CN104063843B - A kind of method of the integrated three-dimensional imaging element image generation based on central projection - Google Patents

Abstract

The invention discloses a kind of method of the integrated three-dimensional imaging element image generation based on central projection, 3 D stereo scene is set up first with computer, the coordinate database corresponding with information of stereo scene is obtained；Virtual lenticule optical parametric is set, the optical parametric of true lenticule is complied with, shown in the optical system of integrated stereo imaging system；All three-dimensional scenic coordinates are gone into world coordinates from local coordinate；According to the position of virtual lenticule camera and spatial scene, eye coordinates are determined；Virtual 3D targets are converted into 2D images according to different points of view, element image is generated according to eye coordinates.The present invention is proposed using geometric projection, mapping techniques, virtual microlens array element image is constituted by computer, the characteristics of element image of acquisition has broader angular field of view, high-resolution and the big depth of field, the interference between the element image array obtained based on microlens array is overcome, clearly integrated stereo-picture has been reconstructed.

Description

A kind of method of the integrated three-dimensional imaging element image generation based on central projection

Technical field

The invention belongs to integrated (solid) technical field of imaging, more particularly to it is a kind of based on central projection it is integrated it is three-dimensional into The method generated as element image.

Background technology

Integrated (solid) imaging technique (Integral Imaging, abbreviation II are translated into three-dimensional panorama imaging technique again), be A kind of image technique for recording and showing 3d space scene information by microlens array.Integrated (solid) imaging technique it is prominent The characteristics of going out is that (1) has spatially reproduced actual stereoscopic images, and retains correct displaying ratio.Any observation is not needed to set It is standby, and do not limited by observer's visual range.(2) actual stereoscopic images of continuous viewpoint are provided to observer, are overcome Eyes concentrate adaptability regulation collision problems.(3) it is a kind of passive display technique, and overcoming needs fill-in light in holography The problem of source is to show stereo-picture.(4) system composition is relatively easy.

Integrated (solid) imaging technique record and the basic process reproduced：3D object spaces scene by microlens array (or Pin hole matrix) after be recorded on corresponding film, each lenticule (or pin hole) records a part of sky from different directions Between scene, the small figure of a width accordingly generated is referred to as " element image (subgraph) ".How many lenticule is individual with regard to how many Accordingly " element image ".The parallax information at space any point is all by this various " element image " dispersed record in whole On individual film or on CCD.It is corresponding aobvious when being placed on recording film after one microlens array thin slice with same parameter Show after the light-ray condensing that microlens array comes out various " element image (subgraph) " transmission/reflection/angles it is reducible go out it is original 3d space.

The acquisition system of current integrated three-dimensional imaging generally obtains the image of three-dimensional scenic using optical micro lens array, Optical system for collecting causes the obscurity boundary of each element image due to the diffraction of light, there is interference, causes integrated solid The problems such as picture contrast is poor, visual angle is small.

The content of the invention

The purpose of the embodiment of the present invention is to provide a kind of integrated three-dimensional imaging element image generation based on central projection Method, it is intended to the acquisition system for solving current integrated three-dimensional imaging generally obtains three-dimensional scenic using optical micro lens array Image, optical system for collecting causes the obscurity boundary of each element image due to the diffraction of light, there is interference, causes collection Into the problem of three-dimensional picture contrast is poor, visual angle is small.

The embodiment of the present invention is achieved in that a kind of integrated three-dimensional imaging element image generation based on central projection Method, the method for integrated three-dimensional imaging element image generation that should be based on central projection comprises the following steps：

Step one, 3 D stereo scene is set up first with computer, the coordinate for obtaining stereo scene is corresponding with information Database；

Step 2, sets virtual lenticule optical parametric, the optical parametric of true lenticule is complied with, in integrated solid Shown in the optical system of imaging system；

All three-dimensional scenic coordinates are gone to world coordinates by step 3 from local coordinate；

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates；

Step 5,2D images are converted into by virtual 3D targets according to different points of view, and element image is generated according to eye coordinates.

