the energy function for minimizing a special designing
It solves.Energy function is defined usually using color, gradient and texture, and is optimized by different optimization algorithms, such as
This drawing algorithm of snake model, Dijet and figure are cut.Due to needing to calculate various cost of energy and being determined by optimization algorithm
Optimal splicing line, such methods equally exist the disadvantage that time overhead is big, inefficient.Therefore, how accurately and rapidly
Obtaining full-view image is always a photogrammetric hot issue in computer vision field.
Summary of the invention
In order to more accurately and efficiently obtain full-view image, it is mutual based on multiple cameras that the invention discloses one kind
Geometry site full-view image joining method.
The technical scheme is that being established complete using the inside and outside calibrating parameters and camera imaging geometrical relationship of multiple cameras
Scape mapping model obtains full-view image, comprising the following steps:
Step 1, it assembles multicamera system and is demarcated, the multicamera system is made of multiple cameras；
Step 2, panoramic coordinates system is established, the outer ginseng between each camera and panoramic coordinates system is obtained；
Step 3, distortion rectification is carried out to original distorted image, acquisition meets the correction of object point-optical center-picture point three point on a straight line
Then image afterwards removes the region that partly overlaps between the image of adjacent cameras shooting, and the image of duplicate removal poststack is mapped to entirely
On scape spherical surface；
Step 4, panorama development of a sphere is obtained into spliced full-view image.
Further, multicamera system described in step 1 includes 6 cameras, wherein one camera in top, optical axis are directed toward day
Direction is pushed up, horizontal side is in 5 cameras of regular pentagon regular distribution, is used for side shooting level direction scene, 5 camera photocentres
It is substantially distributed on a circle.
Further, the parameter demarcated in step 1 include in multicamera system the internal reference of each camera and each camera exist
Outer ginseng of the moment relative to Calibration Field coordinate system, wherein internal reference includes focal length (fx, fy), principal point (x0, y0) and distortion system
Number (k1, k2, p1, p2), reflect the physical characteristic and distortion situation of camera itself imaging；Outer ginseng includes a translation vector (Xs,
Ys, Zs) and three rotation anglesDefine pose of the camera coordinates system relative to reference frame.
Further, the specific implementation of calibration for cameras internal reference and outer ginseng is as follows,
Multicamera system is placed in the high-precision close-range photogrammetry Calibration Field manually established, with two or more
There is the camera in the public visual field while shooting the control point of known coordinate in Calibration Field and obtain calibration image, is measured in calibration image
The pixel coordinate at these control points and as observation, disposably calculates in camera according to the collinearity equation in photogrammetric
Ginseng and outer ginseng,
Wherein (1) is radial tangential distortion model formula, wherein (δx, δy) it is picture point offset caused by distortion, k1、k2
For coefficient of radial distortion, p1、p2For tangential distortion coefficient, Δ x=xd-x0, Δ y=yd-y0, r2=Δ x2+Δy2, (xd, yd) be
The actual pixels coordinate at control point；It (2) is collinearity equation, (Xa, Ya, Za) be control point three-dimensional coordinate,For
By three rotation anglesThe spin matrix of definition.
Further, in step 2 panoramic coordinates system to establish mode as follows,
Using any one camera of horizontal direction as benchmark camera lens, the Z axis of panoramic coordinates system is directed toward zenith direction, and X-axis is just
Direction is consistent with the optical axis direction of basic lens, and Y-axis is determined according to the right-hand rule.
Further, it is obtained in step 2 according to the outer ginseng between adjacent cameras outer between each camera and panoramic coordinates system
Ginseng, wherein the outer ginseng calculation method between adjacent cameras is as follows,
Wherein,It is defined as follows,
b1=cos ω sin κ
b2=cos ω cos κ
b3=-sin ω
Wherein, the subscript 1 and 2 of R, T are the number of two neighboring camera.
