Patent Publication Number: US-11640774-B2

Title: Display method for display system, display method for display apparatus, and display system

Description:
The present application is based on, and claims priority from JP Application Serial Number 2021-127739, filed Aug. 3, 2021, the disclosure of which is hereby incorporated by reference herein in its entirety. 
     BACKGROUND 
     1. Technical Field 
     The present disclosure relates to a display method for a display system, a display method for a display apparatus, and the display system. 
     2. Related Art 
     There has been a known technology for correcting luminance unevenness of an image displayed by a display apparatus on a display surface. 
     For example, JP-A-2016-180921 discloses a display system including an image processing apparatus that corrects luminance nonuniformity resulting from the luminance distribution of a screen and a projector that displays an image based on an image output signal corrected by the image processing apparatus. 
     When a plurality of display apparatuses display images, there is conceivably a case where luminance unevenness of the images needs to be corrected. The disclosure in JP-A-2016-180921 is, however, not intended to be applied to the case where a plurality of display apparatuses display images. An approach to correction of luminance unevenness of the displayed images is therefore desired. 
     SUMMARY 
     An aspect of the present disclosure relates to a display method for a display system, the method including determining a first target value by correcting a first luminance value representing luminance at a first position in a first image, which is displayed by a first display apparatus on a display surface, based on a second luminance value representing luminance at a second position in the first image, causing the first display apparatus to display on the display surface a first corrected image generated by correcting the first image in such a way that the luminance at the first position in the first image becomes the first target value, determining a second target value by correcting a third luminance value representing luminance at a third position in a second image, which is displayed by a second display apparatus on the display surface, based on a fourth luminance value representing luminance at a fourth position in the second image, causing the second display apparatus to display on the display surface a second corrected image generated by correcting the second image in such a way that the luminance at the third position in the second image becomes the second target value, changing the first target value based on the second target value when the first target value is greater than the second target value and causing the first display apparatus to display on the display surface a third corrected image generated by using the changed first target value, and changing the second target value based on the first target value when the second target value is greater than the first target value and causing the second display apparatus to display on the display surface a fourth corrected image generated by using the changed second target value. 
     Another aspect of the present disclosure relates to a display method for a display apparatus, the method including determining a first target value by correcting a first luminance value representing luminance at a first position in a first image, which is displayed by a display apparatus on a display surface, based on a second luminance value representing luminance at a second position in the first image, causing the display apparatus to display on the display surface a first corrected image generated by correcting the first image in such a way that a luminance at the first position in the first image becomes the first target value, and changing the first target value based on the second target value when the second target value, which is determined by correcting a third luminance value representing luminance at a third position in the second image, which is displayed by another display apparatus different from the display apparatus on the display surface, based on a fourth luminance value representing luminance at a fourth position in the second image, is smaller than the first target value and causing the display apparatus to display on the display surface a third corrected image generated by using the changed first target value. 
     Another aspect of the present disclosure relates to a display system including a first display apparatus that displays a first image on a display surface, a second display apparatus that displays a second image on the display surface, and a control apparatus that controls the first display apparatus and the second display apparatus, and the control apparatus determines a first target value by correcting a first luminance value representing luminance at a first position in the first image based on a second luminance value representing luminance at a second position in the first image, causes the first display apparatus to display on the display surface a first corrected image generated by correcting the first image in such a way that the luminance at the first position in the first image becomes the first target value, determines a second target value by correcting a third luminance value representing luminance at a third position in the second image based on a fourth luminance value representing luminance at a fourth position in the second image, causes the second display apparatus to display on the display surface a second corrected image generated by correcting the second image in such a way that the luminance at the third position in the second image becomes the second target value, changes the first target value based on the second target value when the first target value is greater than the second target value and causes the first display apparatus to display on the display surface a third corrected image generated by using the changed first target value, and changes the second target value based on the first target value when the second target value is greater than the first target value and causes the second display apparatus to display on the display surface a fourth corrected image generated by using the changed second target value. 
     Another aspect of the present disclosure relates to a display apparatus including a display section that displays a first image on a display surface; and a control section that controls the display section, and the control section determines a first target value by correcting a first luminance value representing luminance at a first position in the first image, which is displayed by the display apparatus on the display surface, based on a second luminance value representing luminance at a second position in the first image, causes the display apparatus to display on the display surface a first corrected image generated by correcting the first image in such a way that the luminance value at the first position in the first image becomes the first target value, and changes the first target value based on a second target value, which is determined by correcting a third luminance value representing luminance at a third position in a second image, which is displayed by another display apparatus different from the display apparatus on the display surface, based on a fourth luminance value representing luminance at a fourth position in the second image, when the second target value is smaller than the first target value and causes the display apparatus to display on the display surface a third corrected image generated by using the changed first target value. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    shows an example of a system configuration of a display system. 
         FIG.  2    shows an example of the configuration of a control apparatus. 
         FIG.  3    shows an example of the configuration of a first projector. 
         FIG.  4    shows an example of the configuration of an image projection section. 
         FIG.  5    shows an example in which luminance unevenness occurs in an overall image displayed by the projectors. 
         FIG.  6    is a flowchart showing the action of the display system. 
         FIG.  7    is a flowchart showing the action of the display system. 
         FIG.  8    is a flowchart showing the action of the display system. 
         FIG.  9    is a flowchart showing the action of the first projector. 
     
    
    