Further, it is somebody's turn to do concretely comprising the following steps for the method that the integrated three-dimensional imaging element image based on central projection is generated：

Step one, 3 D stereo scene is set up first with computer, the coordinate for obtaining stereo scene is corresponding with information Database, such as the database of three-dimensional scenic directly sets up three-dimensional scenic voxel database corresponding with coordinate；

Step 2, sets virtual lenticule optical parametric, meets the optical parametric of true lenticule, in integrated three-dimensional imaging Shown in the optical system of system, the dot matrix number of lenticule is 50 × 50, the focal length of lens is 3.5mm, and lenticule spacing is 1mm Optical parametric in the case of, the virtual microlens array number of default be 50 × 50, the resolution ratio 150 × 150 of lens；

All three-dimensional scenic coordinates are gone to world coordinates by step 3 from local coordinate；

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates, according to parameter setting, The eye coordinates Z of virtual lenticule_cam(virtual camera coordinate) has 50 × 50, Z_camThe 1st row the 1st row coordinate for (75, 75, Z) (upper left corner of dot chart), the row coordinate of the 1st row the 2nd is (75,225, Z), the like be to the row coordinate of the 1st row the 50th (75,49 × 150+75, Z), the same row coordinate of 2nd row the 1st is (225,75, Z), the like be to the row coordinate of the 50th row the 1st (49 × 150+75,75, Z), so has 2500 viewpoints；

Step 5, is converted into 2D images according to different points of view by virtual 3D targets, element image is generated according to eye coordinates, After the parameter setting of a lenticule is good, in this step, sets the value at visual angle and constitute integrated image element image It is long and wide, corresponding 2D central projections figure constitution element image, the quantity and element of viewpoint are obtained according to each different viewpoint Pattern matrix number is identical；

Viewpoint translation matrix is as follows：

(x, y, z) is three-dimensional scenic coordinate information in above formula, and (X', Y', Z') is that virtual lenticule projects areal coordinate, you can It is viewpoint starting point coordinate (upper left corner), W to complete (X, Y) in the acquisition of virtual lenticule EI images, formula_widthAnd H_heightFor member The length and width of sketch map picture, the system set the resolution ratio of element image as 150 × 150, i.e. W_width, 150, H_height=150, formula Middle MinZ is MinZ=16 in 3D scenes and the nearest distance in perspective plane, this example, MaxZ be 3D scenes with perspective plane it is farthest away from From this data changes with the change in depth of 3D scenes, according to above formula, can set up out each element image.Due to element image Resolution ratio be 150 × 150 (M × N), (X, Y) is that viewpoint starting point coordinate is (75,75) in formula, in addition virtual lenticule Dot matrix number is 50 × 50, therefore has 2500 viewpoint element images, and (X, Y) coordinate of each viewpoint can be released according to step 4 Value.

Further, the method for integrated three-dimensional imaging element image generation that should be based on central projection includes：

Step one, three-dimensional scene information is generated by computer；

Step 2, sets virtual lenticule optical parametric；

Step 3, world coordinates is gone to by three-dimensional scene information from local coordinate；

Mobile variable on object is represented with vector Δ p：

P '=p+ Δs p (1)

Here, p ' is the point after conversion, p is origin, and Δ p is mobile vector.According to coordinate relation, p (x, y) and p ' There is following relation between (x ', y ')：

In equation (2), Δ x and Δ y are to move variable along x and y directions；

According to homogeneous coordinates, a point turns into a column vector, and unit is 1, to three-dimensional coordinate system, is write as following homogeneous Coordinates matrix form：

In equation (3), Δ x, Δ y, Δ z are mobile vector Δ p (Δ x, Δ y, Δ z) coordinate variable；

Change of scale is that scene is zoomed in or out, that is, target rotation or zoom function, is determined according to change of scale Justice, to 3D systems, homogeneous coordinates are expressed as follows：

Here, Δ x, Δ y, Δ z represent X, Y, the scale coefficient of Z-direction；

ON is through any one zeroaxial axle.P points are moved to along any anglec of rotation Ω of ON axles, at this moment P points P1 points, according to the anglec of rotation and the coordinate of axial direction and p points, the coordinate of p1 points is as follows：

A in formula₁₁…a₃₃For spin matrix coefficient；

For any one vectorial Q=q₁i+q₂j+q₃K, unit vector is defined as follows：WhereinFor vector magnitude, i, j, k is unit vector, therefore；

Spin matrix：

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates；

Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') is respectively random plane With projection coordinate face, according to similitude (the Δ POZ of triangle_cam, Δ P'Z_surfZ_cam), obtain following equation：

Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') is respectively random plane With projection coordinate face.In view of Z coordinate axle, final equation is：

When being write by matrix-style, above formula is changed into：

Step 5, virtual 3D targets be converted into 2D conversion, in this step, is set the value at visual angle and is constituted collection Into the length and width of pictorial element image.After the parameter setting of a lenticule is good, it can be obtained according to each different viewpoint Obtain corresponding 2D central projections figure constitution element image.The quantity of viewpoint is identical with element image number of arrays, according to equation (10), Viewpoint translation matrix is as follows：

The acquisition of virtual lenticule EI images can be completed according to above formula.

