JP2014187515A - Projector and control method therefor - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce a measurement error of a normal vector on a projection surface.SOLUTION: A projector includes: a projection unit for projecting an image indicated by a video signal on the projection surface through a lens; an imaging unit for imaging the projection surface on which the image is projected by the projection unit; and a calculation unit for calculating the normal vector on the projection screen in an unknown state of a tertial rotation matrix, indicative of relative rotation of an optical axis of the imaging unit relative to the optical axis of the lens. The projection unit includes an optical modulator for modulating light according to the video signal. The calculation unit calculates the normal vector on the basis of a first conversion matrix for performing projective transformation of the image at the optical modulator into an imaged image taken by the imaging unit.

Description

  The present invention relates to a projector and a projector control method.

  A technique for measuring the inclination of a projection surface on which an image is projected by a projector using triangulation is known. Patent Document 1 describes that three points projected on a projection surface are imaged with a digital camera, and an inclination angle of the projection optical axis with respect to the projection surface is calculated in the vertical direction and the horizontal direction. Patent Document 2 describes that the same target point is imaged by a plurality of cameras, and the three-dimensional position of the target point is detected from the physical position of the target point on each imaging element surface.

Japanese Patent Laying-Open No. 2005-4169 JP 2005-229415 A

In order to use triangulation, the relative positional relationship (position and angle) between optical systems such as a projection optical system or an imaging optical system needs to be known. In order to measure the tilt of the projection surface by the technique described in Patent Document 1, the positional relationship between the projection lens and the imaging lens must be known. In order to detect the three-dimensional position of the target point by the technique described in Patent Document 2, the positional relationship between the lenses of the two cameras must be known. Therefore, when the positional relationship between the optical systems changes due to some external factor (for example, when an impact is applied to the projector, or when the projector housing is distorted due to turning projection), a method using triangulation Then, there is a problem that the measurement error increases.
An object of the present invention is to reduce the measurement error of the normal vector of the projection surface.

  In order to solve the above-described problems, the present invention provides a projection unit that projects an image indicated by a video signal onto a projection surface via a lens, an imaging unit that captures a projection surface on which an image is projected by the projection unit, There is provided a projector including a calculation unit that calculates a normal vector of the projection plane in a state where a third-order rotation matrix indicating the relative rotation of the optical axis of the imaging unit with respect to the optical axis of the lens is unknown. According to this projector, the measurement error of the normal vector on the projection surface is reduced as compared with the case where triangulation is used.

  In another preferable aspect, the projection unit includes an optical modulator that modulates light according to the video signal, and the calculation unit converts an image in the optical modulator into a captured image captured by the imaging unit. The normal vector is calculated based on a first transformation matrix for projective transformation. According to this projector, the normal vector of the projection surface is calculated in a state where the relative rotation of the optical axis of the imaging unit with respect to the optical axis of the lens is unknown.

  In another preferable aspect, the projection unit projects a calibration image including four or more feature points onto the projection surface, the imaging unit images the projection surface on which the calibration image is projected, and The calculation unit calculates the first conversion matrix calculated based on the feature points included in the captured image, a second conversion matrix for perspective-converting world coordinates to coordinates in the light modulator, and the world coordinates. Based on the relationship between a known third transformation matrix that is perspective-transformed into coordinates in the captured image, a spatial vector indicating the relative position of the imaging unit with respect to the lens, the rotation matrix, and the normal vector, The image processing apparatus includes a correction unit that calculates a normal vector and corrects an image in the optical modulator based on the normal vector calculated by the calculation unit. According to this projector, the normal vector of the projection surface is calculated based on the relationship between the image and the captured image in the optical modulator.

ここで、Ｈは前記第１の変換行列、λは任意定数、Ｂは前記第３の変換行列、Ｒは前記回転行列、Ｅは単位行列、ｔは前記空間ベクトル、ｎは前記法線ベクトル、Ａは前記第２の変換行列をそれぞれ示す。このプロジェクターによれば、連立方程式を解くことにより投射面の法線ベクトルが算出される。 In another preferable aspect, the calculation unit calculates the normal vector by the following equation (1).

