Patent Publication Number: US-10319111-B2

Title: Image projection device for 3D measurement and calibration method for calibration of camera and projector

Description:
CROSS REFERENCE TO RELATED APPLICATIONS 
     This application claims the benefit of Japanese Priority Patent Application JP 2013-273260 filed Dec. 27, 2013, the entire contents of which are incorporated herein by reference. 
     BACKGROUND 
     The technology disclosed in the present specification relates to an image projection device capable of performing three-dimensional measurement by photographing a projection image with a camera and a calibration method thereof. There is known a three-dimensional measurement device combining a projector and a camera. In such a kind of device, a projector projects a known pattern image on an object, and the object on which the pattern image is projected is photographed with a camera. Then, the photographed image is subjected to image processing, thereby three-dimensional information of the object can be obtained. 
     In the device combining a projector and a camera, it is necessary to perform calibration of parameters regarding both the projector and the camera. The estimation of parameters with high accuracy has a problem of long man-hours for adjustment. For example, the method for projecting a calibration pattern using a calibration marker attached on a plane mirror, a screen, and a projection device is proposed for a three-dimensional form measurement device capable of performing calibration of projector parameters and camera parameters using only the inner structure of the three-dimensional measurement device without requiring arrangement of a special marker in calibration, by embedding a reference object for calibration in the system and automatically calculating world coordinates using a length of the plane mirror that is an invariant (see JP 2013-214206A, for example). 
     Moreover, in the projector calibration, there is proposed a three-dimensional form measurement device capable of preventing projector parameters from being inaccurate by using a group of intersection coordinates of a horizontal slit pattern and a vertical slit pattern as image coordinates used for projector calibration without including therein coordinates outside the image coordinate range used in camera calibration (see JP 2007-309660A, for example). 
     SUMMARY 
     It is desirable to provide an excellent image projection device capable of performing three-dimensional measurement by photographing a projection image with a camera and performing calibration of parameters with high accuracy with a small number of man-hours for adjustment, and a calibration method thereof. 
     The present disclosure is made in view of the above problems. According to an embodiment of the present disclosure, there is provided an image projection device including a camera, a projector configured to project an image, a camera calibration unit configured to perform calibration of the camera, a projector calibration unit configured to perform calibration of the projector, and an image correction unit configured to correct the image projected from the projector based on a result of the calibration. The projector calibration unit performs ray tracing of a known checker pattern on which structural light is projected by the projector, and estimates parameters by acquiring correspondence relation between a lattice point of the checker pattern and projector coordinates. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may perform calibration while considering lens distortion of the projector or without using a calibration result by the camera calibration unit. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may estimate distortion parameters by evaluating a distortion amount based on a group of lattice points supposed to be in a straight line on the projector coordinates, and estimates parameters of the projector based on correspondence relation between a lattice point on an image after distortion correction and world coordinates. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may estimate the distortion parameters of the projector by a Levenberg-Marquardt (LM) method, with an inclination difference between two candidates of straight lines on which a group of lattice points are supposed to be in a straight line as a distortion evaluation amount. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may estimate a perspective projection matrix including internal parameters and external parameters of the projector by nonlinear optimization, based on correspondence relation between the lattice point on the image after distortion correction and the world coordinates. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may estimate the perspective projection matrix by performing the nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by the LM method. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may find correspondence relation between the lattice point of the checker pattern and the projector coordinates with sub-pixel accuracy. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may find LocalHomography of calibration of projector pixels limited to surroundings of the lattice point. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may find LocalHomography of the projector pixels with a limit to a surrounding area of the lattice point small enough to ignore influences of lens distortion of the projector. 
     According to another embodiment of the present disclosure, the projector calibration unit of the image projection device according to the embodiment may find the LocalHomography of the projector pixels by performing robust estimation while considering a decoding error of the structural light. 
     According to another embodiment of the present disclosure, the camera calibration unit of the image projection device according to the embodiment may detect the lattice point from an image obtained by photographing the known checker pattern with the camera, estimates distortion parameters by evaluating a distortion amount based on a group of lattice points supposed to be in a straight line, and estimates parameters of the camera based on correspondence relation between a lattice point on an image after distortion correction and world coordinates. 
     According to another embodiment of the present disclosure, the camera calibration unit of the image projection device according to the embodiment may estimate the distortion parameters of the camera by an LM method, with an inclination difference between two candidates of straight lines on which a group of lattice points are supposed to be in a straight line as a distortion evaluation amount. 
     According to another embodiment of the present disclosure, the camera calibration unit of the image projection device according to the embodiment may estimate a perspective projection matrix including internal parameters and external parameters of the camera by nonlinear optimization, based on correspondence relation between the lattice point on the image after distortion correction and the world coordinates. 