     DESCRIPTION OF EXEMPLARY EMBODIMENTS 
     1. System Configuration 
       FIG.  1    shows an example of a system configuration of a display system  1 . 
     The display system  1  includes a control apparatus  100  and a plurality of projectors  200 , which are connected to the control apparatus  100  via cables  50 . The control apparatus  100  and the projector  200  communicate data to each other via the cables  50 . The present embodiment will be described with reference to a case where the control apparatus  100  and the projectors  200  are wired to each other, and the control apparatus  100  and the projectors  200  may be wirelessly connected to each other. 
     The control apparatus  100  is, for example, a computer apparatus, such as a personal computer and a tablet computer. The control apparatus  100  is an apparatus that supplies the projectors  200  connected thereto with image data. The projectors  200  then display images based on the image data supplied from the control apparatus  100  on a projection surface  10 . The image data with which the control apparatus  100  supplies the projectors  200  may be video data or still image data. The control apparatus  100  controls the plurality of projectors  200  to correct luminance unevenness of the images displayed by the projectors  200 . The projection surface  10  corresponds to a display surface. 
     The display system  1  according to the present embodiment includes two projectors  200 . In the following description, the two projectors  200  are called a first projector  200 A and a second projector  200 B. The first projector  200 A corresponds to a first display apparatus, and the second projector  200 B corresponds to a second display apparatus. In the following description, the first projector  200 A and the second projector  200 B are collectively referred to as projectors  200 . The number of projectors  200  provided in the display system  1  is not limited to two and may be three or more. 
     The first projector  200 A and the second projector  200 B are arranged in a single row in the horizontal direction of the projection surface  10 , as shown in  FIG.  1   . The first projector  200 A and the second projector  200 B are not necessarily arranged in a single horizontal row and may instead be arranged in a single vertical row. The plurality of projectors  200  may be arranged in a matrix formed of N rows and M columns. N and M are each a natural number greater than or equal to two. 
     The projection surface  10 , on which the projectors  200  display images, is, for example, a screen and may instead, for example, be a curved or irregular surface, a wall surface of a building, or a flat surface of an installed object. 
     The display system  1  displays one large image by linking the images displayed by the first projector  200 A and the second projector  200 B to each other on the projection surface  10 . The projection form described above is called tiling projection. The control apparatus  100  divides the image data into a plurality of divided image data portions and supplies the first projector  200 A and the second projector  200 B with the divided image data portions. 
     The first projector  200 A projects image light onto a first projection area  11 , which is a left area when viewed in the direction toward the projection surface  10 . A first image is thus displayed in the first projection area  11 . The second projector  200 B projects image light onto a second projection area  13 , which is a right area when viewed in the direction toward the projection surface  10 . A second image is thus displayed in the second projection area  13 . 
     Furthermore, when the display system  1  performs the tiling projection, the first projector  200 A displays an image on the projection surface  10  in such a way that the image partially overlap with the second projection area  13 , and the second projector  200 B displays an image on the projection surface  10  in such a way that the image partially overlap with the first projection area  11 . In the example shown in  FIG.  1   , a right portion of the first projection area  11  when viewed in the direction toward the projection surface  10  and a left portion of the second projection area  13  when viewed in the direction toward the projection surface  10  are superimposed on each other to form a superimposed area  15 . 
     The image light projected by each of the two projectors, the image light from the first projector  200 A and the image light from the second projector  200 B are projected onto the superimposed area  15 . The luminance in the superimposed area  15  is therefore higher than that in the area of the first projection area  11  other than the superimposed area  15 . Furthermore, the luminance in the superimposed area  15  is higher than that in the area of the second projection area  13  other than the superimposed area  15 . Therefore, the first projector  200 A lowers the luminance of the image to be displayed in the superimposed area  15  to a value lower than the luminance of the image to be displayed in the area other than the superimposed area  15  to make the difference in luminance between the superimposed area  15  and the other area less noticeable. Similarly, the second projector  200 B lowers the luminance of the image to be displayed in the superimposed area  15  to a value lower than the luminance of the image to be displayed in the area other than the superimposed area  15  to make the difference in luminance between the superimposed area  15  and the other area less noticeable. The display system  1  thus suppresses luminance unevenness of the entire image including the first and second images. 
     2. Configuration of Control Apparatus  100   
       FIG.  2    shows an example of the configuration of the control apparatus  100 . 
     The configuration of the control apparatus  100  will be described with reference to  FIG.  2   . 
     The control apparatus  100  includes a first interface  110 , an operation section  120 , a display section  130 , and a first control section  150 . An interface is hereinafter also abbreviated to an I/F. 
     The first I/F  110  is a wired interface having terminals, such as a USB (universal serial bus) connector and an Ethernet connector, and an interface circuit. The first I/F  110  may instead be an interface for wireless communication. Ethernet is a registered trademark. 
     The operation section  120  includes an input device, for example, a keyboard and a mouse, and accepts a user&#39;s operation. The operation section  120  outputs an operation signal corresponding to the accepted operation to the first control section  150 . 
     The display section  130  includes a display panel, such as a liquid crystal panel and an organic electroluminescence (EL) panel. The display section  130  displays a display screen generated by the first control section  150 . 
     The first control section  150  is a computer apparatus including a first storage  151  and a first processor  153 . 
     The first storage  151  includes a volatile memory, such as a RAM (random access memory), and a nonvolatile memory, such as a ROM (read only memory). The first storage  151  further includes an auxiliary storage device, such as an SSD (solid state drive) and an HDD (hard disk drive). 
     The first storage  151  stores a control program  151 A to be executed by the first processor  153  and image data  151 B to be supplied to the projectors  200 . The control program  151 A contains an application program that corrects luminance unevenness of the images displayed on the projection surface  10  by the first projector  200 A and the second projector  200 B. The image data  151 B may be data received by the control apparatus  100  from an external source or may be data generated by the user through operation of the operation section  120 . 
     The first processor  153  is an arithmetic operation device formed of a CPU (central processing unit) or an MPU (micro-processing unit). The first processor  153  executes the control program  151 A to control each portion of the control apparatus  100 . 
     The first control section  150  reads the image data from the first storage  151  and divides one frame of the read image data into two image data portions, left and right image data portions into which the image data is divided in the horizontal direction. Out of the two left and right image data portions, the first control section  150  transmits the left image data portion to the first projector  200 A and the right image data portion to the second projector  200 B. 
     When the application program is activated through operation of the control section  120 , the first control section  150  executes the application program. The first control section  150  that executes the application program controls the first projector  200 A to generate first correction values that correct the luminance unevenness of the image displayed by the first projector  200 A. Similarly, the first control section  150  that executes the application program controls the second projector  200 B to generate second correction values that correct the luminance unevenness of the image displayed by the second projector  200 B. The first control section  150  uses the first correction values to correct the image displayed by the first projector  200 A, so that the first control section  150  corrects the luminance at a first position in the image displayed by the first projector  200 A from a first luminance value to a first target value. Similarly, the first control section  150  uses the second correction values to correct the image displayed by the second projector  200 B, so that the first control section  150  corrects the luminance at a third position in the image displayed by the second projector  200 B from a third luminance value to a second target value. 