Here, H is the first transformation matrix, λ is an arbitrary constant, B is the third transformation matrix, R is the rotation matrix, E is a unit matrix, t is the space vector, n is the normal vector, A represents the second transformation matrix. According to this projector, the normal vector of the projection surface is calculated by solving simultaneous equations.

  In another preferred embodiment, the second transformation matrix is known. According to this projector, when the lens of the projection unit is a single focus lens, the measurement error of the normal vector of the projection surface is reduced.

  In another preferred embodiment, the space vector is known. According to this projector, even if the lens of the projection unit is a zoom lens, the measurement error of the normal vector on the projection surface is reduced.

  In another preferred embodiment, the sum of the number of unknown parameters in the rotation matrix, the second transformation matrix, the space vector, the normal vector, and the arbitrary constant is expressed by an equation represented by Equation (1). The calculation unit may calculate the normal vector by an iterative method or a least square method. According to this projector, the normal vector of the projection surface is calculated even when the total number of unknown parameters is not equal to the number of equations indicated by Equation (1).

  The present invention also includes a step of projecting an image indicated by a video signal onto a projection surface via a lens, a step of an imaging unit imaging the projection surface on which the image is projected, and the imaging with respect to the optical axis of the lens. And a step of calculating a normal vector of the projection plane in a state where a third-order rotation matrix indicating relative rotation of the optical axis of the unit is unknown. According to this projector control method, the measurement error of the normal vector on the projection surface is reduced as compared with the case where triangulation is used.

The figure explaining the operation | movement outline | summary of a projector. The block diagram which shows the functional structure of a projector. The block diagram which shows the hardware constitutions of a projector. The flowchart which shows a distortion correction process. The figure which shows the example of a calibration image. The figure which shows the example of a captured image.

  FIG. 1 is a diagram illustrating an outline of the operation of a projector 1 according to an embodiment of the invention. The projector 1 is a device that projects an image (hereinafter referred to as “input image”) indicated by a video signal onto a screen SC. The screen SC is a plane (projection surface) on which an image projected from the projector 1 is projected. When the projection axis of the projector 1 is tilted from an ideal state with respect to the screen SC, an image projected on the screen SC (hereinafter referred to as “projected image”) is distorted into a trapezoid as shown by a broken line. It becomes. The projector 1 has a function of correcting this distortion (trapezoidal distortion). In the example of FIG. 1, the projector 1 projects an image Ipr as a corrected image on the screen SC. The trapezoidal distortion is corrected using the normal vector of the screen SC.

  FIG. 2 is a block diagram illustrating a functional configuration of the projector 1. The projector 1 includes a projection unit 101, a calibration image storage unit 102, an imaging unit 103, a feature point detection unit 104, a projective transformation matrix calculation unit 105, a normal vector calculation unit 106, and a correction value calculation unit 107. An adjustment value calculation unit 108, a lens driving unit 109, a video signal acquisition unit 110, and a distortion correction unit 111. The projection unit 101 projects the input image and the calibration image onto the screen SC via the lens. The calibration image is an image used for calculating a normal vector of the screen SC (hereinafter referred to as “normal vector n”), which is used to correct the trapezoidal distortion. The calibration image includes four or more feature points. The projection unit 101 includes an optical modulator that modulates light from a light source (not shown) according to a video signal. The calibration image storage unit 102 stores image data indicating a calibration image. The imaging unit 103 captures the screen SC on which the calibration image is projected by the projection unit 101. The feature point detection unit 104 detects feature points included in an image captured by the imaging unit 103 (hereinafter referred to as “captured image”). Projection transformation matrix calculation section 105 calculates a first transformation matrix (hereinafter referred to as “projection transformation matrix H”) based on the feature points detected by feature point detection section 104. The projective transformation matrix H is a cubic square matrix for projectively transforming an image in the optical modulator into a captured image. The normal vector calculation unit 106 (an example of a calculation unit) rotates the rotation of the optical axis of the imaging unit 103 relative to the optical axis of the lens based on the projection transformation matrix H calculated by the projection transformation matrix calculation unit 105 (rotation). The normal vector n is calculated with the unknown state (represented by the matrix R). The correction value calculation unit 107 calculates a correction value for correcting the image in the optical modulator based on the normal vector n calculated by the normal vector calculation unit 106. The adjustment value calculation unit 108 calculates an adjustment value for adjusting the focus of the lens based on the normal vector n calculated by the normal vector calculation unit 106. The lens driving unit 109 uses the adjustment value calculated by the adjustment value calculation unit 108 to adjust the focus of the lens. The video signal acquisition unit 110 acquires a video signal from an external device. The distortion correction unit 111 corrects the image in the optical modulator using the correction value calculated by the correction value calculation unit 107.