     According to another embodiment of the present disclosure, the camera calibration unit of the image projection device according to the embodiment may estimate the perspective projection matrix by performing the nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by the LM method. 
     According to another embodiment of the present disclosure, the image projection device according to the embodiment may further include a ray tracing formulation unit configured to formulate ray tracing for tracing world coordinates obtained by projecting a pixel on the projector coordinates with ray influenced by lens distortion. 
     According to another embodiment of the present disclosure, the image projection device according to the embodiment may further include a reverse ray tracing formulation unit configured to formulate reverse ray tracing for tracing a pixel on the projector coordinates irradiated with the ray for projecting world coordinates while considering influences of lens distortion. 
     According to another embodiment of the present disclosure, the reverse ray tracing formulation unit of the image projection device according to the embodiment may perform ray tracing of a gray code projected by the projector on the checker pattern with known world coordinates, calculates a corresponding point of the world coordinates and the projector coordinates in a state with projector distortion, estimates a distortion correction function, obtains correspondence relation between the world coordinates and projection coordinates having no distortion, and formulates reverse ray tracing. 
     According to another embodiment of the present disclosure, the ray tracing formulation unit of the image projection device according to the embodiment may estimate a reverse distortion correction function D′ for correcting the projector coordinates having no distortion to projector coordinates having distortion, and formulates ray tracing for tracing world coordinates projected on a projector pixel. 
     According to another embodiment of the present disclosure, at least one of the camera calibration unit and the projector calibration unit of the image projection device according to the embodiment may estimate the parameters with high accuracy with a small number of photographed images, using known depth information of a depth from the camera to a checker board. 
     According to another embodiment of the present disclosure, a calibration method of an image projection device including a camera and a projector, the calibration method including performing ray tracing of a known checker pattern on which structural light is projected by the projector, and estimating parameters by acquiring correspondence relation between a lattice point of the checker pattern and projector coordinates. In the technology disclosed in the present specification, it is possible to provide an excellent image projection device capable of performing three-dimensional measurement by photographing a projection image with a camera and performing calibration of parameters with high accuracy with a small number of man-hours for adjustment, and a calibration method thereof. 
     An image projection device to which the technology disclosed in the present specification is applied can perform calibration of a projector without using a result by a camera calibration unit and estimate parameters of the projector with high accuracy. Moreover, the image projection device to which the technology disclosed in the present specification is applied can estimate parameters with high accuracy while considering lens distortion of the projector and find correspondence relation between world coordinates and projector pixels with sub-pixel accuracy. 
     Moreover, the image projection device to which the technology disclosed in the present specification is applied can formulate ray tracing and reverse ray tracing while considering projector distortion. 
     Moreover, the image projection device to which the technology disclosed in the present specification is applied can estimate, using known depth information, parameters with high accuracy based on a small number of photographed images. 
     Note that the effects described in the present specification are merely examples, and the effects of the present disclosure are not limited thereto. Moreover, the present disclosure may exert additional effects other than the above-described effects. 
     Other intentions, features, and advantages of the technology disclosed in the present specification will become clear by the following detail description based on the later-described embodiment and appended drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram schematically illustrating a configuration of a projection-type image display device  100  according to an embodiment of the technology disclosed in the present specification; 
         FIG. 2  is a diagram illustrating an inner configuration example of a projection unit  101 ; 
         FIG. 3  is a diagram illustrating an inner configuration example of an image processing unit  102 ; 
         FIG. 4  is a diagram for explaining a basic view of calibration; 
         FIG. 5  is a diagram for explaining a basic view of calibration; 
         FIG. 6  is a diagram for explaining a basic view of calibration; 
         FIG. 7  is a diagram illustrating a processing flow of calibration of a camera; 
         FIG. 8  is a diagram illustrating a processing flow of calibration of a projector; 
         FIG. 9  is a diagram for explaining a projector coordinate calculation method using gray codes; 
         FIG. 10  is a diagram for explaining a projector coordinate calculation method using gray codes; 
         FIG. 11  is a diagram for explaining a projector coordinate calculation method using gray codes; 
         FIG. 12  is a diagram illustrating a situation in which a checker board  1201  on which the projection unit  101  projects structural light  1202  is photographed by a camera unit  104 ; 
         FIG. 13  is a diagram illustrating a situation in which the ray tracing of the structural light  1202  projected by the projection unit  101  is performed to obtain correspondence relation between a lattice point of the checker pattern and projector coordinates; 
         FIG. 14  is a diagram for explaining a method of finding, with sub-pixel accuracy, projector coordinates at a lattice point of the checker pattern (with sub-pixel accuracy of a camera); 
         FIG. 15  is a diagram schematically illustrating a method of ray tracing considering projector distortion; 
         FIG. 16  is a diagram schematically illustrating a method of reverse ray tracing considering projector distortion; 
         FIG. 17  is a diagram for explaining a method of performing ray tracing and reverse ray tracing considering projector distortion of the projection unit  101 ; and 
         FIG. 18  is a diagram illustrating a situation in which the checker board is photographed using known depth information. 
     