     When there is differences in luminance between the image displayed by the first projector  200 A and the image displayed by the second projector  200 B, the first control section  150  generates third corrections value that correct the differences in luminance between the images. The process of generating the first, second, and third correction values will be described later in detail. The first, second, and third correction values are parameters used in the process of correcting luminance, and are in the present embodiment numerical values to be added to or subtracted from luminance values. The first, second, and third correction values may instead be parameters in an arithmetic operation of changing luminance values. The first, second, and third correction values may still instead be arithmetic expressions or matrices used to carry out the arithmetic operation of changing luminance values. 
     3. Configuration of Projectors  200   
       FIG.  3    is a block diagram showing an example of the configuration of the first projector  200 A. 
     The configuration of the first projector  200 A will be described with reference to  FIG.  3   . The second projector  200 B has substantially the same configuration as that of the first projector  200 A. The configuration of the second projector  200 B will not therefore be described in detail. In the following description, each component provided in the first projector  200 A has a reference character followed by “A”, and each component provided in the second projector  200 B has a reference character followed by “B”. For example, a second control section  250  provided in the first projector  200 A is called a second control section  250 A, and the second control section  250  provided in the second projector  200 B is called a second control section  250 B. 
     The first projector  200 A includes a remote control light receiver  211 A, an operation panel  213 A, an imaging section  215 A, a second I/F  221 A, an image processing section  223 A, a frame memory  225 A, an image projection section  230 A, and the second control section  250 A. 
     The remote control light receiver  211 A receives an infrared signal transmitted by a remote control  201 . The remote control light receiver  211 A outputs an operation signal corresponding to the received infrared signal to the second control section  250 A. The operation signal is a signal corresponding to an operated switch of the remote control  201 . 
     The operation panel  213 A is mounted, for example, on an enclosure of the first projector  200 A and includes, for example, a variety of switches, such as a power switch that powers on and off the first projector  200 A. When any of the switches on the operation panel  213 A is operated, an operation signal corresponding to the operated switch is outputted from the operation panel  213 A to the second control section  250 A. 
     The imaging section  215 A includes an imaging lens, an imaging device, such as a CCD (charge coupled device) and a CMOS (complementary MOS) device, and a data processing circuit. An imaging optical system, the imaging device, and the data processing circuit are not shown. Under the control of the second control section  250 A, the imaging section  215 A captures an image in the projection direction in which the image projection section  230 A projects the image light. The imaging range, that is, the angle of view of the imaging section  215 A covers the projection surface  10  and regions therearound. The imaging section  215 A outputs the captured image generated by the image capturing operation to the second control section  250 A. 
     The second I/F  221 A is a wired interface having terminals, such as a USB connector and an Ethernet connector, and an interface circuit. The second I/F  221 A may instead be an interface for wireless communication. 
     The frame memory  225 A is coupled to the image processing section  223 A. The frame memory  225 A includes a plurality of banks. The banks each have storage capacity that allows image data corresponding to one frame to be written to the bank. The frame memory  225 A is formed, for example, of an SDRAM (synchronous dynamic random access memory). The image processing section  223 A develops image data inputted via the second I/F  221 A in the frame memory  225 A. 
     The image processing section  223 A performs image processing on the image data developed in the frame memory  225 A. The image processing performed by the image processing section  223 A includes, for example, resolution conversion or resizing, distortion correction, shape correction, digital zooming, and adjustment of image hue and brightness. The image processing section  223 A carries out a process specified by the second control section  250 A and uses, as required, parameters inputted from the second control section  250 A. The image processing section  223 A can, of course, perform a plurality of types of the image processing described above in combination. The image processing section  223 A reads the image data developed in the bank selected by the second control section  250 A from the frame memory  225 A and outputs the read image data to image projection section  230 A. 
     The image processing section  223 A and the frame memory  225 A are, for example, formed of integrated circuits. The integrated circuits include an LSI, an ASIC (application specific integrated circuit), a PLD (programmable logic device), an FPGA (field-programmable gate array), an SoC (system-on-a-chip), and other devices. An analog circuit may form part of the configurations of the integrated circuits, or the second control section  250 A and the integrated circuits may be combined with each other. 
       FIG.  4    shows an example of the configuration of the image projection section  230 A. 
     The configuration of the image projection section  230 A will now be described with reference to  FIG.  4   . 
     The image projection section  230 A modulates the light outputted from a light source  231 A to generate image light, and an optical unit  235 A enlarges the generated image light and projects the enlarged image light. The image projection section  230 A includes the light source  231 A, three liquid crystal panels  233 A(r),  233 A(g), and  233 A(b) as light modulators, the optical unit  235 A, and a panel driver  237 A. The liquid crystal panels  233 A(r),  233 A(g), and  233 A(b) provided in the first projector  200 A are hereinafter collectively referred to as liquid crystal panels  233 A. The image projection section  230 A and the components provided therein, the light source  231 A, the liquid crystal panels  233 A, the optical unit  235 A, and the panel driver  237 A, are an example of a display section. 
     The light source  231 A includes a discharge-type light source lamp, such as an ultrahigh-pressure mercury lamp and a metal halide lamp, or a solid-state light source, such as a light emitting diode and a semiconductor laser. The light outputted from the light source  231 A enters the liquid crystal panels  233 A. The liquid crystal panels  233 A(r),  233 A(g), and  233 A(b) are each formed, for example, of a transmissive liquid crystal panel including a liquid crystal material encapsulated between a pair of transparent substrates. The liquid crystal panel  233 A(r) modulates red light, the liquid crystal panel  233 A(g) modulates green light, and the liquid crystal panel  233 A(b) modulates blue light. The liquid crystal panels each have a pixel area formed of a plurality of pixels arranged in a matrix, and a drive voltage is applicable to the liquid crystal material on a pixel basis. 
     The image data outputted by the image processing section  223 A is inputted to the panel driver  237 A. The panel driver  237 A applies a drive voltage according to the inputted image data to each of the pixels in the pixel areas to set the pixel to have optical transmittance according to the image data. The light outputted from the light source  231 A passes through pixel areas of the liquid crystal panels  233 A(r),  233 A(g), and  233 A(b) and is therefore modulated on a pixel basis to form image light corresponding to the image data on a color basis. The thus formed red image light, green image light, and blue image light are combined with one another on a pixel basis by a light combining system that is not shown into image light representing a color image. The optical unit  235 A includes a projection lens and other components, enlarges the image light modulated by liquid crystal panels  233 A(r),  233 A(g) and  233 A(b), and projects the enlarged image light onto the first projection area  11  of projection surface  10 . 
     Referring back to  FIG.  3   , the configuration of the second control section  250 A will be described. 
     The second control section  250 A is a computer apparatus including a second storage  260 A and a second processor  270 A. 