  FIG. 3 is a block diagram illustrating a hardware configuration of the projector 1. The projector 1 includes a central processing unit (CPU) 10, a read only memory (ROM) 11, a random access memory (RAM) 12, an IF (interface) unit 13, an image processing circuit 14, a projection unit 15, The camera 16, the light receiving unit 17, the operation panel 18, and the input processing unit 19 are included. The CPU 10 is a control device that controls each unit of the projector 1 by executing the control program 11A. The ROM 11 is a non-volatile storage device that stores various programs and data. The ROM 11 stores a control program 11A executed by the CPU 10. The RAM 12 is a volatile storage device that stores data. The RAM 12 has a frame memory 12a. The frame memory 12a is an area for storing an image for one frame of the video indicated by the video signal.

  The IF unit 13 communicates with an external device such as a DVD (Digital Versatile Disc) player or a personal computer. The IF unit 13 has various terminals (for example, a VGA terminal, a USB terminal, a wired or wireless LAN interface, an S terminal, an RCA terminal, an HDMI (High-Definition Multimedia Interface: registered trademark) terminal) for connecting to an external device. Prepare. The IF unit 13 extracts vertical and horizontal synchronization signals from the video signal acquired from the external device. The image processing circuit 14 performs predetermined image processing on the image indicated by the video signal. The image processing circuit 14 writes the image after image processing in the frame memory 12a.

  The projection unit 15 includes a light source 151, a liquid crystal panel 152, an optical system 153, a light source drive circuit 154, a panel drive circuit 155, and an optical system drive unit 156. The light source 151 includes a lamp such as a high-pressure mercury lamp, a halogen lamp, or a metal halide lamp, or a light emitter such as an LED (Light Emitting Diode) or a laser diode, and irradiates the liquid crystal panel 152 with light. The liquid crystal panel 152 is an optical modulator that modulates light emitted from the light source 151 in accordance with image data. In this example, the liquid crystal panel 152 has a plurality of pixels arranged in a matrix. The liquid crystal panel 152 has, for example, an XGA (eXtended Graphics Array) resolution and a display area configured by 1024 × 768 pixels. In this example, the liquid crystal panel 152 is a transmissive liquid crystal panel, and the transmittance of each pixel is controlled according to image data. The projector 1 includes three liquid crystal panels 152 corresponding to the three primary colors RGB. The light from the light source 151 is separated into three color lights of RGB, and each color light enters the corresponding liquid crystal panel 152. The color light modulated by passing through each liquid crystal panel is synthesized by a cross dichroic prism or the like and emitted to the optical system 153. The optical system 153 includes a projection lens 1531 that enlarges the light modulated into image light by the liquid crystal panel 603 and projects the light onto the screen SC, and a focus lens 1532 that adjusts the focus of the projected image. A single focus lens is used as the projection lens 1531. The light source driving circuit 154 drives the light source 151 according to the control of the CPU 10. The panel drive circuit 155 drives the liquid crystal panel 152 according to the image data output from the CPU 10. The optical system drive unit 156 includes a motor that adjusts the focus of the focus lens 1532 and a drive circuit that drives the motor according to the control of the CPU 10.