    
    
     DETAILED DESCRIPTION OF THE EMBODIMENT(S) 
     Hereinafter, preferred embodiments of the present disclosure will be described in detail with reference to the appended drawings. Note that, in this specification and the appended drawings, structural elements that have substantially the same function and structure are denoted with the same reference numerals, and repeated explanation of these structural elements is omitted. 
       FIG. 1  schematically illustrates a configuration of the projection-type image display device  100  according to an embodiment of the technology disclosed in the present specification. One use of the projection-type image display device  100  is enlarged projection of a screen, and another use is three-dimensional measurement. The projection-type image display device  100  illustrated in  FIG. 1  includes a projection unit  101 , the image processing unit  102 , an image input unit  103 , the camera unit  104 , and a parameter calculation detection unit  105 . Hereinafter, each unit will be described. The image input unit  103  inputs an image signal from a projection image supply source such as a personal computer, a television (TV) receiver, a Blu-ray Disc disk reproducing device, and a game machine (any of them is not illustrated). 
     The image processing unit  102  processes an image projected from the projection unit  101 . The image output from the image processing unit  102  is an external image supplied from the image input unit  103  and a test pattern generated in the image processing unit  102 . The image processing unit  102  also corrects an input image from the image input unit  103  based on parameters supplied from the parameter calculation unit  105 . 
     The projection unit  101  projects an image output from the image processing unit  102  on a body to be projected through a projection lens  101 A. The body to be projected is an object displaying an enlarged image of a screen, for example, and an object of three-dimensional measurement, for example. 
     The camera unit  104  is disposed at a position different from an irradiation position of the projection unit  101 , and an optical axis is set such that a photographed range includes an irradiation range of the projection unit  101  as much as possible. Then, an image obtained by light condensed through the condenser lens  104 A is photographed. In the embodiment, the camera unit  104  photographs a screen or an object to be measured in a state where an image such as a test pattern is projected by the projection unit  101 . An imaging element of the camera unit  104  is a charge coupled device (CCD) or a complementary metal oxide semiconductor (CMOS), for example, and in the following, a pixel is also referred to as a “camera pixel”. In addition, the coordinate system of a camera pixel is also referred to as “camera coordinates”. 
     The parameter calculation unit  105  calculates parameters using a projection image photographed with the camera  104  and outputs them to the image processing unit  102 . The parameters calculated by the parameter calculation unit  105  include parameters contained in a distortion correction function for correcting lens distortion, internal parameters of the projection unit  101  and the camera unit  104 , and external parameters of the projection unit  101  and the camera unit  104 . According to the technology disclosed in the present specification, the parameter calculation unit  105  calculates parameters with high accuracy with a small number of man-hours for adjustment. The detail will be described later. 
       FIG. 2  illustrates an inner configuration example of the projection unit  101 . The projection unit  101  illustrated in  FIG. 2  includes a liquid crystal panel  201 , an illumination optical unit  202 , a liquid crystal panel drive unit  204 , and a projection optical unit  203 . The liquid crystal panel drive unit  204  drives the liquid crystal panel  201  based on image signals input from the image processing unit  102  and draws a presentation image or a test pattern on the display screen. A pixel of the liquid crystal panel  201  is also referred to as a “projector pixel” in the following. Moreover, the coordinate system of the liquid crystal panel  201  is also referred to as “projector coordinates”. 
     The illumination optical unit  202  irradiates the liquid crystal panel  201  from the back face. When the projection-type image display device  100  is a pico-projector, a light emitting diode (LED) or laser, for example, is used as a light source of the illumination optical unit  202 . The projection lens  101 A includes one or two or more optical lenses, and performs enlarged projection of light passing through the liquid crystal panel  201  on a body to be projected (not illustrated). 
     The projection unit  101  projects an input image to the image input unit  103  or a test pattern generated in the projection-type image display device  100 . In the embodiment, the projection unit  101  projects gray codes of a vertical pattern and a horizontal pattern as a test pattern, and the camera unit  104  photographs them. The detail will be described later. 
       FIG. 3  illustrates an inner configuration example of the image processing unit  102 . The image processing unit  102  illustrated in  FIG. 3  includes an image writing/reading control unit  301 , a frame memory  302 , an image correction unit  303 , an image quality adjustment unit  304 , a test pattern generation unit  305 , and an output image switching unit  305 . The frame memory  302  stores images supplied from the image input unit  103 . The image writing/reading control unit  301  controls writing and reading of image frames relative to the frame memory  302 . 
     The image correction unit  303  corrects an image read out from the frame memory  302  based on parameters received from the parameter calculation unit  105  so that distortion occurred when projected on a screen from the projection unit  101  is solved. 
     The image quality adjustment unit  304  performs image quality adjustment of brightness, contrast, synchronization, tracking, color density, and color tone, for example, so that the projection image after distortion correction is in a desired display state. 
     The test pattern generation unit  305  generates a test pattern used when the correction amount detection unit  105  calculates projective transformation parameters. In the embodiment, the gray codes having a vertical pattern and a horizontal pattern are used as test patterns. 
     The output image switching unit  306  switches images output to the projection unit  101 . For example, when input images from an image supply source such as a personal computer, a TV receiver, a media reproducing device, and a game machine (any of them is not illustrated) are projected on a screen to make a presentation, for example, the output image switching unit  306  outputs output images from the image quality correction unit  304  to the projection unit  101 . Moreover, when parameters of the projection unit  101  and the camera unit  104  are calculated, the output image switching unit  306  outputs a test pattern generated by the test pattern generation unit  305  to the projection unit  101 . When three-dimensional measurement is performed using the projector (projection unit  101 ) and the camera (camera unit  104 ) such as the projection-type image display device  100  illustrated in  FIG. 1 , it is necessary to perform calibration of internal parameters of the projector and the camera and external parameters of the projector and the camera. The technology disclosed in the present specification aims at calculating parameters with high accuracy with a small number of man-hours for adjustment. 
     Here, the internal parameters of the camera include an image center (main point) (o x , o y ), a focal length f, and an effective size of a pixel (a size per pixel) (k x , k y ). Moreover, the external parameters of the camera are determined depending on a position T and an attitude R of a camera coordinate system in a world coordinate system. The position T moves in parallel and is expressed by a 3×1 vector. The attitude R rotates and is represented by a 3×3 matrix. The basic view of calibration will be described with reference to  FIG. 4  to  FIG. 6 . First, as illustrated in  FIG. 4 , the camera unit  104  of the projection-type image display device  100  photographs an object  401  with known world coordinates (X, Y, Z). As illustrated in  FIG. 5 , image coordinates (x′, y′) of a photographed image  501  by the camera unit  104  has distortion. When the distortion correction is performed on the image coordinates (x′, y′) having distortion, the image coordinates (x, y) not having distortion is obtained, as illustrated in  FIG. 6 . 
     Moreover, the projection unit  101  of the projection-type image display device  100  projects the object  401  with the known world coordinates (X, Y, Z). As illustrated in  FIG. 5 , imaging surface observed coordinates (x′, y′) of the projection image  501  by the projection unit  101  has distortion. When the distortion correction is performed on the image coordinates (x′, y′) having distortion, an image  601  with the image coordinates (x, y) not having distortion is presented, as illustrated in  FIG. 6 . The model expression of the camera and the projector is as the following expression (1), as a relational expression of the image coordinates (x, y) having no distortion, the imaging surface image coordinates (x′, y′), and the world coordinates (X, Y, Z). 
     