Further, specific implementation image being mapped on panorama spherical surface in step 3 is as follows,
Assuming that object A is in camera OnIn be imaged as a0, wherein n is the number of camera, its pixel coordinate is (x, y), therefore
a0Coordinate in camera coordinates system isWhereinThe respectively principal point and coke of camera
Away from, they are obtained by demarcating multicamera system,Due to On、a0, a three point on a straight line, a is a0In panorama
The mapping position of spherical surface, thereforeSimultaneouslyWherein t be than
Example coefficient；VectorIt is expressed as in panoramic coordinates systemPixel a in this way0In the mapping position a of panorama spherical surface
(X, Y, Z) is obtained by simultaneous (3), (4), and wherein r is the radius of panorama ball；
X2+Y2+Z2=r2 (4)
WhereinOuter ginseng of the expression camera to panoramic coordinates system.
Further, the implementation that panorama development of a sphere is obtained spliced full-view image by step 4 is as follows,
Image that each camera obtains by distortion rectification and after going overlap processing, is mapped on panorama spherical surface and obtains one
Group is located at discrete three-dimensional point, establishes kd tree to three-dimensional point, is denoted as K；Then panoramic pixel p (u, v) is calculated in panoramic coordinates system
Position P (X, Y, Z)；Finally in K query point P closest point, (R, G, B) value of closest point is assigned to panoramic pixel p,
Full-view image is obtained, (u, v) corresponding coordinate (X, Y, Z) in panoramic coordinates system is defined by the formula,
Wherein, (w, h) indicates the wide height of film size of full-view image.
The advantages of the present invention are as follows: outer between all cameras after being integrated due to multicamera system assembly
Ginseng is definite value, thus only need to inside and outside parameter Accurate Calibration to camera system it is primary.In addition, the solution of the present invention does not need
It treats to spell image progress feature extraction and matching or define other features and establishes energy function.Because of image to be spelled and panorama shadow
The corresponding relationship of picture is fixed, therefore can quickly splice to obtain full-view image, can achieve real-time level substantially.
Detailed description of the invention
Fig. 1 is the structural schematic diagram (a) and each camera coordinates system and panoramic coordinates system's schematic diagram (b) of multicamera system.
Fig. 2 is the high-precision close-range photogrammetry Calibration Field manually established.
Fig. 3 is one group of calibration image of two camera shootings for having the public visual field.
Fig. 4 is panorama mapping model schematic diagram.
Fig. 5 is that two adjacent cameras remove overlapping zone concepts figure.
Fig. 6 is overlapping region processing schematic example, wherein (a) is to become the image plane of 1, No. 2 camera by rotation
Result schematic diagram after changing (b) is top view.
Fig. 7 is the overview flow chart of present example.
Specific embodiment
Below in conjunction with attached drawing and the embodiment of the present invention, detailed analysis explanation is carried out to technical solution of the present invention, it is specific real
Steps flow chart such as attached drawing 7 when applying, the specific implementation process of embodiment can be summarized as following 5 steps:
Step 1: calibration multicamera system.
Use six imaging parameters and the similar high-quality wide angle camera of performance according to (a) of Fig. 1 in the embodiment of the present invention
(b) structure shown in assembles multicamera system.Wherein 5 are mounted on side shooting level direction scene, and camera photocentre is substantially
It is upper (numbering respectively by clock-wise order is 1,2,3,4,5) to be distributed in a circle, another camera is mounted on top and optical axis refers to
To zenith direction (number 6).Outer ginseng (rotation and translation) after multicamera system is integrated between the coordinate system of each camera is no
Become.Multicamera system parameter to be calibrated is divided into internal reference and outer ginseng two major classes.Internal reference includes focal length (fx, fy), principal point (x0,
y0) and distortion factor (k1, k2, p1, p2), reflect the physical characteristic and distortion situation of camera itself imaging；Outer ginseng includes one
Translation vector (Xs, Ys, Zs) and three rotation anglesDefine pose of the camera coordinates system relative to reference frame.