  The camera 16 is a digital camera that captures an image of the screen SC and generates image data. For example, the camera 16 images the screen SC at an angle of view including the maximum range in which the projection unit 15 can project a projection image. The light receiving unit 17 receives the infrared signal transmitted from the controller RC, decodes the received infrared signal, and outputs the decoded infrared signal to the input processing unit 19. The operation panel 18 has buttons and switches for turning on / off the projector 1 or performing various operations. The input processing unit 19 generates information indicating the operation content by the controller RC or the operation panel 18 and outputs the information to the CPU 10.

  In the projector 1, the CPU 10 executing the program is an example of a feature point detection unit 104, a projective transformation matrix calculation unit 105, a normal vector calculation unit 106, a correction value calculation unit 107, and an adjustment value calculation unit 108. The projection unit 15 (excluding the optical system driving unit 156) controlled by the CPU 10 executing the program is an example of the projection unit 101. The optical system driving unit 156 controlled by the CPU 10 executing the program is an example of the lens driving unit 109. The camera 16 that is controlled by the CPU 10 executing the program is an example of the imaging unit 103. The ROM 11 is an example of the calibration image storage unit 102. The IF unit 13 controlled by the CPU 10 executing the program is an example of the video signal acquisition unit 110. The image processing circuit 14 controlled by the CPU 10 executing the program is an example of the distortion correction unit 111.

  FIG. 4 is a flowchart showing a process in which the projector 1 corrects the trapezoidal distortion of the projected image (hereinafter referred to as “distortion correction process”). The distortion correction processing is started when, for example, the projector 1 is turned on or when the user inputs an instruction to start the distortion correction processing by operating the controller RC to the projector 1. Is done. In step S1, the CPU 10 projects a calibration image on the screen SC. Specifically, the CPU 10 reads out image data indicating a calibration image from the ROM 11 and outputs the image data to the panel drive circuit 155.

  FIG. 5 is a diagram illustrating an example of a calibration image. FIG. 5 shows a calibration image Ic displayed on the liquid crystal panel 152. In FIG. 5, a solid line represents the outline of the display area of the liquid crystal panel 152, and a broken line represents the outline of the calibration image Ic. In this example, the calibration image Ic is an image that is transparent and has a rectangular area other than the feature points. In the example of FIG. 5, the calibration image Ic has four feature points from point U1 to point U4. In this example, four vertices are feature points. The feature points are displayed on the liquid crystal panel 152 as a set of a plurality of pixels. The coordinates of each feature point on the liquid crystal panel 152 (here, the coordinates of the centers of a plurality of pixels constituting the feature point) are stored in the ROM 11 in advance. In FIG. 5, the coordinates on the liquid crystal panel 152 of the feature points from the point U1 to the point U4 are U1 (X0, Y0), U2 (X1, Y1), U3 (X2, Y2), U4 (X3, Y3). is there. When the optical axis of the projection lens 1531 is tilted from the ideal state with respect to the screen SC, the calibration image Ic displayed on the screen SC is distorted.

  Refer to FIG. 4 again. In step S2, the CPU 10 captures the calibration image Ic projected on the screen SC. The CPU 10 stores the captured image obtained by capturing the calibration image Ic in the RAM 12. In step S3, the CPU 10 detects a feature point from the captured image obtained by capturing the calibration image Ic. Specifically, the CPU 10 detects four feature points included in the captured image and calculates the coordinates of each feature point in the captured image. The CPU 10 stores the calculated coordinates of each feature point in the RAM 12.

  FIG. 6 is a diagram illustrating the captured image Iph. The captured image Iph is an image obtained by capturing the calibration image Ic projected on the screen SC. In FIG. 6, the solid line represents the contour of the captured image Iph (frame of the camera 16), and the broken line represents the contour of the calibration image Ic. Each feature point from point u1 to point u4 in the captured image Iph corresponds to each feature point from point U1 to point U4 in the calibration image Ic. In the example of FIG. 6, the coordinates on the captured image Iph of the feature points from the point u1 to the point u4 are u1 (x0, y0), u2 (x1, y1), u3 (x2, y2), u4 (x3, y3). ).