       
         
           
             
               
                 
                   
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                   = 
                   
                     
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                       ⁡ 
                       
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                             | 
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     In the above expression (1), the D is a distortion correction function. 
     With distortion center coordinates (d cx , d cy ), a distance r from the distortion center is expressed as the following expression (2). Moreover, with distortion coefficients k 1  to k 3 , radius distortion Δr is expressed as the following expression (3). Moreover, with tangent distortion coefficients p 1 , p 2 , tangent distortion Δt x , Δt y  is expressed as the following expressions (4), (5), respectively. The imaging surface observed coordinates (x′, y′) can be expressed as the following expression (6) using the distance r from the distortion center, the radius distortion Δr, and the tangent distortion Δt x , Δt y . 
     
       
         
           
             
               
                 
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     In the above expression (1), the K is internal parameters, and [R|T] is external parameters. The K[R|T] is a perspective projection matrix and is expressed as the following expression (7). 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
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     In the internal parameters, f=(fx, fy) is a focal length and c=(cx, cy) is a main point. In the external parameters, the R is a rotating component, and the T is a translation component. 
     In the above expression (1), the estimation of a perspective projection matrix based on the corresponding point of the world coordinates (X, Y, Z) and the image coordinates (x′, y′) is an optimization problem. It is possible to estimate the above internal parameters and external parameters by resolving such an optimization problem. With the image coordinates (x, y) detected by photographing by the camera  104  and the image coordinates (x′, y′) re-projected by the projection unit  101 , a re-projection error is expressed as the following expression (8). The perspective projection matrix can be estimated by performing nonlinear optimization of a geometrically significant re-projection error using the Levenberg-Marquardt (LM) method.
 
sqrt((x−x′) 2 +(y−y′) 2 )  (8)
 
     The processing flow of calibration of the camera will be described with reference to  FIG. 7 . The camera unit  104  photographs, from a plurality of distances Z 1  and Z 2 , a checker board  701  with a latticed pattern, as an object with known world coordinates (F 701 ). It is supposed that the depth information of the distances Z 1  and Z 2  is known. 
     The parameter calculation unit  105  detects lattice points of the checker pattern based on the photographed image of the checker board  701  (F 702 ). Next, a group of lattice points supposed to be in a line is extracted, and distortion parameters are estimated by nonlinear optimization such as the LM method, for example, with a difference of inclination of two straight lines  702 ,  703  on which a group of lattice points are supposed to be arranged, as a distortion evaluation amount (F 703 ). As described above, the distortion parameters include distortion center coordinates (d cx , d cy ), distortion coefficients k 1  to k 3 , and tangent distortion coefficients p 1 , p 2  (as described above). 
     Next, the photographed image coordinates (x′, y′) are corrected to image coordinates (x, y) having no distortion using the estimated distortion parameters (F 704 ). The relation of the corresponding point of the world coordinates (X, Y, Z) and the image coordinates (x, y) is expressed as the following expression (9) using the perspective projection matrix K[R|T]. The perspective projection matrix is estimated by nonlinear optimization such as the LM method based on the corresponding point of the world coordinates (X, Y, Z) and the image coordinates (x, y) (F 705 ). The K is internal parameters, and the R and the T are respectively a rotating component and a translation component relative to the checker board  701  in the external parameters. 
     