     The second storage  260 A includes a volatile memory such as a RAM, and a nonvolatile memory, such as a ROM and a flash memory. The second storage  260 A stores, for example, a control program  261 A to be executed by the second processor  270 A, and first pattern image data  263  and second pattern image data  265 , which are used in the process of correcting luminance unevenness. In the present embodiment, solid white image data is used as the first pattern image data  263 , and solid black image data is used as the second pattern image data  265 . 
     The second processor  270 A is an arithmetic operation device formed of a CPU or an MPU. The second processor  270 A executes the control program  261 A to control each portion of the first projector  200 A. The second processor  270 A may be formed of a single processor or a plurality of processors. The second processor  270 A may be formed of an SoC integrated with part or entirety of the second storage  260 A and other circuits. The second processor  270 A may instead be formed of a combination of a CPU that executes a program and a DSP (digital signal processor) that performs predetermined arithmetic processing. Further, the entire functions of the second processor  270   a  may be implemented in hardware or may be implemented by using a programmable device. 
     The second control section  250 A controls the image processing section  223 A and the image projection section  230 A in accordance with instructions received from the control apparatus  100  to display an image on the projection surface  10 . The second control section  250 A causes the imaging section  215 A to capture an image of the projection surface  10  in accordance with an instruction received from the control apparatus  100 , and transmits the captured image generated by the image capturing operation to the control apparatus  100 . 
     4. Correction of Luminance Unevenness 
     The first control section  150  controls the first projector  200 A and the second projector  200 B to generate the first correction values that correct the luminance unevenness of the image displayed by the first projector  200 A, as described above. The first control section  150  further controls the first projector  200 A and the second projector  200 B to generate the second correction values that correct the luminance unevenness of the image displayed by the second projector  200 B. 
     In general, it is known that luminance unevenness occurs in the images displayed by the projectors  200  on the projection surface  10 . The luminance unevenness is caused, for example, by the characteristics of the screen, and the structures of the projection lens and the projectors  200 . In many cases, it is known that the luminance unevenness occurs in such a way that the luminance is higher at a position closer to the center of the projection surface  10 , and the luminance is lower at a position closer to the periphery of the projection surface  10 . 
       FIG.  5    shows an example in which the luminance unevenness occurs in the overall image displayed by the projectors  200 . 
       FIG.  5    shows 25 blocks into which the overall image displayed by the projectors  200  is divided, five vertical blocks and five horizontal blocks. The blocks each contain a preset number of pixels.  FIG.  5    also shows the luminance of representative blocks. The luminance is the average of the luminance values of the pixels contained in each of the representative blocks, the luminance expressed in the form of percentage, that is, the ratio of the luminance of the block of interest to the luminance of a block B 33  located at the center of the image and expressed as 100%. 
     In the example shown in  FIG.  5   , the luminance of blocks B 11  and B 51 , which are located at the upper left end and the lower left end viewed in the direction toward the image, and the luminance of blocks B 15  and B 55 , which are located at the upper right end and the lower right end viewed in the direction toward the image, are 66% with respect to the luminance of the block B 33 , which is located at the center of the image. 
     The luminance of blocks B 13  and B 53 , which are located at the center of the image in the horizontal direction and at the upper end and the lower end in the vertical direction, is 80% with respect to the luminance of the block B 33 , which is located at the center of the image. 
     The luminance of blocks B 31  and B 35 , which are located at the center of the image in the vertical direction and at the left end and the right end in the horizontal direction, is 72% with respect to the luminance of the block B 33 , which is located at the center of the image. 
     The luminance of a block B 22 , which is located in the second row counted from above in the vertical direction and in the second column counted from left in the horizontal direction when viewed in the direction toward the image, and the luminance of a block B 24 , which is located in the second row counted from above in the vertical direction and in the fourth column counted from left in the horizontal direction when viewed in the direction toward the image, are 80% with respect to the luminance of the block B 33 , which is located at the center of the image. 
     The luminance of a block B 42 , which is located in the fourth row counted from above in the vertical direction and in the second column counted from left in the horizontal direction when viewed in the direction toward the image, and the luminance of a block B 44 , which is located in the fourth row counted from above in the vertical direction and in the fourth column counted from left in the horizontal direction when viewed in the direction toward the image, are 80% with respect to the luminance of the block B 33 , which is located at the center of the image. 
     As described above, in the example shown in  FIG.  5   , a block closer to the center of the image has higher luminance, and a block farther from the center toward the periphery has lower luminance, resulting in a difference in luminance depending on the position in the projected image. 
     The first control section  150  carries out the following processes to reduce the difference in luminance depending on the position in the image projected by the first projector  200 A. 
     The first control section  150  first identifies the range of the first projection area  11  in the captured image captured by the imaging section  215 A. For example, the first control section  150  causes the first projector  200 A to project a second pattern image that is an image based on the second pattern image data  265 , and causes the imaging section  215 A to capture an image of the projection surface  10 . The second pattern image is a solid black image. The first control section  150  receives the captured image from the first projector  200 A and identifies the range of the second pattern image displayed in the received captured image to identify the range of the first projection area  11  in the captured image. The first control section  150  generates first range information representing the identified range of the first projection area  11  in the captured image. 
     The first control section  150  then causes the first projector  200 A to display a first pattern image that is an image based on the first pattern image data  263 . The first pattern image is a solid white image. The first control section  150  further causes the second projector  200 B to display the second pattern image based on the second pattern image data  265 . The present embodiment will be described with reference to the case where the second projector  200 B displays the solid black image based on the second pattern image data  265 , and may instead be described with reference to a case where the light from a light source  231 B provided in the second projector  200 B is not allowed to leak out of the second projector  200 B. For example, the light source  231 B may be turned off or a shutter associated with the projection lens may be closed so that the light from the light source  231 B does not leak out of the second projector  200 B. 
     The first control section  150  then instructs the first projector  200 A to capture an image and receives the captured image captured by the imaging section  215 A from the first projector  200 A. Having received the captured image from the first projector  200 A, the first control section  150  uses the first range information to identify the range of the first projection area  11  in the received captured image. 
     The first control section  150  then determines the first position and a second position and calculates the first correction value that corrects the luminance at the first position from the first luminance value to the first target value. 
     The first position is the position of a pixel or a block in the first projection area  11 , the pixel or the block being subject to the luminance value correction. The second position is the position of a pixel or a block in the first projection area  11 , the pixel or the block serving as a luminance value reference when the luminance value at the first position is corrected. 
     For example, the second position is a position that satisfies the conditions below. 
     In a two-dimensional coordinate system so set that the origin is located at the upper left corner of the first projection area  11  and axes X and Y extend in the horizontal and vertical directions respectively, the coordinate X of the second position is an integer ax, which satisfies the condition expressed by Expression (1) or (2) below,
 