具体的には、ＣＰＵ１０は、液晶パネル１５２における各特徴点（点Ｕ１から点Ｕ４）の座標をＲＯＭ１１から、撮像画像Ｉｐｈにおける各特徴点（点ｕ１から点ｕ４）の座標をＲＡＭ１２からそれぞれ読み出して、以下の式（３）に示す８元連立一次方程式を解くことにより、射影変換行列Ｈを算出する。なお、射影変換行列Ｈのパラメーターｉ₀は、定数（ｉ₀＝１）である。ＣＰＵ１０は、算出した射影変換行列ＨをＲＡＭ１２に記憶する。

Refer to FIG. 4 again. In step S4, the CPU 10 calculates a projective transformation matrix H shown in the following equation (2) based on the coordinates of each feature point on the liquid crystal panel 152 and the coordinates of each feature point in the captured image Iph.

Specifically, the CPU 10 reads the coordinates of each feature point (points U1 to U4) on the liquid crystal panel 152 from the ROM 11, and reads the coordinates of each feature point (points u1 to u4) on the captured image Iph from the RAM 12, respectively. The projective transformation matrix H is calculated by solving an 8-ary simultaneous linear equation shown in the following equation (3). The parameter i ₀ of the projective transformation matrix H is a constant (i ₀ = 1). The CPU 10 stores the calculated projective transformation matrix H in the RAM 12.

各記号はそれぞれ以下の数または行列を示す。
λ：任意定数
Ｂ：世界座標を撮像画像における座標に透視変換するための座標変換行列（３次正方行列）
Ｒ：投射レンズ１５３１の光軸に対するカメラ１６の光軸の相対的な回転を示す３次の回転行列
Ｅ：３次の単位行列
ｔ：投射レンズ１５３１に対するカメラ１６の相対的な位置を示す空間ベクトル（３行１列の行列）
Ａ：世界座標を液晶パネル１５２における座標に透視変換するための座標変換行列（３次正方行列）
なお、座標変換行列Ａおよび座標変換行列Ｂは、３次元の世界座標を２次元の平面上の座標に変換する行列であり、ある２次元の平面上の座標を他の２次元の平面上の座標に変換する射影変換行列Ｈとは異なる種類の行列である。 In step S <b> 5, the CPU 10 calculates a normal vector n using the projective transformation matrix H. Specifically, the CPU 10 reads the projective transformation matrix H from the RAM 12 and calculates a normal vector n (a matrix of 3 rows and 1 column) by solving the nine simultaneous equations shown in the following equation (4). . In Expression (4), “T” represents transposition of a certain matrix.

Each symbol indicates the following number or matrix.
λ: Arbitrary constant B: Coordinate transformation matrix (third-order square matrix) for perspective transformation of world coordinates to coordinates in the captured image
R: Third-order rotation matrix indicating relative rotation of the optical axis of the camera 16 with respect to the optical axis of the projection lens 1531 E: Third-order unit matrix t: Space vector indicating the relative position of the camera 16 with respect to the projection lens 1531 (3 rows and 1 column matrix)
A: Coordinate transformation matrix (third-order square matrix) for perspective transformation of world coordinates to coordinates on the liquid crystal panel 152
Note that the coordinate transformation matrix A and the coordinate transformation matrix B are matrices for transforming three-dimensional world coordinates into coordinates on a two-dimensional plane. It is a different type of matrix from the projective transformation matrix H that converts to coordinates.