       
         
           
             
               
                 
                   
                     [ 
                     
                       
                         
                           x 
                         
                       
                       
                         
                           y 
                         
                       
                       
                         
                           1 
                         
                       
                     
                     ] 
                   
                   = 
                   
                     
                       K 
                       ⁡ 
                       
                         [ 
                         
                           R 
                           | 
                           T 
                         
                         ] 
                       
                     
                     ⁡ 
                     
                       [ 
                       
                         
                           
                             X 
                           
                         
                         
                           
                             Y 
                           
                         
                         
                           
                             Z 
                           
                         
                         
                           
                             1 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   9 
                   ) 
                 
               
             
           
         
       
     
     Subsequently, the processing flow of calibration of the projector will be described with reference to  FIG. 8 . 
     First, a calibration camera photographs, from the distance Z 1 , a checker board  801  with a latticed pattern, as an object with known world coordinates (F 801 ). The calibration camera may be the camera unit  104 . It is supposed that the depth information of the distances Z 1  is known. Next, the projection unit  101  alternately projects  24  patterns of gray codes constituted by the combination of vertical straight lines  802  and  20  patterns of gray codes constituted by the combination of horizontal straight lines  803  on the checker board  801 , and the calibration camera photographs the gray codes every time they are projected (F 802 ). Then, the distance from the checker board  801  to the calibration camera is changed to Z 2 , and the photographing of the checker board  801  by the calibration camera and the projection and the photographing of the gray codes are performed repeatedly (F 803 ). It is supposed that the depth information of the distance Z 2  is known. 
     Here, the gray codes are projected by the projection unit  101  and photographed by the calibration camera in order to find which ray (ray from which pixel) of the projection unit  101  is projected on a lattice point, that is, projector coordinates. The projection unit  101  does not photograph an image (an image projected by the projection unit  101 ) like a camera. Thus, in the embodiment, the projector coordinates are acquired using the gray code pattern projection method. The calculation method of the projector coordinates using the gray code will be described with reference to  FIG. 9  to  FIG. 11 . First, as illustrated in  FIG. 9 , a checker board  901  is photographed with the calibration camera to obtain a checker photographed image  902 . Next, as illustrated in  FIG. 10 , the projection unit  101  projects gray codes constituted by 24 binary patterns of vertical straight lines and gray codes constituted by 20 binary patterns of horizontal straight lines while switching the patterns in time series, and the calibration camera photographs the gray codes every time they are projected. The binary patterns of the gray codes are projected sequentially, whereby it is possible to divide space to areas expressed by the gray codes. Then, as illustrated in  FIG. 11 , a code in time series is acquired to decode the gray codes for every remarked point in the checker photographed image  902  and acquire projector coordinates, that is, the corresponding pixel position. The remarked point is a lattice point of the checker, for example. When a code “ . . . 0 0 0 1 1 0 0 0 . . . ” (in which 1 is light and 0 is dark), for example, is obtained at a remarked lattice point, as a result of projection and photographing of the gray codes in time series, it is possible to acquire the corresponding pixel position. 
     The description of the processing flow of calibration of the projector will be continued with reference to  FIG. 8  again. Using the gray code projection method, which ray (ray from which pixel) of the projection unit  101  is projected on a lattice point, that is, projector coordinates (x′, y′) is calculated (F 804 ). 
     Subsequently, distortion parameters are estimated by nonlinear optimization such as the LM method, with a difference of inclination of two straight lines  804 ,  805  on which a group of lattice points are supposed to be arranged, as a distortion evaluation amount (F 805 ). As described above, the distortion parameters include distortion center coordinates (d cx , d cy ), distortion coefficients k 1  to k 3 , and tangent distortion coefficients p 1 , p 2  (as described above). Next, the projector coordinates (x′, y′) are corrected to projector coordinates (x, y) having no distortion, using the estimated distortion parameters (F 806 ). 
     The relation of the corresponding point of the world coordinates (X, Y, Z) and the projector coordinates (x, y) is expressed as the above expression (9) using the perspective projection matrix K[R|T]. The perspective projection matrix is estimated by nonlinear optimization such as the LM method based on the corresponding point of the world coordinates (X, Y, Z) and the image coordinates (x, y) (F 807 ). The K is internal parameters, and the R and T are respectively a rotating component and a translation component relative to the checker board  701  in the external parameters. 
     In the past, the system including a projector and a camera generally performs calibration of the projector using a calibration result of the camera. For example, after the calibration of the camera is performed by photographing a checker pattern with a known size and form with the camera, the calibration of the projector is performed by projecting the checker pattern by the projector and photographing the projection image with the camera to find a size and positional relation of the checker pattern. However, when the calibration of the projector is performed using a calibration result of the camera, there occurs a problem in which the calibration of the projector is influenced by a camera error. 
     For such a problem, the projection-type image display device  100  according to the embodiment projects structural light from the projection unit  101  and traces the ray. One example of the structural light is a gray code. The binary patterns of the gray code are projected sequentially, whereby the space is divided to areas expressed by the gray codes. 
     The camera unit  104  photographs the image obtained by projecting the structural light  1202  on the checker board  1201  by the projection unit  101  (see  FIG. 12 ). Thus, the ray (ray from a pixel) with which a lattice point on the checker board  1201  is irradiated is traced (see  FIG. 13 ) to obtain the correspondence relation between the lattice point of the checker and the projector coordinates. The obtaining of the correspondence relation between the lattice point of the checker and the projector coordinates by ray tracing of the structural light indicates obtaining of the relation by photographing the checker pattern by the projector, and a calibration result of the camera unit  104  is not used to obtain the correspondence relation. When the correspondence relation between each lattice point of the checker pattern and the projector coordinates is obtained, the calibration processing of the projector can be performed in pixel units by the procedure same as the calibration processing of the camera including distortion estimation (F 805 ), distortion correction (F 806 ), and parameter estimation (F 807 ) (see  FIG. 8 ), without using a calibration result of the camera. 