The method for the generation of the integrated three-dimensional imaging element image based on central projection that the present invention is provided, first with calculating Machine sets up 3 D stereo scene, obtains the coordinate database corresponding with information of stereo scene；Set virtual lenticule Optical Parametric Number, complies with the optical parametric of true lenticule, is shown in the optical system of integrated stereo imaging system；By all three-dimensionals Scene coordinate goes to world coordinates from local coordinate；According to the position of virtual lenticule camera and spatial scene, determine that viewpoint is sat Mark；Virtual 3D targets are converted into 2D images according to different points of view, element image is generated according to eye coordinates.The present invention proposes to adopt With geometric projection, mapping techniques, virtual microlens array element image is constituted by computer, the element image of acquisition has more The characteristics of wide angular field of view, high-resolution and big depth of field, overcome the element image array that is obtained based on microlens array it Between interference, reconstructed clearly integrated stereo-picture.

Brief description of the drawings

Fig. 1 is the method stream of the integrated three-dimensional imaging element image generation provided in an embodiment of the present invention based on central projection Cheng Tu；

Fig. 2 is the stereo-picture acquisition system and display system of integration imaging technology provided in an embodiment of the present invention；

Fig. 3 is three-dimensional scenic target provided in an embodiment of the present invention with rotation transformation schematic diagram at any angle；

Fig. 4 is the viewpoint provided in an embodiment of the present invention based on central projection method and the relation schematic diagram of projection plane.

Embodiment

In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention It is further elaborated.It should be appreciated that the specific embodiments described herein are merely illustrative of the present invention, it is not used to Limit the present invention.

Below in conjunction with the accompanying drawings and specific embodiment to the present invention application principle be further described.

As shown in figure 1, the method for the generation of the integrated three-dimensional imaging element image based on central projection of the embodiment of the present invention Comprise the following steps：

S101：3 D stereo scene is set up first with computer, the coordinate number corresponding with information of stereo scene is obtained According to storehouse；

S102：Set virtual lenticule optical parametric, comply with the optical parametric of true lenticule, it is integrated it is three-dimensional into Shown in the optical system of picture system；

S103：All three-dimensional scenic coordinates are gone into world coordinates from local coordinate；

S104：According to the position of virtual lenticule camera and spatial scene, eye coordinates are determined；

S105：Virtual 3D targets are converted into 2D images according to different points of view, element image is generated according to eye coordinates.

The present invention's concretely comprises the following steps：

Step one, 3 D stereo scene is set up first with computer, the coordinate for obtaining stereo scene is corresponding with information Database, such as the database of three-dimensional scenic can directly set up three-dimensional scenic voxel database corresponding with coordinate；

Step 2, sets virtual lenticule optical parametric, the optical parametric of true lenticule is complied with, in integrated solid Shown in the optical system of imaging system, the dot matrix number of lenticule is 50 × 50, the focal length of lens is 3.5mm, lenticule spacing In the case of 1mm optical parametric, the virtual microlens array number of default is 50 × 50, the resolution ratio 150 × 150 of lens；

All three-dimensional scenic coordinates are gone to world coordinates by step 3 from local coordinate；

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates, according to parameter setting, The eye coordinates Z of virtual lenticule_cam(virtual camera coordinate) has 50 × 50, Z_camFirst coordinate be (75,75, Z) (point The upper left corner of the system of battle formations), second horizontal direction coordinate is (75,225, Z), the like；

Step 5, the conversion for be converted into 2D by virtual 3D targets generates element image, when the parameter of a lenticule After setting, in this step, set the value at visual angle and constitute the length and width of integrated image element image, according to each difference Viewpoint can obtain corresponding 2D central projections figure constitution element image, the quantity of viewpoint is identical with element image number of arrays；