When calibration, two or more, which have the camera in the public visual field while shooting the control point of known coordinate in Calibration Field, is obtained
To calibration image, the pixel coordinate at these control points is measured in calibration image and as observation, in photogrammetric
Collinearity equation disposably calculate camera internal reference and outer ginseng, and it is mutual using Calibration Field coordinate system as intermediary to obtain camera
Outer ginseng.It is specific as follows:
Multicamera system is demarcated using the high-precision close-range photogrammetry Calibration Field manually established, in the Calibration Field
There is a control point more than 200, the three-dimensional coordinate at these control points is obtained by all-station instrument accurate measurement, sees Figure of description 2.Make adjacent
Two cameras regard altogether Calibration Field shooting calibration image, as shown in Figure 3 left and right two images shot respectively by 1, No. 2 camera
It arrives.The pixel coordinate that enough control points are chosen from two images is used as observation by linearizing collinearity equation
Least square-fit iteratively solves parameter to be calibrated.
It (1) is radial tangential distortion model formula, wherein (δx, δy) it is picture point offset caused by distortion, k1、k2For diameter
To distortion factor, p1、p2For tangential distortion coefficient, Δ x=xd-x0, Δ y=yd-y0, r2=Δ x2+Δy2, (xd, yd) it is control
The actual pixels coordinate of point.It (2) is collinearity equation, (Xa, Ya, Za) be control point three-dimensional coordinate,For by three
A rotation angleThe spin matrix of definition.No. 1 camera and No. 2 cameras are calculated separately out by two calibration images of Fig. 3
Calibrating parameters, then using Calibration Field coordinate system as intermediary calculate No. 1 camera and No. 2 cameras outer ginseng (R12, T12), calculating side
Method is as follows,
Wherein,It is defined as follows,
b1=cos ω sin κ
b2=cos ω cos κ
b3=-sin ω
We regard close-range photogrammetry according to the order of (1,2), (2,3), (3,4), (4,5), (5,6), (6,1) respectively altogether
Calibration Field shoots calibration image, obtains (R by collinearity equation12, T12)、(R23, T23)、(R34, T34)、(R45, T45)、(R56,
T56)、(R61, T61) join outside six groups.
Step 2: panoramic coordinates system being established according to the calibration result of multicamera system, and obtains each camera coordinates system and complete
The outer ginseng of scape coordinate system.
Shown in the foundation of panoramic coordinates system such as Fig. 1 (b), origin is the geometric center of five camera photocentres in side；Z axis and top
The optical axis of portion's camera is parallel, and positive direction is directed toward zenith direction；X-axis is parallel with the optical axis of No. 1 camera, positive direction and No. 1 camera
Optical axis is directed toward consistent；Y-axis is determined by the right-hand rule.Here illustrate two o'clock: (1) due to the micro error assembled, integrated, No. 1 phase
The optical axis of machine may not with the optical axis exact vertical of No. 6 cameras, but deviate it is minimum；(2) when the present invention establishes panoramic coordinates system
Be reference with No. 1 camera, be actually distributed in five of side it is magazine any one all can be used as reference.It is sat according to panorama
Mark the definition of system, the outer ginseng (R between No. 1 camera and panoramic coordinates system1, T1) can be obtained by following formula,
Wherein, T21、T31、T41、T51Respectively 2,3,4, No. 5 cameras are to the translation vector in the outer ginseng of No. 1 camera.Consider
Two coordinate systems, are denoted as i and j, it is assumed that the outer ginseng of i coordinate system to j coordinate system is (Rij, Tij), then j coordinate system to i coordinate system
Outer ginseng (Rji, Tji) can be obtained by following formula,
In this way according to (R12, T12)、(R23, T23)、(R34, T34)、(R45, T45)、(R56, T56)、(R61, T61) can be obtained by
2, outer ginseng (R of 3,4,5, No. 6 cameras to No. 1 camera21, T21)、(R31, T31)、(R41, T41)、(R51, T51)、(R61, T61), then
Other cameras are obtained to the outer ginseng of panoramic coordinates system by intermediary of No. 1 camera again, and the present invention is uniformly denoted as
Wherein n is the number of camera, translation vector
Step 3: distortion rectification being carried out to original distorted image, acquisition meets the correction of object point-optical center-picture point three point on a straight line
Image afterwards, and get rid of adjacent two correct after the extra overlapping region of image, the shadow that six are gone after overlapping and distortion rectification
As being mapped in the way of in Fig. 4 on panorama spherical surface.