  Here, each parameter of the coordinate transformation matrix B is a value unique to the camera 16, and a known value measured when the projector 1 is manufactured is stored in the ROM 11. Each parameter of the coordinate transformation matrix A is a value determined by the projection lens 1531. In the present embodiment, since the projection lens 1531 is a single focus lens (because the focal length does not change), each parameter of the coordinate transformation matrix A has a constant value. Therefore, for each parameter of the coordinate transformation matrix A, known values measured when the projector 1 is manufactured are stored in the ROM 11. The space vector t can be normalized to a unit vector, and the remaining parameters can be calculated based on two of the three parameters. That is, the number of unknown parameters of the space vector t can be reduced to two. Therefore, for the right side of equation (4), the total number of unknown parameters is 9 for the arbitrary constant λ, 3 for the rotation matrix R, 2 for the space vector t, and 3 for the normal vector n. Become. Since this is equal to the number of equations obtained from the equation (4), the normal vector n is calculated by solving the nine simultaneous equations shown in the equation (4). Note that solving the nine simultaneous equations shown in the equation (4) provides two solutions of the normal vector n, but the CPU 10 makes the calculated rotation matrix R and the space vector t closer to the initial values. The normal vector n is used. Initial values of the rotation matrix R and the space vector t are stored in the ROM 11 in advance. The CPU 10 stores data indicating the calculated normal vector n in the RAM 12.

  According to equation (4), the normal vector n is calculated even when the rotation matrix R is unknown. Therefore, the measurement error of the normal vector n is reduced compared to the case where triangulation is used. For example, the relative rotation of the optical axis of the camera 16 with respect to the optical axis of the projection lens 1531 is an external factor (for example, when an impact is applied to the projector 1 or when the casing of the projector 1 is distorted due to turning projection) ), The normal vector n with high accuracy is calculated.

  In step S <b> 6, the CPU 10 calculates the inclination of the screen SC with respect to the projection lens 1531 using the normal vector n. Specifically, the CPU 10 reads data indicating the normal vector n and data indicating the direction vector of the optical axis of the projection lens 1531 from the RAM 12, and an angle formed by the normal vector n and the optical axis of the projection lens 1531. θ is calculated. Data indicating the direction vector of the optical axis of the projection lens 1531 is measured in advance and stored in the RAM 12 before the distortion correction processing is started. The CPU 10 stores the calculated angle θ in the RAM 12.

In step S <b> 7, the CPU 10 calculates a projective transformation matrix (hereinafter referred to as “projective transformation matrix F”) for correcting trapezoidal distortion according to the inclination of the screen SC. The projective transformation matrix F is a cubic square matrix that performs projective transformation of coordinates on the liquid crystal panel 152 to coordinates in the input image. Specifically, the CPU 10 specifies a projection image when the trapezoidal distortion is not corrected based on the inclination of the screen SC, and based on the specified projection image, the projection transformation matrix shown in the following formula (5) F is calculated. The CPU 10 stores the calculated projective transformation matrix F in the RAM 12. Each parameter of the projective transformation matrix F is an example of a correction value.

ＣＰＵ１０は、入力画像における座標（Ｘｋ，Ｙｋ）の画素の階調値を、液晶パネル１５２における座標（Ｘｊ，Ｙｊ）の画素の階調値としてフレームメモリー１２ａに書き込む。なお、式（６）を用いた演算において、入力画像における座標が小数で算出された場合には、対応する階調値が存在しないことになる。この場合、ＣＰＵ１０は、画素補間（畳み込み演算）を行い、入力画像における複数の座標の階調値から一の階調値を算出する。ＣＰＵ１０は、画素補間により算出された階調値を、液晶パネル１５２における座標（Ｘｊ，Ｙｊ）の画素の階調値としてフレームメモリー１２ａに書き込む。このように、液晶パネル１５２についてＸ座標およびＹ座標を走査することにより、液晶パネル１５２が有するすべての画素について、その階調値が決定される。ステップＳ９において、ＣＰＵ１０は、液晶パネル１５２を駆動する。具体的には、ＣＰＵ１０は、フレームメモリー１２ａに書き込まれた画像データを読み出して、パネル駆動回路１５５に出力する。ステップＳ９の処理により、投射画像は、台形歪みのないものとなる。このように、本実施形態では、式（４）により算出された法線ベクトルｎに基づいて入力画像の射影変換が行われるため、三角測量により法線ベクトルｎが算出された場合に比べて、台形歪みの補正の精度が高くなる。 In step S8, the CPU 10 performs projective transformation of the input image using the projective transformation matrix F. Specifically, the CPU 10 performs coordinate conversion on the coordinates (Xj, Yj) on the liquid crystal panel 152 by the following equation (6), and calculates the coordinates (Xk, Yk) in the input image.