0≤ ax≤ 0.1 X  max  (1)
 
0.9 X  max≤ ax≤X  max  (2)
 
where Xmax represents the maximum coordinate of the first projection area  11  in the axis-X direction, and Ymax represents the maximum coordinate of the first projection area  11  in the axis-Y direction.
 
     The second position may instead be a position that satisfies the conditions below. 
     The coordinate system is so set that the origin is located at the upper left corner of the first projection area  11  and the axes X and Y extend in the horizontal and vertical directions, respectively, as described above. Under the definition that Xmax represents the maximum coordinate of the first projection area  11  in the axis-X direction, and Ymax represents the maximum coordinate of the first projection area  11  in the axis-Y direction, the coordinate Y of the second position is an integer by, which satisfies the condition expressed by Expression (3) or (4) below.
 
0≤ by≤ 0.1 Y  max  (3)
 
0.9 Y  max≤ by≤Y  max  (4)
 
     The first and second positions may instead be positions that satisfy the condition below. 
     Assuming that (cx, dy) are the coordinates X and Y of the first position and (ax, by) are the coordinates X and Y of the second position, the coordinates (ax, by) and the coordinates (cx, dy) satisfy the relationship expressed by Expression (5) below. Note that cx is the coordinate X of the first position, and that dy is the coordinate Y of the first position. 
     
       
         
           
             
               
                 
                   
                     
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     That is, the second position in the first projection area  11 , i.e., the image displayed by the first projector  200 A is located outward from the first position. 
     The second position may still instead be a position that satisfies the conditions below. 
     The coordinates X and Y of the second position (ax, by) are (0, 0), (0, Ymax), (Xmax, 0), or (Xmax, Ymax). 
     The first position may still instead be a position that satisfies the condition below. 
     The first position is the pixel located at the center of the first projection area  11 , that is, the center of the image projected by the first projector  200 A, which means that the coordinates of the first position (cx, dy) are cx=Xmax/2 and dy=Ymax/2. That is, the first position is located substantially at the center of the image. 
     The following description, provided that the entire horizontal width of the first projection area  11  is considered to be 100%, will be made on the assumption that the second position is the position of the pixel shifted rightward by 10% of the entire horizontal width from the left end of the first projection area  11  or leftward by 10% of the entire horizontal width from the right end of the first projection area  11 . The second position is located outward from the first position in the image. That is, the description will be made on the assumption that the first position is located inward from the second position in the image. 
     The first and second positions may each be set as the position of a pixel of the image or a block containing a plurality of pixels. In particular, the second position may be a block containing a pixel shifted leftward by 10% of the entire horizontal width from the right end of the first projection area  11 , or a block containing a pixel shifted leftward by 10% of the entire horizontal width from the right end of the first projection area  11 . In this case, whether or not the first position is located inward from the second position in the image can be evaluated based, for example, on the length of the straight line that connects the center of the image to the center of the block. For example, it is assumed in  FIG.  5    that the block containing the second position is the block B 22 . In this case, the distance between the center of the block B 33  located at the center of the image and the center of the block B 22  is longer than the distance between the center of the block B 33  located at the center of the image and the center of a block B 23 . Therefore, when the block containing the second position is the block B 22 , the block B 23  can be determined as a block located inward from the block B 22  containing the second position, so that any of the pixels contained in the block B 23  can be set as a pixel located at the first position, or the block B 23  may be set as a block containing the first position. 
     Once the first and second positions are determined, the first control section  150  determines the first target value by correcting the first luminance value, which represents the luminance at the first position, based on a second luminance value representing the luminance at the second position. 
     The first control section  150  calculates the first correction value that corrects the luminance at the first position in the image displayed by the first projector  200 A from the first luminance value to the first target value. In the present embodiment, the first control section  150  determines the second luminance value at the second position as the first target value and calculates the first correction value that corrects the first luminance value at the first position to the second luminance value at the second position. That is, the first control section  150  sets the value as a result of subtraction of the first luminance value at the first position from the second luminance value at the second position as the first correction value. 
     It is noted that the first target value may not be equal to the second luminance value. For example, the first target value only needs to be closer to the second luminance value than the first luminance value. For example, let (r1, g1, b1) be the RGB values of the first luminance value, (r2, g2, b2) be the RGB values of the second luminance value, and (r3, g3, b3) be the RGB values of the first target value, and the RGB values of the first target value may be so determined that the integers r3, g3, b3 satisfy all conditions expressed by Expressions (6), (7), and (8) below.
 
 r 2≤ r 3&lt; r 1  (6)
 
 g 2≤ g 3&lt; g 1  (7)
 
 b 2≤ b 3&lt; b 1  (8)
 