First using the principal point (x in multicamera system calibration result0, y0) and distortion factor (k1, k2, p1, p2According to
(1) formula calculates picture point offset (δ caused by distortionx, δy), it then finds out ideal pixel coordinate and completes to original distortion image
Distortion rectification, obtain meeting image after the correction of object point-optical center-picture point three point on a straight line.
Then overlap processing is carried out.As shown in figure 5, O1And O2It is two adjacent cameras light in multicamera system respectively
The heart, it is about A on the circle of 6cm that they, which are located substantially at a radius,1B1And A2B2For corresponding image plane.If adjacent cameras
Optical center is overlapped imaging, such as image plane A '1B′1And A2B2, the overlapping region between two images is A ' at this time1D1And D2B2.Right 2
A '1E sections of Ds of the corresponding scene at left2E sections of imagings, left EB2ED of the corresponding scene of section at right 21Section imaging.Utilize two
A camera coordinates system carries out two image planes to convert the intersection of latter two plane relative to the spin matrix of panoramic coordinates system, hands over
Line position is point E.If removing A ' according to this intersection1E and EB2This two sections of regions that partly overlap do not have any scene letter
The loss of breath, and the intersection of left and right 2, scene information be be not interrupted, continuously transition.Due to assembling polyphaser
Two camera photocentres of system cannot be overlapped when system, and actual imaging mode is as shown in left and right 1, between two image centers
There are certain offsets.O1E ' and O2E is parallel, is now placed between this two parallel lines and the public visual field model of two cameras
Object in enclosing is imaged on A on right 11E ' section is imaged on EB in left on piece2Section, if getting rid of A1E ' and EB2Section, there will be
Least a portion of scene information loss.But be about on the spherical surface of 6cm since the optical center of 6 camera lenses is substantially in a radius, because
This O1E ' and O2Range between E is the space of a very little, can only lose few scene information in this way, is not influenced last complete
Scape image.
It is illustrated by taking 1, No. 2 camera as an example below.Assuming that the image plane of 1, No. 2 camera is denoted as P respectively1、P2, they
Equation be expressed as z1=f1、z2=f2, normal vector n1=(0,0,1), n2=(0,0,1), this is because image plane is
Perpendicular to camera optical axis.It is respectively n ' after the transformation of spin matrix1=R1n1、n′2=R2n2。P1、P2On two o'clock p1
(0,0, f1)、p2(0,0, f2) it is respectively p ' after the transformation of spin matrix1=R1p1、p′2=R2p2.Remember P1、P′2By rotation
It is P ' after matrixing1、P′2, their equattion root strong point French can be expressed as n '1 T(x′1-p′1)=0, n '2 T(x′2-p
′2).As shown in fig. 6, (a) is the result schematic diagram by the image plane of 1, No. 2 camera after rotation transformation, it is (b) vertical view
Figure.As described above, B1E and A2E is the part (grey) for needing to retain, A1E and B2E is then the part to be removed (black).It is located at
A1The point x ' of E1With P '2On point p '2The vector of compositionWith n '2Inner product be greater than zero, i.e. θ1For acute angle, and it is located at B1E's
Point x '2With p '2On point p '2The vector of compositionWith n '2Inner product less than zero, i.e. θ2For obtuse angle.B can similarly be removed2E is protected
Stay A2E.The processing mode of the image overlap area of other cameras is similar.