     Moreover, the calibration of the camera is performed by finding Homography between an image obtained by photographing a checker pattern having a known size and form with the camera and the original checker pattern, that is, a projective transformation matrix. In the past method in which the calibration processing of the projector is performed by photographing a checker pattern projected by a projector with a camera and finding a size and positional relation of the checker pattern using Homography of calibration of the camera (see JP 2013-214206A, for example), the lens distortion of the projector is not considered. Thus, there occurs a problem in which the parameters of the projector are not estimated with high accuracy. 
     By contrast, in the projection-type image display device  100  of the embodiment, the projection unit  101  projects the structural light  1202  on the checker board  1201 , and the ray is traced (see  FIG. 12 ) to obtain the correspondence relation between a lattice point of the checker and the projector coordinates. Thus, similarly to the calibration processing of the camera considering lens distortion, the calibration processing considering distortion of the lens  101 A of the projection unit  101  is performed (see  FIG. 13 ). 
     Moreover, in the embodiment, the structural light  1202  projected on the checker board  1201  from the projection unit  101  is ray-traced, and the correspondence relation between a lattice point of the checker pattern and the projector coordinates is found with sub-pixel accuracy of the pixel of the projection unit  101 , so as to perform calibration processing of the projector in sub-pixel units. 
     First, the method of performing calibration processing of the projector while considering lens distortion will be described. The camera unit  104  photographs the image obtained by projecting the structural light  1202  on the checker board  1201  by the projection unit  101  (see  FIG. 12 ). Thus, the ray (ray from a pixel) with which a lattice point on the checker board  1201  is irradiated is traced (see  FIG. 13 ) to obtain the correspondence relation between the lattice point of the checker pattern and the projector coordinates. Such obtaining indicates obtaining of the relation by photographing the checker pattern by the projector. Moreover, similarly to the calibration processing of the camera, the distortion of the lens  101 A of the projection unit  101  is considered. Thus, it is possible to estimate parameters of the projector with high accuracy. 
     Furthermore, the following will describe the method of finding projector coordinates at a lattice point (with sub-pixel accuracy of the camera) of the checker pattern with sub-pixel accuracy. 
       FIG. 14  illustrates an image  1403  obtained by photographing, with the camera unit  104 , a checker pattern  1401  on which structural light  1402  is projected from the projection unit  101 , and the surroundings of a lattice point  1404  remarked on the photographed image  1403 . In the surrounding of the lattice point  1404  in  FIG. 14 , projector pixels  1405  of the projection unit  101  and camera pixels of the camera unit  104  are also illustrated. The projector pixels  1405  obtained with pixel accuracy by ray tracing are illustrated. The correspondence relation between the camera pixels  1404  of the camera unit  104  and the projector pixels  1405  of the projection unit  101  is known. Moreover, the pixel size of the camera pixel  1406  of the camera unit  104  is smaller than the pixel size of the projector pixel  1405  of the projection unit  101 . 
     First, using the fact that the correspondence relation between the camera pixel  1406  of the camera unit  104  and the projector pixel  1405  of the projection unit  101  is known, LocalHomography of calibration of the projector pixels  1405  limited to the surroundings of the lattice point  1404  is found based on the information of the calibration result of the camera unit  104  in the surroundings of the lattice point  1404 . Here, LocalHomography of the projector pixels  1405  is found with a limit to the surrounding area of the lattice point  1404  small enough to ignore influences of distortion of the lens  101 A of the projection unit  101 . Moreover, the robust estimation is performed while considering a decoding error of the structural light  1402  to find LocalHomography of the projector pixels  1405 . Therefore, it is possible to find projector coordinates with sub-pixel accuracy of the projector pixel  1405  of the projection unit  101 . 
     Moreover, the projection-type image display device  100  according to the embodiment formulates both ray tracing and reverse ray tracing considering projection distortion of the projection unit  101 . 
       FIG. 15  schematically illustrates a method of ray tracing considering projector distortion. The ray tracing considering projector distortion is tracing of a position (X, Y, Z) [mm] on world coordinates obtained by projecting a pixel (u, v) [pix] on projector coordinates with ray  1501  influenced by distortion of the lens  101 A. The formulation of ray tracing for tracing the world coordinates (X, Y, Z) based on the projector pixel (u, v) can be used when the three-dimensional measurement is performed in the projection-type image display device  100 . 
       FIG. 16  schematically illustrates a method of reverse ray tracing considering projector distortion. The reverse ray tracing considering projector distortion is tracing of a pixel (u, v) [pix] on projector coordinates irradiated with ray  1601  for projecting a position (X, Y, Z) [mm] on world coordinates while considering influences of distortion of the lens  101 A. The formulation of reverse ray tracing for tracing the projector pixel (u, v) based on the world coordinates (X, Y, Z) can be used when the projection image control is performed in the projection-type image display device  100 . 
     The method of performing ray tracing and reverse ray tracing considering projector distortion of the projection unit  101  will be described with reference to  FIG. 17 . First, the projection unit  101  projects gray codes on a checker board  1701  with a latticed pattern as an object with known world coordinates, and the camera unit  104  photographs the projection image for ray tracing (F 1701 ) to calculate which ray (ray from which pixel) of the projection unit  101  is projected on a lattice point, that is, a corresponding point  1701  of the lattice point (X, Y, Z) on the world coordinates and the projector coordinates (x′, y′) in a state with projector distortion. 
     Next, the straight line on which a group of lattice points are supposed to be arranged is fit by the lens model, and distortion parameters are estimated by nonlinear optimization such as the LM method, for example (F 1702 ). As described above, the distortion parameters include distortion center coordinates (d cx , d cy ), distortion coefficients k 1  to k 3 , and tangent distortion coefficients p 1 , p 2  (as described above). As a result of distortion estimation (F 1702 ), it is possible to obtain the correspondence relation between the projector coordinates (x′, y′) having distortion and the projector coordinates (x, y) having no distortion, as illustrated in the following expression (10).
 