     The first correction value may, for example, be the value as a result of subtraction of the RGB values of the first luminance value (r1, g1, b1) from the RGB values of the first target value (r3, g3, b3). Since the luminance at the first position in the image displayed by the first projector  200 A is corrected by the first correction value to the first target value, which is closer to the second luminance value than the first luminance value, the luminance at the first position becomes closer to the luminance at the second position, whereby the effect of luminance unevenness of the image displayed by the first projector  200 A can be reduced. 
     When the first and second positions are each set as the position of a pixel of the image, the first control section  150  calculates the first correction value for each of the pixels of the image. When the first and second positions are each set as the position of a block containing a plurality of pixels, the first control section  150  calculates the first correction value for each of the blocks. When the first and second positions are each set as the position of a block containing a plurality of pixels, the first luminance value may be the average of the luminance values of the plurality of pixels contained in the block set as the block located at the first position. Similarly, the second luminance value may be the average of the luminance values of the plurality of pixels contained in the block set as the block located at the second position. The first control section  150  transmits the calculated first correction values to the first projector  200 A. 
     Having received the first correction values from the control apparatus  100 , the second control section  250 A of the first projector  200 A outputs the received first correction values to the image processing section  223 A. The image processing section  223 A corrects the luminance values of the image data by using the inputted first correction values, and outputs the corrected image data to the image projection section  230 A. A first corrected image that is an image in which the luminance values of the image data have been corrected by the first correction values is thus displayed in the first projection area  11  of the projection surface  10 . 
     As for the second image projected by the second projector  200 B, the first control section  150  similarly determines the second target value by correcting the third luminance value representing the luminance at the third position based on a fourth luminance value representing the luminance at a fourth position in the image. 
     The third position is a position located inward from the fourth position in the image displayed by the second projector  200 B, and is the position of a pixel or a block in the second image, the pixel or the block being subject to the luminance value correction, as the first position in the image displayed by the first projector  200 A is. The fourth position is a position located outward from the third position in the image displayed by the second projector  200 B, and is the position of a pixel or a block in the second image, the pixel or the block serving as the luminance value reference when the luminance value at the third position is corrected, as the second position in the image displayed by the first projector  200 A is. 
     In the present embodiment, the first control section  150  determines the second target value by using the fourth luminance value at the fourth position. The first control section  150  determines the fourth luminance value at the fourth position as the second target value and calculates the second correction value that corrects the third luminance value at the third position to the fourth luminance value at the fourth position. That is, the first control section  150  sets the value as a result of subtraction of the third luminance value at the third position from the fourth luminance value at the fourth position as the second correction value. 
     It is noted that the second target value may not be equal to the fourth luminance value, as the first target value is not. The second target value only needs to be closer to the fourth luminance value than the third luminance value. The second correction value may be a correction value that corrects the third luminance value at the third position to the second target value. For example, the value as a result of subtraction of the third luminance value from the second target value may be set as the second correction value. The first control section  150  calculates the second correction value for each of the pixels or blocks of the image displayed by the second projector  200 B. The first control section  150  transmits the calculated second correction values to the second projector  200 B. 
     Having received the second correction values from the control apparatus  100 , the second control section  250 B of the second projector  200 B outputs the received second correction values to the image processing section  223 B. The image processing section  223 B corrects the luminance values of the image data by using the inputted second correction values, and outputs the corrected image data to the image projection section  230 B. A second corrected image that is an image in which the luminance values of the image data have been corrected by the second correction values is thus displayed in the second projection area  13  of the projection surface  10 . 
     The first control section  150  then generates the third correction values. The third correction values are correction values that correct the differences in luminance between the image displayed by the first projector  200 A and the image displayed by the second projector  200 B. 
     The first control section  150  changes the first target value based on the second target value when the first target value is greater than the second target value, that is, when the second luminance value is greater than the fourth luminance value. The first control section  150  then generates the third correction value that corrects the luminance at the first position in the image displayed by the first projector  200 A to the changed first target value. That is, the first control section  150  generates the third correction values that correct the second luminance value in the first image to the fourth luminance value in the second image. 
     The first control section  150  changes the second target value based on the first target value when the second target value is greater than the first target value, that is, when the fourth luminance value is greater than the second luminance value. The first control section  150  then generates the third correction value that corrects the luminance at the third position in the image displayed by the second projector  200 B to the changed second target value. That is, the first control section  150  generates the third correction values that correct the fourth luminance value in the second image to the second luminance value in the first image. 
     When the first target value is greater than the second target value, the first control section  150  transmits the third correction values to the first projector  200 A. When the second target value is greater than the first target value, the first control section  150  transmits the third correction values to the second projector  200 B. 
     Having received the third correction values from the control apparatus  100 , the second control section  250 A outputs the received third correction values to the image processing section  223 A. The image processing section  223 A corrects the luminance values of the image data by using the inputted third correction value, and outputs the image data having the corrected luminance values to the image projection section  230 A. A third corrected image that is an image in which the luminance values of the image data have been corrected by the third correction values is thus displayed in the first projection area  11  of the projection surface  10 . 
     Having received the third correction values from the control apparatus  100 , the second control section  250 B outputs the received third correction values to the image processing section  223 B. The image processing section  223 B corrects the luminance values of the image data by using the inputted third correction values, and outputs the image data having the corrected luminance values to the image projection section  230 B. A fourth corrected image that is an image in which the luminance values of the image data have been corrected by the third correction values is then displayed in the second projection area  13  of the projection surface  10 . 
     The first control section  150  then accepts settings of a blended area for the tiling projection and sets luminance by which the luminance in the set blended area is lowered. 
     The blended area is the area where the first projectors  200 A and second projector  200 B lower the luminance of the images, and the blended area may coincide with the superimposed area  15  or may be broader than the superimposed area  15 . 
     The first control section  150  accepts operations that set the blended area. For example, the first control section  150  causes the display section  130  to display figures corresponding to the first projection area  11  and the second projection area  13  on the projection surface  10  and accepts operations that set the blended area. Based on the accepted operations, the first control section  150  generates first setting information representing the ratio, expressed in percentage, of the blended area extending from the right end of the first projection area  11  to halfway therein to the entire first projection area  11  and second setting information representing the ratio, expressed in percentage, of the blended area extending from the left end of the second projection area  13  to halfway therein to the entire second projection area  13 . 
     The first control section  150  then transmits control data instructing the first projector  200 A and the second projector  200 B to display the first pattern image. The first control section  150  then transmits the first setting information and the second setting information received by the operation section  120  to the first projector  200 A and the second projector  200 B, respectively. 
     The first control section  150  then transmits to the first projector  200 A control data instructing the first projector  200 A to lower by a preset setting value the luminance values in the blended area set by the first setting information. Similarly the first control section  150  transmits to the second projector  200 B control data instructing the second projector  200 B to lower by a preset setting value the luminance values in the blended area set by the second setting information. The setting value by which the luminance values in the blended area is lowered may be set in advance by the user via the operation section  120 , or by using an initial value held by the application program executed by the first control section  150 . 