Viewpoint translation matrix is as follows：

(x, y, z) is three-dimensional scenic coordinate information in above formula, and (X', Y', Z') is that virtual lenticule projects areal coordinate, you can It is viewpoint starting point coordinate (upper left corner) (75,75), W to complete (X, Y) in the acquisition of virtual lenticule EI images, formula_widthWith H_heightFor the length and width of element image, the system sets the resolution ratio of element image as 150 × 150, i.e. W_width, 150, H_height =150, MinZ is MinZ=16 in 3D scenes and the nearest distance in perspective plane, this example in formula, and MaxZ is 3D scenes and perspective plane Farthest distance, this data change with the change in depth of 3D scenes, according to above formula, can set up out each element image.

The specific embodiment of the present invention：

Step one, three-dimensional scene information is generated by computer；

Step 2, sets virtual lenticule optical parametric；

Step 3, world coordinates is gone to by three-dimensional scene information from local coordinate；

Mobile variable on object is represented with vector Δ p：

P '=p+ Δs p (1)

Here, p ' is the point after conversion, p is origin, and Δ p is mobile vector.According to coordinate relation, p (x, y) and p ' There is following relation between (x ', y ')：

In equation (2), Δ x and Δ y are to move variable along x and y directions；

According to homogeneous coordinates, a point turns into a column vector, and its unit is 1, to three-dimensional coordinate system, can be write as with Lower homogeneous coordinates matrix form：

In equation (3), Δ x, Δ y, Δ z are mobile vector Δ p (Δ x, Δ y, Δ z) coordinate variable；

Change of scale is that scene is zoomed in or out, that is, target rotation or zoom function, is determined according to change of scale Justice, to 3D systems, homogeneous coordinates are expressed as follows：

Here, Δ x, Δ y, Δ z represent X, Y, the scale coefficient of Z-direction；

It is through any one zeroaxial axle to understand that rotation transformation refer to ON in Fig. 3, Fig. 3.P points are along ON Any anglec of rotation Ω of axle, at this moment P points be moved to P1 points, according to the anglec of rotation and the coordinate of axial direction and p points, the coordinate of p1 points is such as Under：

A in formula₁₁…a₃₃For spin matrix coefficient；

For any one vectorial Q=q₁i+q₂j+q₃K, unit vector can be defined as follows：WhereinFor vector magnitude, i, j, k is unit vector, therefore；

Spin matrix：

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates；

Mapping transformation is the two dimension performance of three-dimensional scenic, and the present invention uses central projection method, confirms eye coordinates, projection Plane, Fig. 4 illustrates the position of virtual camera in central projection method；

In Fig. 4, Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') be respectively with Plane of anticipating and projection coordinate face, according to similitude (the Δ POZ of triangle_cam, Δ P'Z_surfZ_cam), following equation can be obtained：

Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') is respectively random plane With projection coordinate face.In view of Z coordinate axle, final equation is：

When being write by matrix-style, above formula is changed into：

Step 5, virtual 3D targets be converted into 2D conversion, in this step, is set the value at visual angle and is constituted collection Into the length and width of pictorial element image.After the parameter setting of a lenticule is good, it can be obtained according to each different viewpoint Obtain corresponding 2D central projections figure constitution element image.The quantity of viewpoint is identical with element image number of arrays, according to equation (10), Viewpoint translation matrix is as follows：

The acquisition of virtual lenticule EI images can be completed according to above formula.

The foregoing is merely illustrative of the preferred embodiments of the present invention, is not intended to limit the invention, all essences in the present invention Any modifications, equivalent substitutions and improvements made within refreshing and principle etc., should be included in the scope of the protection.

Claims (2)

1. a kind of method of the integrated three-dimensional imaging element image generation based on central projection, it is characterised in that center should be based on The method of the integrated three-dimensional imaging element image generation of projection comprises the following steps：

Step one, 3 D stereo scene is set up first with computer, obtains the coordinate data corresponding with information of stereo scene Storehouse, such as the database of three-dimensional scenic directly sets up three-dimensional scenic voxel database corresponding with coordinate；

Step 2, sets virtual lenticule optical parametric, meets the optical parametric of true lenticule, in integrated stereo imaging system Optical system in show, the dot matrix number of lenticule is 50 × 50, and the focal length of lens is f=3.5mm, and lenticule spacing is p= In the case of 1mm optical parametric, the virtual microlens array number of default is m × n=50 × 50, resolution ratio M × N=of lens 150×150；