Finally according to mode shown in Fig. 4, treated that image is mapped on panorama spherical surface by six.Object A is in camera On
In be imaged as a0, its pixel coordinate is (x, y), therefore a0Coordinate in camera coordinates system is
WhereinThe respectively principal point and focal length of camera, they are obtained by demarcating multicamera system,Due to On、a0, a three point on a straight line, thereforeSimultaneouslyWherein t is proportionality coefficient.VectorIt is expressed as in panoramic coordinates systemThe pixel a of image in this way after distortion rectification0Panorama spherical surface mapping position a (X, Y, Z) by simultaneous (3),
(4) it obtains, wherein r is the radius of panorama ball.
X2+Y2+Z2=r2 (10)
Step 4: being unfolded panorama ball to obtain full-view image
The mapping result to image after six distortion rectifications after overlapping regional processing is obtained by step 3.Due to original
The quantity of sequence image pixel is limited, if the panorama ball that mapping obtains directly is unfolded to will cause the panorama being directly unfolded
There are the panoramic pixels of many unknown pixel values in image.The present invention is by transforming to panoramic pixel in panoramic coordinates system, root
Panoramic pixel value is determined according to the distance relation between the mapping point on panoramic pixel and panorama spherical surface.Specific practice is as follows: by six
Image obtains one group positioned at discrete three-dimensional point after distortion rectification after being mapped on panorama spherical surface, establishes kd tree to three-dimensional point, is denoted as
K；Then the position P (X, Y, Z) of panoramic pixel p (u, v) in panoramic coordinates system is calculated；Finally in K query point P it is closest
(R, G, B) value of closest point is assigned to panoramic pixel p, obtains full-view image by point.Assuming that it is respectively w that the width of panoramic picture is high
And h, (u, v) corresponding coordinate (X, Y, Z) in panoramic coordinates system are defined by the formula,
Itself inside and outside ginseng of multicamera systemN=1,2,3,4,5,6, it is filled in system
With being definite value after the completion, after determining panorama radius of a ball r (it is proposed that 10 meters of panorama radius of a ball selection or bigger), map
Obtained panorama spherical surface point set is also changeless.After the film size of full-view image wide high (w, h) determines, according to (5), (6)
The corresponding query point P (X, Y, Z) of panoramic pixel p (u, v) is also constant known to formula.Therefore for the given panorama radius of a ball and
The wide height of film size, the corresponding relationship of image pixel is also constant after panoramic pixel and distortion rectification, in this way for different scenes
Shadow can quickly obtain full-view image, can reach the level spliced in real time.
Specific implementation example described herein only illustrates that spirit of the invention.Technology belonging to the present invention
The technical staff in field can make various modifications or additions to the described embodiments or by a similar method
Substitution, however, it does not deviate from the spirit of the invention or beyond the scope of the appended claims.
Claims (8)
1. a kind of full-view image joining method based on camera geometry site, which comprises the following steps:
Step 1, it assembles multicamera system and is demarcated, the multicamera system is made of multiple cameras；
Step 2, panoramic coordinates system is established, the outer ginseng between each camera and panoramic coordinates system is obtained；
Step 3, distortion rectification is carried out to original distorted image, acquisition meets shadow after the correction of object point-optical center-picture point three point on a straight line
Then picture removes the region that partly overlaps between the image of adjacent cameras shooting, and the image of duplicate removal poststack is mapped to panorama ball
On face；
Step 4, panorama development of a sphere is obtained into spliced full-view image.
2. a kind of full-view image joining method based on camera geometry site as described in claim 1, it is characterised in that:
Multicamera system described in step 1 includes 6 cameras, wherein one camera in top, optical axis are directed toward zenith direction, horizontal side is in
5 cameras of regular pentagon regular distribution, are used for side shooting level direction scene, and 5 camera photocentres are substantially distributed in a circle
On.