     The first control section  150  transmits control data instructing the first projector  200 A to capture an image of the projection surface  10 . When receiving the captured image from the first projector  200 A, the first control section  150  analyzes the captured image to determine the luminance values in the blended area and the non-blended area. For example, the first control section  150  determines the luminance values in a preset central area of the first projection area  11  and a preset central area of the blended area. The first control section  150  then determines the difference between the calculated luminance values and evaluates whether or not the determined difference in the luminance value is smaller than or equal to a predetermined value. 
     When the calculated difference in luminance is not smaller than or equal to the predetermined value, the first control section  150  transmits to the first projector  200 A and the second projector  200 B control data instructing the two projectors to further lower the luminance values in the blended area by the preset setting value. When the calculated difference in the luminance value is smaller than or equal to the predetermined value, the first control section  150  terminates the process procedure and starts supplying the first projector  200 A and the second projector  200 B with image data to be projected on the projection surface  10 . 
     5. Action of Display System 
       FIG.  6    is a flowchart showing the action of the display system  1 . 
     The action of the display system  1 , primarily the action of the control apparatus  100 , will be described with reference to the flowchart shown in  FIG.  6   . The process procedure is carried out, for example, after the control apparatus  100  is coupled to the first projectors  200 A and  200 B and when the application program is activated. 
     The first control section  150  first controls the first projector  200 A to calculate the first correction values that correct the luminance of the image displayed by the first projector  200 A (step S 1 ). 
     The first control section  150  then controls the second projector  200 B to calculate the second correction values that correct the luminance of the image displayed by the second projector  200 B (step S 2 ). The processes in steps S 1  and S 2  will be described later in detail with reference to the flowchart of  FIG.  7   . 
     The first control section  150  then transmits the first correction values calculated in step S 1  to the first projector  200 A, and causes the first projector  200 A to display the first corrected image on the projection surface  10 . The first control section  150  transmits the second correction values calculated in step S 2  to the second projector  200 B, and causes the second projector  200 B to display the second corrected image on the projection surface  10  (step S 3 ). 
     The first control section  150  then calculates the third correction values that correct the luminance unevenness of the overall image displayed on the projection surface  10  by the first projector  200 A and the second projector  200 B (step S 4 ). The process described above will be described in detail with reference to the flowchart shown in  FIG.  8   . The first control section  150  transmits the generated third correction values to the first projector  200 A or the second projector  200 B, both of which are subject to the correction of luminance unevenness of the overall image. Furthermore, the first control section  150  causes the first projector  200 A or second projector  200 B to which the third correction values have been transmitted to display the third corrected image on the projection surface  10  (step S 5 ). 
     The first control section  150  then accepts operations that set the blended area (step S 6 ). For example, the first control section  150  causes the display section  130  to display figures corresponding to the first projection area  11  and the second projection area  13  on the projection surface  10  and accepts operations that set the blended area on the figures. The setting operation described above contains the first setting information representing the ratio, expressed in percentage, of the blended area extending from the right end of the first projection area  11  to halfway therein to the overall first projection area  11  and the second setting information representing the ratio, expressed in percentage, of the blended area extending from the left end of the second projection area  13  to halfway therein to the overall second projection area  13 . 
     The first control section  150  then transmits the control data instructing the first projector  200 A and the second projector  200 B to display the first pattern image (step S 7 ). The first control section  150  then transmits the first setting information and the second setting information received via the operation section  120  to the first projector  200 A and the second projector  200 B, respectively (step S 8 ). 
     The first control section  150  then transmits to the first projector  200 A the control data instructing the first projector  200 A to lower by a preset setting value the luminance in the blended area set by the first setting information (step S 9 ). Similarly, the first control section  150  transmits to the second projector  200 B the control data instructing the second projector  200 B to lower by a preset setting value the luminance in the blended area set by the second setting information (step S 10 ). 
     The first control section  150  then transmits the control data instructing the first projector  200 A to capture an image of the projection surface  10  (step S 11 ). Having instructed capture of an image of the projection surface  10 , the first control section  150  evaluates whether or not the first control section  150  has received the captured image captured by the first projector  200 A (step S 12 ). Having received no captured image (NO in step S 12 ), the first control section  150  waits for reception of the captured image. 
     Having received the captured image (YES in step S 12 ), the first control section  150  analyzes the captured image to determine the luminance values in the blended area and the non-blended area (step S 13 ). For example, the first control section  150  determines the luminance in a preset central area of the first projection area  11  and a preset central area of the blended area. The first control section  150  then determines the difference in the calculated luminance value between the two areas and evaluates whether or not the determined difference in the luminance is smaller than or equal to a predetermined value (step S 14 ). 
     When the calculated difference in the luminance is not smaller than or equal to the predetermined value (NO in step S 14 ), the first control section  150  returns to the process in step S 9 . The first control section  150  transmits to the first projector  200 A and the second projector  200 B the control data instructing the two projectors to further lower the luminance in the blended area by the preset setting value. 
     When the calculated difference in the luminance is smaller than or equal to the predetermined value (YES in step S 14 ), the first control section  150  terminates the process procedure and starts supplying the first projector  200 A and the second projector  200 B image data to be projected on the projection surface  10 . 
       FIG.  7    is a flowchart showing the action of the display system  1  and shows step S 1  in detail. 
     Step S 1  will be described in detail with reference to  FIG.  7   . 
     The first control section  150  first transmits control data instructing the first projector  200 A to display the second pattern image (step S 101 ). The first control section  150  then transmits to the first projector  200 A control data instructing the first projector  200 A to capture an image of the projection surface  10  and transmit the captured images generated by the image capturing operation (step S 102 ). The first control section  150  then evaluates whether or not the first control section  150  has received the captured image from the first projector  200 A (step S 103 ). Having received no captured image (NO in step S 103 ), the first control section  150  waits for reception of the captured image. 
     When receiving the captured image from the first projector  200 A (YES in step S 103 ), the first control section  150  analyzes the received captured image to detect the area where an image of the second pattern image has been captured and identifies the first projection area  11  of the captured image (step S 104 ). The first control section  150  generates the first range information representing the range of the first projection area  11  of the captured image (step S 104 ). 
     The first control section  150  then transmits the control data instructing the first projector  200 A to display the first pattern image (step S 105 ) and the control data instructing the second projector  200 B to display the second pattern image (step S 106 ). 
     The first control section  150  then transmits to the first projector  200 A the control data instructing the first projector  200 A to capture an image of the projection surface  10  and transmit the captured images generated by the image capturing operation (step S 107 ). The first control section  150  then evaluates whether or not the first control section  150  has received the captured image from the first projector  200 A (step S 108 ). Having received no captured image (NO in step S 108 ), the first control section  150  waits for reception of the captured image. 
     Having received the captured image (YES in step S 108 ), the first control section  150  identifies the first projection area  11  of the received captured image based on the first range information generated in step S 104  (step S 109 ). 
     The first control section  150  then determines the luminance at the second position set in advance in the identified first projection area  11  (step S 110 ). For example, provided that the entire horizontal width of the first projection area  11  of the captured image is considered to be 100%, the first control section  150  uses the position shifted leftward by 10% of the entire horizontal width from the right end of the first projection area  11  as the horizontal coordinate of the second position. Provided that the entire vertical width of the first projection area  11  is considered to be 100%, the first control section  150  uses the position separate by 50% of the entire vertical width from the upper end of the first projection area  11 , in other words at the center of the first projection area  11 , as the vertical coordinate of the second position. 
     The first control section  150  then calculates the average of the luminance values in the block at the first position out of the blocks into which the captured image is so divided that the blocks each contain a predetermined number of pixels (step S 111 ). The first control section  150  then determines the first target value based on the second luminance value representing the luminance at the second position calculated in step S 110  and the first luminance value representing the average of the luminance values in the block at the first position. In the present embodiment, the second luminance value representing the luminance at the second position is determined as the first target value. 