The CPU 10 writes the gradation value of the pixel at the coordinates (Xk, Yk) in the input image in the frame memory 12a as the gradation value of the pixel at the coordinates (Xj, Yj) in the liquid crystal panel 152. In the calculation using the equation (6), when the coordinates in the input image are calculated with decimal numbers, there is no corresponding gradation value. In this case, the CPU 10 performs pixel interpolation (convolution operation) and calculates one gradation value from the gradation values of a plurality of coordinates in the input image. The CPU 10 writes the gradation value calculated by pixel interpolation in the frame memory 12a as the gradation value of the pixel at the coordinates (Xj, Yj) on the liquid crystal panel 152. Thus, by scanning the X coordinate and the Y coordinate of the liquid crystal panel 152, the gradation values of all the pixels included in the liquid crystal panel 152 are determined. In step S <b> 9, the CPU 10 drives the liquid crystal panel 152. Specifically, the CPU 10 reads the image data written in the frame memory 12 a and outputs it to the panel drive circuit 155. By the processing in step S9, the projection image becomes free of trapezoidal distortion. As described above, in the present embodiment, the projective transformation of the input image is performed based on the normal vector n calculated by the equation (4). Therefore, compared to the case where the normal vector n is calculated by triangulation, The accuracy of correction of trapezoidal distortion increases.

In step S10, the CPU 10 calculates a distance dSC from the projection lens 1531 to the screen SC using the normal vector n. Specifically, the CPU 10 reads data indicating the normal vector n from the RAM 12, and calculates the distance dSC by the following equation (7). The CPU 10 stores the calculated distance dSC in the RAM 12.

  In step S11, the CPU 10 calculates an adjustment value for adjusting the focus of the focus lens 1532 according to the distance dSC. The CPU 10 reads a predetermined formula from the ROM 11 and calculates an adjustment value corresponding to the distance dSC. The CPU 10 stores data indicating the calculated adjustment value in the RAM 12. In step S12, the CPU 10 adjusts the focus of the focus lens 1532 using the adjustment value. Specifically, the CPU 10 reads data indicating the adjustment value from the RAM 12 and outputs the data to the optical system driving unit 156. As described above, in the present embodiment, since the focus is adjusted based on the normal vector n calculated by Expression (4), the focus vector is compared with the case where the normal vector n is calculated by triangulation. The accuracy of adjustment is increased.

<Modification>
The present invention is not limited to the above-described embodiments, and various modifications can be made. Hereinafter, some modifications will be described. Of the modifications described below, two or more may be used in combination.

(1) Modification 1
In the embodiment described above, the case where the projection lens 1531 is a single focus lens and each parameter of the coordinate transformation matrix A is known has been described. In this regard, the projection lens 1531 is a zoom lens whose focal length changes, and one of the parameters of the coordinate transformation matrix A may be unknown. In this case, in the simultaneous equations shown in Expression (4), known values measured at the time of manufacturing the projector 1 are used for the parameters of the space vector t. The value of each parameter of the space vector t is stored in the ROM 11 in advance. Thus, for the right side of equation (4), the total number of unknown parameters is one for the arbitrary constant λ, three for the rotation matrix R, three for the normal vector n, and one for the coordinate transformation matrix A. There will be eight. Since this is less than the number of equations obtained from Equation (4), the normal vector n is calculated by solving an 8-ary simultaneous equation consisting of nine equations shown in Equation (4). When the number of unknown parameters is smaller than the number of equations obtained from Equation (4), the CPU 10 calculates the normal vector n by an iterative method or a least square method. Note that both of the parameters of the coordinate transformation matrix A and the space vector t may be known.

(2) Modification 2
When the projection lens 1531 is a zoom lens, the projector 1 may include a configuration for acquiring the focal length of the projection lens 1531. For example, when the focal length of the projection lens 1531 is controlled by changing the resistance value of the variable resistor, the focal length may be acquired based on the resistance value. In this case, the total number of unknown parameters for the right side of Equation (4) is a total of nine as in the embodiment. Therefore, the normal vector n is calculated by the same method as in the embodiment.