3. a kind of full-view image joining method based on camera geometry site as described in claim 1, it is characterised in that:
The parameter demarcated in step 1 include in multicamera system the internal reference of each camera and each camera in moment relative to calibration
The outer ginseng of field coordinate system, wherein internal reference includes focal length (fx, fy), principal point (x0, y0) and distortion factor (k1, k2, p1, p2), reflection
The physical characteristic and distortion situation of camera itself imaging；Outer ginseng includes a translation vector (Xs, Ys, Zs) and three rotation anglesDefine pose of the camera coordinates system relative to reference frame.
4. a kind of full-view image joining method based on camera geometry site as claimed in claim 3, it is characterised in that:
The specific implementation of calibration for cameras internal reference and outer ginseng is as follows,
Multicamera system is placed in the high-precision close-range photogrammetry Calibration Field manually established, there are public affairs with two or more
The control point that the camera in the visual field shoots known coordinate in Calibration Field simultaneously altogether obtains calibration image, measures these in calibration image
The pixel coordinate at control point and as observation, according to the collinearity equation in photogrammetric disposably calculate camera internal reference and
Outer ginseng,
Wherein (1) is radial tangential distortion model formula, wherein (δx, δy) it is picture point offset caused by distortion, k1、k2For radial direction
Distortion factor, p1、p2For tangential distortion coefficient, Δ x=xd-x0, Δ y=yd-y0, r2=Δ x2+Δy2, (xd, yd) it is control point
Actual pixels coordinate；It (2) is collinearity equation, (Xa, Ya, Za) be control point three-dimensional coordinate,For by three
Rotation angleThe spin matrix of definition.
5. a kind of full-view image joining method based on camera geometry site as described in claim 1, it is characterised in that:
In step 2 panoramic coordinates system to establish mode as follows,
Using any one camera of horizontal direction as benchmark camera lens, the Z axis of panoramic coordinates system is directed toward zenith direction, X-axis positive direction
Consistent with the optical axis direction of basic lens, Y-axis is determined according to the right-hand rule.
6. a kind of full-view image joining method based on camera geometry site as described in claim 1, it is characterised in that:
The outer ginseng between each camera and panoramic coordinates system is obtained according to the outer ginseng between adjacent cameras in step 2, wherein between adjacent cameras
Outer ginseng calculation method it is as follows,
Wherein,It is defined as follows,
bi=cos ω sin κ
b2=cos ω cos κ
b3=-Sin ω
Wherein, the subscript 1 and 2 of R, T are the number of two neighboring camera.
7. a kind of full-view image joining method based on camera geometry site according to claim 1, feature exist
In: the specific implementation that image is mapped on panorama spherical surface in step 3 is as follows,
Assuming that object A is in camera OnIn be imaged as a0, wherein n is the number of camera, its pixel coordinate is (x, y), therefore a0?
Coordinate in camera coordinates system isWhereinThe respectively principal point and focal length of camera, it
By demarcate multicamera system obtain,Due to On、a0, a three point on a straight line, a is a0In panorama spherical surface
Mapping position, thereforeSimultaneouslyWherein t is ratio system
Number；VectorIt is expressed as in panoramic coordinates systemPixel a in this way0Panorama spherical surface mapping position a (X,
Y, Z) it is obtained by simultaneous (3), (4), wherein r is the radius of panorama ball；
X2+Y2+Z2=r2 (4)
WhereinOuter ginseng of the expression camera to panoramic coordinates system.
8. a kind of full-view image joining method based on camera geometry site according to claim 1, feature exist
In: the implementation that panorama development of a sphere is obtained spliced full-view image by step 4 is as follows,
Image that each camera obtains by distortion rectification and after going overlap processing, is mapped on panorama spherical surface and obtains one group of position
In discrete three-dimensional point, kd tree is established to three-dimensional point, is denoted as K；Then the position of panoramic pixel p (u, v) in panoramic coordinates system is calculated
Set P (X, Y, Z)；Finally in K query point P closest point, (R, G, B) value of closest point is assigned to panoramic pixel p, is obtained
Full-view image, (u, v) corresponding coordinate (X, Y, Z) in panoramic coordinates system are defined by the formula,
Wherein, (w, h) indicates the wide height of film size of full-view image.
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