( x,y )= D ( x′,y ′)  (10)
 
     Moreover, based on the result of distortion estimation (F 1702 ), it is possible to obtain a corresponding point  1702  of a lattice point (X, Y, Z) on the world coordinates and projector coordinates (x, y) having no distortion. Therefore, the distortion estimation (F 1702 ) enables reverse ray tracing for tracing the projector pixel (u, v) based on which the world coordinates (X, Y, Z) are projected. That is, the estimation of a distortion correction function D for correcting the projector coordinates (x′, y′) having distortion to the projection coordinates (x, y) having no distortion indicates formulation of reverse ray tracing  1703  considering distortion. The relation of a corresponding point of the world coordinates (X, Y, Z) and the projector coordinates (x, y) is expressed as the above expression (9) using the perspective projection matrix K[R|T]. The perspective projection matrix is estimated by non-linear optimization such as the LM method, based on the corresponding points of the world coordinates (X, Y, Z) and the image coordinates (x, y) (F 1703 ). The K is internal parameters, and the R and T are respectively a rotating component and a translation component relative to the checker pattern in the external parameters. 
     On the other hand, when a reverse distortion correction function D′ for correcting the projector coordinates (x, y) having no distortion to the projector coordinates (x′, y′) having distortion is estimated, as illustrated in the following expression (11), it is possible to perform ray tracing for tracing world coordinates (X, Y, Z) projected based on the projector pixel (u, v) while considering projector distortion. That is, the estimation of the reverse distortion correction function D′ for correcting the projector coordinates (x, y) having no distortion to the projection coordinates (x′, y′) having distortion indicates formulation of ray tracing  1704  considering distortion.
 
( x′,y ′)= D ′( x,y )  (11)
 