All three-dimensional scenic coordinates are gone to world coordinates by step 3 from local coordinate；

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates, according to parameter setting, virtually The eye coordinates Z of lenticule_cam, i.e. virtual camera coordinate has 50 × 50, Z_camThe 1st row the 1st row coordinate for (75,75, Z), the row coordinate of the 1st row the 2nd be (75,225, Z), the like to the row coordinate of the 1st row the 50th be (75,49 × 150+75, Z), together The row coordinate of the 2nd row of sample the 1st be (225,75, Z), the like to the row coordinate of the 50th row the 1st be (49 × 150+75,75, Z), this Sample has 2500 viewpoints；

Step 5, is converted into 2D images according to different points of view by virtual 3D targets, element image is generated according to eye coordinates, when one The parameter setting of individual lenticule well after, in this step, set visual angle value and constitute integrated image element image length and Width, corresponding 2D central projections figure constitution element image, the quantity and element image of viewpoint are obtained according to each different viewpoint Number of arrays is identical；

Viewpoint translation matrix is as follows：

$\left[\begin{array}{c}{X}^{\′}\\ Y^{\′}\\ Z^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}\frac{W_{width}}{2}& 0& 0& 0\\ 0& -\frac{H_{height}}{2}& 0& 0\\ 0& 0& MaxZ-MinZ& 0\\ X-\frac{W_{width}}{2}& Y-\frac{H_{height}}{2}& MinZ& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]$

(x, y, z) is three-dimensional scenic coordinate information in above formula, and (X', Y', Z') is that virtual lenticule projects areal coordinate, you can completed (X, Y) is viewpoint starting point coordinate in the acquisition of virtual lenticule EI images, formula, and positioned at the upper left corner, W_widthAnd H_heightFor member The length and width of sketch map picture, the resolution ratio of default element image is 150 × 150, i.e. W_width=150, H_height=150, in formula MinZ is 3D scenes and the nearest distance in perspective plane, and MinZ=16, MaxZ is 3D scenes and the farthest distance in perspective plane, this data Change with the change in depth of 3D scenes, according to above formula, can build

Found out each element image；Because resolution ratio M × N of element image is 150 × 150, viewpoint starting point coordinate in formula (X, Y it is) (75,75), the dot matrix number of virtual lenticule is 50 × 50 in addition, therefore has 2500 viewpoint element images, according to step Rapid four can release (X, Y) coordinate value of each viewpoint.

2. the method that the integrated three-dimensional imaging element image based on central projection is generated as claimed in claim 1, its feature exists In three-dimensional scene information is gone to world coordinates by step 3 from local coordinate；

Mobile variable on object is represented with vector Δ p：

P '=p+ Δs p (1)

Here, p ' is the point after conversion, p is origin, and Δ p is mobile vector；Foundation coordinate relation, p (x, y) and p ' (x ', Y ') between there is following relation：

$\left\{\begin{array}{c}{x}^{\′}=x+\mathrm{\Δ}x\\ y^{\′}=y+\mathrm{\Δ}y\end{array}\right.---\left(2\right)$

In equation (2), Δ x and Δ y are to move variable along x and y directions；

According to homogeneous coordinates, a point turns into a column vector, and unit is 1, to three-dimensional coordinate system, is write as following homogeneous coordinates Matrix form：

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}1& 0& 0& 0\\ 0& 1& 0& 0\\ 0& 0& 1& 0\\ \mathrm{\Δ}x& \mathrm{\Δ}y& \mathrm{\Δ}z& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]---\left(3\right)$

In equation (3), Δ x, Δ y, Δ z are mobile vector Δ p (Δ x, Δ y, Δ z) coordinate variable；

Change of scale is that scene is zoomed in or out, that is, target rotation or zoom function, right according to change of scale definition 3D systems, homogeneous coordinates are expressed as follows：

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}1/\mathrm{\Δ}x& 0& 0& 0\\ 0& 1/\mathrm{\Δ}y& 0& 0\\ 0& 0& 1/\mathrm{\Δ}z& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]---\left(4\right)$