(3) Other Modifications The processing performed in the distortion correction processing is not limited to the processing shown in FIG. For example, the process related to the focus adjustment of the focus lens 1532 (step S10 to step S12) may be performed before the process related to projective conversion of the input image (step S6 to step S9).
The calibration image is not limited to that shown in FIG. For example, the calibration image may be displayed on the liquid crystal panel 152 such that the contour is perceived by the user. In another example, the calibration image may include more than 4 feature points.
The hardware configuration of the projector 1 is not limited to the configuration shown in FIG. The projector 1 may have any hardware configuration as long as the processing of each step shown in FIG. 4 can be executed. For example, instead of the liquid crystal panel 152, a digital mirror device (DMD) may be used as the light modulator.

  DESCRIPTION OF SYMBOLS 1 ... Projector, 101 ... Projection part, 102 ... Calibration image memory | storage part, 103 ... Imaging part, 104 ... Feature point detection part, 105 ... Projection transformation matrix calculation part, 106 ... Normal vector calculation part, 107 ... Correction value calculation part , 108 ... adjustment value calculation unit, 109 ... lens drive unit, 110 ... video signal acquisition unit, 111 ... distortion correction unit, 10 ... CPU, 11 ... ROM, 12 ... RAM, 13 ... IF unit, 14 ... image processing circuit, DESCRIPTION OF SYMBOLS 15 ... Projection unit, 151 ... Light source, 152 ... Liquid crystal panel, 153 ... Optical system, 1531 ... Projection lens, 1532 ... Focus lens, 154 ... Light source drive circuit, 155 ... Panel drive circuit, 156 ... Optical system drive part, 16 ... Camera 17, light receiving unit 18, operation panel 19, input processing unit

Claims (8)

A projection unit that projects an image indicated by the video signal onto a projection surface via a lens;
An imaging unit that captures a projection surface on which an image is projected by the projection unit;
And a calculation unit that calculates a normal vector of the projection plane in a state where a third-order rotation matrix indicating the relative rotation of the optical axis of the imaging unit with respect to the optical axis of the lens is unknown. The projection unit includes an optical modulator that modulates light according to the video signal,
The said calculation part calculates the said normal vector based on the 1st conversion matrix which carries out projective conversion of the image in the said optical modulator to the picked-up image imaged by the said imaging part. The projector described. The projection unit projects a calibration image including four or more feature points onto the projection surface,
The imaging unit images a projection surface on which the calibration image is projected,
The calculation unit includes the first conversion matrix calculated based on the feature points included in the captured image, a second conversion matrix for perspective-converting world coordinates to coordinates in the light modulator, and the world coordinates. Based on a relationship between a known third transformation matrix for perspective-transforming into a coordinate in the captured image, a space vector indicating a relative position of the imaging unit with respect to the lens, the rotation matrix, and the normal vector, Calculating the normal vector;
The projector according to claim 2, further comprising: a correction unit that corrects an image in the optical modulator based on the normal vector calculated by the calculation unit. The projector according to claim 3, wherein the calculation unit calculates the normal vector by the following equation (1).

Here, H is the first transformation matrix, λ is an arbitrary constant, B is the third transformation matrix, R is the rotation matrix, E is a unit matrix, t is the space vector, n is the normal vector, A represents the second transformation matrix. The projector according to claim 3, wherein the second transformation matrix is known. The projector according to claim 3, wherein the space vector is known. The sum of the number of unknown parameters in the rotation matrix, the second transformation matrix, the space vector, the normal vector, and the arbitrary constant is less than the number of equations represented by Equation (1),
The projector according to claim 4, wherein the calculation unit calculates the normal vector by an iterative method or a least square method. Projecting an image indicated by the video signal onto a projection surface via a lens;
An imaging unit imaging the projection surface on which the image is projected;
Calculating a normal vector of the projection plane in a state where a third-order rotation matrix indicating the relative rotation of the optical axis of the imaging unit with respect to the optical axis of the lens is unknown.

Images