     Note that when the calibration is performed using an image obtained by photographing a checker board with known feature points by the camera unit  104  (see  FIG. 7 , for example), it is necessary to photograph a plurality of images of the checker board while changing a visual point so as to perform calibration with high accuracy. When the number of visual points is small or the visual points have deviation, there occurs a problem in which the parameters are not estimated with high accuracy. Then, in the embodiment, the parameters are estimated with high accuracy with a small number of photographed images, using known depth information of a depth from the camera unit  104  to the checker board. As illustrated in  FIG. 18 , a distance from the camera unit  104  to a checker board  1801  is set to Z 1 , and the checker board  1801  is photographed first. Then, the distance is changed to Z 2  (Z 1 &gt;Z 2 ), and the checker board  1801  is photographed while an attitude angle of the camera unit  104  relative to the checker board  1801  is kept same. 
     The camera unit  104  is fixed based on such two different pieces of depth information, whereby it is possible to estimate parameters with high accuracy with a small number of man-hours for adjustment. It is obvious that the parameters can be estimated with high accuracy even when the checker board  1801  is photographed using three or more distances while an attitude angle of the camera unit  104  is kept same. 
     In the above, the technology disclosed in the present specification has been described in detail with reference to the certain embodiment. However, it is obvious that a person skilled in the art can modify or substitute the embodiment without departing from the scope of the technology disclosed in the specification. In the specification, the embodiment of the projection-type image display device incorporating a camera has been described. Even when a camera is configured to be separable from a body of a projection-type image display device or connected externally to the body, or when a camera is substituted by a method of measuring a position or a size of a projection image based on three-dimensional position relation between a projection unit and a screen, for example, the technology disclosed in the specification can be applied in the same manner. 
     In short, the technology disclosed in the specification has been described using the example, and the description contents of the specification should not be interpreted restrictively. In order to determine the scope of the technology disclosed in the specification, the claims should be taken into consideration. 
     Additionally, the present technology may also be configured as below: 
     (1) An image projection device including: 
     a camera; 
     a projector configured to project an image; 
     a camera calibration unit configured to perform calibration of the camera; 
     a projector calibration unit configured to perform calibration of the projector; and 
     an image correction unit configured to correct the image projected from the projector based on a result of the calibration, 
     wherein the projector calibration unit performs ray tracing of a known checker pattern on which structural light is projected by the projector, and estimates parameters by acquiring correspondence relation between a lattice point of the checker pattern and projector coordinates. 
     (2) The image projection device according to (1), 
     wherein the projector calibration unit performs calibration while considering lens distortion of the projector or without using a calibration result by the camera calibration unit. 
     (3) The image projection device according to (2), 
     wherein the projector calibration unit estimates distortion parameters by evaluating a distortion amount based on a group of lattice points supposed to be in a straight line on the projector coordinates, and estimates parameters of the projector based on correspondence relation between a lattice point on an image after distortion correction and world coordinates. 
     (4) The image projection device according to (3), 
     wherein the projector calibration unit estimates the distortion parameters of the projector by a Levenberg-Marquardt (LM) method, with an inclination difference between two candidates of straight lines on which a group of lattice points are supposed to be in a straight line as a distortion evaluation amount. 
     (5) The image projection device according to (3) or (4), 
     wherein the projector calibration unit estimates a perspective projection matrix including internal parameters and external parameters of the projector by nonlinear optimization, based on correspondence relation between the lattice point on the image after distortion correction and the world coordinates. 
     (6) The image projection device according to (5), 
     wherein the projector calibration unit estimates the perspective projection matrix by performing the nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by the LM method. 
     (7) The image projection device according to (3), 
     wherein the projector calibration unit finds correspondence relation between the lattice point of the checker pattern and the projector coordinates with sub-pixel accuracy. 
     (8) The image projection device according to (3), 
     wherein the projector calibration unit finds LocalHomography of calibration of projector pixels limited to surroundings of the lattice point. 
     (9) The image projection device according to (8), 
     wherein the projector calibration unit finds LocalHomography of the projector pixels with a limit to a surrounding area of the lattice point small enough to ignore influences of lens distortion of the projector. 
     (10) The image projection device according to (9), 
     wherein the projector calibration unit finds the LocalHomography of the projector pixels by performing robust estimation while considering a decoding error of the structural light. 
     (11) The image projection device according to any one of (1) to (10), 
     wherein the camera calibration unit detects the lattice point from an image obtained by photographing the known checker pattern with the camera, estimates distortion parameters by evaluating a distortion amount based on a group of lattice points supposed to be in a straight line, and estimates parameters of the camera based on correspondence relation between a lattice point on an image after distortion correction and world coordinates. 
     (12) The image projection device according to (11), 
     wherein the camera calibration unit estimates the distortion parameters of the camera by an LM method, with an inclination difference between two candidates of straight lines on which a group of lattice points are supposed to be in a straight line as a distortion evaluation amount. 
     (13) The image projection device according to (11), 
     wherein the camera calibration unit estimates a perspective projection matrix including internal parameters and external parameters of the camera by nonlinear optimization, based on correspondence relation between the lattice point on the image after distortion correction and the world coordinates. 
     (14) The image projection device according to (13), 
     wherein the camera calibration unit estimates the perspective projection matrix by performing the nonlinear optimization of a re-projection error between detection image coordinates of the camera and re-projection image coordinates by the LM method. 
     (15) The image projection device according to any one of (1) to (14), further including: 
     a ray tracing formulation unit configured to formulate ray tracing for tracing world coordinates obtained by projecting a pixel on the projector coordinates with ray influenced by lens distortion. 
     (16) The image projection device according to any one of (1) to (15), further including: 
     a reverse ray tracing formulation unit configured to formulate reverse ray tracing for tracing a pixel on the projector coordinates irradiated with the ray for projecting world coordinates while considering influences of lens distortion. 
     (17) The image projection device according to (16), 
     wherein the reverse ray tracing formulation unit performs ray tracing of a gray code projected by the projector on the checker pattern with known world coordinates, calculates a corresponding point of the world coordinates and the projector coordinates in a state with projector distortion, estimates a distortion correction function, obtains correspondence relation between the world coordinates and projection coordinates having no distortion, and formulates reverse ray tracing. 
     (18) The image projection device according to (15), 
     wherein the ray tracing formulation unit estimates a reverse distortion correction function D′ for correcting the projector coordinates having no distortion to projector coordinates having distortion, and formulates ray tracing for tracing world coordinates projected on a projector pixel. 
     (19) The image projection device according to any one of (1) to (18), 
     wherein at least one of the camera calibration unit and the projector calibration unit estimates the parameters with high accuracy with a small number of photographed images, using known depth information of a depth from the camera to a checker board. 
     (20) A calibration method of an image projection device including a camera and a projector, the calibration method including: 
     performing ray tracing of a known checker pattern on which structural light is projected by the projector; and 
     estimating parameters by acquiring correspondence relation between a lattice point of the checker pattern and projector coordinates.