Here, Δ x, Δ y, Δ z represent X, Y, the scale coefficient of Z-direction；

ON is through any one zeroaxial axle；P points are moved to P along any anglec of rotation Ω of ON axles, at this moment P points₁Point, According to the anglec of rotation and the coordinate of axial direction and P points, P₁The coordinate of point is as follows：

$\left[\begin{array}{c}{x}^{\′}\\ y^{\′}\\ z^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}{a}_{11}& a_{12}& a_{13}& 0\\ a_{21}& a_{22}& a_{23}& 0\\ a_{31}& a_{32}& a_{33}& 0\\ 0& 0& 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\\ z\\ 1\end{array}\right]---\left(5\right)$

A in formula₁₁…a₃₃For spin matrix coefficient；

For any one vectorial Q=q₁i+q₂j+q₃K, unit vector is defined as follows：Wherein For vector magnitude, i, j, k is unit vector, therefore；

$\cos \mathrm{\α}=\frac{q_1}{\sqrt{q_1^2+q_2^2+q_3^2}}=n_1,\cos \mathrm{\β}=\frac{q_2}{\sqrt{q_1^2+q_2^2+q_3^2}}=n_2,\cos \mathrm{\γ}=\frac{q_3}{\sqrt{q_1^2+q_2^2+q_3^2}}=n_3---\left(6\right)$

Spin matrix：

$R=\left[\begin{array}{cccc}{n}_1^2+\left(1-n_1^2\right)\cos \mathrm{\Ω}& n_1{n}_2\left(1-\cos \mathrm{\Ω}\right)+n_3\sin \mathrm{\Ω}& n_1{n}_3\left(1-\cos \mathrm{\Ω}\right)-n_2\sin \mathrm{\Ω}& 0\\ n_1{n}_2\left(1-\cos \mathrm{\Ω}\right)-n_3\sin \mathrm{\Ω}& n_2^2+\left(1-n_2^2\right)\cos \mathrm{\Ω}& n_2{n}_3\left(1-\cos \mathrm{\Ω}\right)+n_1\sin \mathrm{\Ω}& 0\\ n_1{n}_3\left(1-\cos \mathrm{\Ω}\right)+n_2\sin \mathrm{\Ω}& n_2{n}_3\left(1-\cos \mathrm{\Ω}\right)-n_1\sin \mathrm{\Ω}& n_3^2+\left(1-n_3^2\right)\cos \mathrm{\Ω}& 0\\ 0& 0& 0& 1\end{array}\right]---\left(7\right);$

Step 4, according to the position of virtual lenticule camera and spatial scene, determines eye coordinates；

Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') is respectively random plane and projection Coordinate surface, according to similitude (the Δ POZ of triangle_cam, Δ P'Z_surfZ_cam), obtain following equation：

$\left\{\begin{array}{c}\frac{X^{\′}}{\left(Z_{cam}-Z_{surf}\right)}=\frac{X}{\left(Z_{cam}-Z\right)}\\ \frac{Y^{\′}}{\left(Z_{cam}-Z_{surf}\right)}=\frac{Y}{\left(Z_{cam}-Z\right)}\end{array}\right.---\left(8\right)$

Z_camFor virtual camera coordinate, Z_surfFor projection surface position, (X, Y, Z) and (X', Y', Z') is respectively random plane and projection Coordinate surface；In view of Z coordinate axle, final equation is：

$\left\{\begin{array}{c}{X}^{\′}=\frac{X\left(Z_{cam}-Z_{surf}\right)}{\left(z_{cam}-z\right)}\\ Y^{\′}=\frac{Y\left(Z_{cam}-Z_{surf}\right)}{\left(Z_{cam}-Z\right)}\\ Z^{\′}=Z-Z_{surf}\end{array}\right.---\left(9\right)$

When being write by matrix-style, above formula is changed into：

$\left[\begin{array}{c}{X}^{\′}\\ Y^{\′}\\ Z^{\′}\\ 1\end{array}\right]=\left[\begin{array}{cccc}\frac{\left(Z_{cam}-Z_{surf}\right)}{\left(Z_{cam}-Z\right)}& 0& 0& 0\\ 0& \frac{\left(Z_{cam}-Z_{surf}\right)}{\left(Z_{cam}-Z\right)}& 0& 0\\ 0& 0& 1& 0\\ 0& 0& 0& -Z_{surf}\end{array}\right]\left[\begin{array}{c}X\\ Y\\ Z\\ 1\end{array}\right]---\left(10\right).$