     The first control section  150  then determines the difference between the luminance at the second position determined as the first target value and the average of the luminance values in the block at the first position. As for each of the other blocks, the first control section  150  similarly determines the difference between the luminance at the second position determined as the first target value and the average of the luminance values in the block. The first control section  150  calculates the difference in luminance calculated on a block basis as the first correction value in the block (step S 112 ). That is, the first correction value is a value that corrects the average of the luminance values in each of the blocks to the luminance at the second position, which is the first target value. 
     The first control section  150  controls the second projector  200 B in accordance with the same procedure as that shown in  FIG.  7    to calculate the second correction value that corrects the average of the luminance values in each of the blocks in the second projection area  13  to the luminance at the reference position. The information representing the range of the second projection area  13  identified by causing the second projector  200 B to display the second pattern image, capturing an image of the second pattern image, and analyzing the captured image is called second range information. 
       FIG.  8    is a flowchart showing the action of the display system  1  and shows a detailed procedure of step S 4 . The detailed procedure of step S 4  will be described with reference to the flowchart shown in  FIG.  8   . 
     The first control section  150  first compares the luminance value at the second position, which is the first target value, in the image displayed by the first projector  200 A on the projection surface  10 , with the luminance value at the fourth position, which is the second target value, in the image displayed by the second projector  200 B on the projection surface  10  (step S 401 ). 
     When the luminance value at the second position is greater than the luminance value at the fourth position (YES in step S 401 ), the first control section  150  calculates the third correction values by subtracting the luminance value at the fourth position, which is the second target value, from the luminance value at the second position, which is the first target value (step S 402 ). The first control section  150  then transmits the calculated third correction values to the first projector  200 A in step S 5 . 
     When the luminance value at the fourth position is greater than the luminance value at the second position (NO in step S 401 ), the first control section  150  calculates the third correction values by subtracting the luminance value at the second position, which is the first target value, from the luminance value at the fourth position, which is the second target value (step S 403 ). The first control section  150  then transmits the third correction values calculated in step S 403  to the second projector  200 B in step S 5 . 
       FIG.  9    is a flowchart showing the action of the first projector  200 A. 
     The action of the first projector  200 A will be described with reference to the flowchart shown in  FIG.  9   . The first projector  200 A and the second projector  200 B operate identically, and the action of the second projector  200 B will not therefore be described in detail. 
     The second control section  250 A first evaluates whether or not the second control section  250 A have received control data from the control apparatus  100  (step T 1 ). The control data includes, for example, the image display instruction, the image capturing and captured image transmission instruction, and the correction values generated by the control apparatus  100 . 
     Having received no control data (NO in step T 1 ), the second control section  250 A transitions to evaluation in step T 10 . Having received control data (YES in step T 1 ), the second control section  250 A evaluates whether or not the received control data is the image display instruction (step T 2 ). When the control data is the image data display instruction (YES in step T 2 ), the second control section  250 A causes the image projection section  230 A to display image data instructed by the control data in the first projection area  11  (step T 3 ). 
     When the received control data is not the image display instruction (NO in step T 2 ), the second control section  250 A evaluates whether or not the received control data is the image capturing and captured image transmission instruction (step T 4 ). When the received control data is the image capturing and captured image transmission instruction (YES in step T 4 ), the second control section  250 A causes the imaging section  215 A to capture an image (step T 5 ). The second control section  250 A then transmits the generated captured image to the control apparatus  100  (step T 6 ). 
     When the received control data is not the image capturing and captured image transmission instruction (NO in step T 4 ), the second control section  250 A evaluates whether or not the received control data is the correction values that correct the luminance values of the image (step T 7 ). The correction values that the first projector  200 A receives from the control apparatus  100  include the first or third correction values. When the received control data is the correction values (YES in step T 7 ), the second control section  250 A outputs the received correction values to the image processing section  223 A. When the image data received by the second I/F  221 A is inputted, the image processing section  223 A corrects the luminance values of the inputted image data by using the first or third correction values and outputs the corrected image data to the image projection section  230 A (step T 8 ). 
     When the received control data is not the correction values (NO in step T 7 ), the second control section  250 A carries out a process corresponding to the received control data (step T 9 ). The process to be carried out at this point corresponds, for example, to the processes in steps S 8  and S 9  shown in  FIG.  6   . Having received the first setting information from the control apparatus  100 , the second control section  250 A lowers the luminance over the range of the image corresponding to the received first setting information by the preset setting value in accordance with the instruction from the control apparatus  100 . 
     Having received no control data in step T 1  (NO in step T 1 ), the second control section  250 A evaluates whether or not the second control section  250 A has received an image data supply start notification from the control apparatus  100  (step T 10 ). Having received no start notification (NO in step T 10 ), the second control section  250 A returns to the evaluation in step T 1 . 
     Having received the start notification (YES in step T 10 ), the second control section  250 A evaluates whether or not the second control section  250 A has received image data from the control apparatus  100  (step T 11 ). Having received no image data (NO in step T 11 ), the second control section  250 A waits for reception of image data. Having received image data (YES in step T 11 ), the second control section  250 A causes the image processing section  223 A to correct the luminance values of the received image data. 
     The image processing section  223 A corrects the luminance values of the image data received via the second I/F  221 A by using the first or third correction values (step T 12 ) and outputs the corrected image data to the image projection section  230 A. The image projection section  230 A displays an image based on the inputted image data in the first projection area  11  of the projection surface  10  (step T 13 ). 
     6. Effects 
     As described above, the display system  1  according to the present embodiment includes the control apparatus  100 , the first projector  200 A, and the second projector  200 B. 
     The control apparatus  100  carries out the processes below. 
     The control apparatus  100  first determines the first target value by correcting the first luminance value representing the luminance at the first position in the first image displayed by the first projector  200 A on the projection surface  10  based on the second luminance value representing the luminance at the second position in the first image. 
     The control apparatus  100  then causes the first projector  200 A to display on the projection surface  10  the first corrected image generated by correcting the first image in such a way that the luminance at the first position in the first image becomes the first target value. 
     The control apparatus  100  then determines the second target value by correcting the third luminance value representing the luminance at the third position in the second image displayed by the second projector  200 B on the projection surface  10  based on the fourth luminance value representing the luminance at the fourth position in the second image. 
     The control apparatus  100  then causes the second projector  200 B to display on the projection surface  10  the second corrected image generated by correcting the second image in such a way that the luminance at the third position in the second image becomes the second target value. 
     Thereafter, when the first target value is greater than the second target value, the control apparatus  100  changes the first target value based on the second target value and causes the first projector  200 A to display on the projection surface  10  the third corrected image generated by using the changed first target value. 
     Thereafter, when the second target value is greater than the first target value, the control apparatus  100  changes the second target value based on the first target value and causes the second projector  200 B to display on the projection surface  10  the fourth corrected image generated by using the changed second target value. 
     Therefore, a luminance value of the first image is corrected to the first target value, and a luminance value of the second image is corrected to the second target value. When the first target value is greater than the second target value, the third corrected image in which the first target value is corrected based on the second target value and the second corrected image having a luminance value equal to the second target value are displayed on the projection surface  10 . Furthermore, when the second target value is greater than the first target value, the fourth corrected image in which the second target value is corrected based on the first target value and the first corrected image having a luminance value equal to the first target value are displayed on the projection surface  10 . Luminance unevenness of images displayed by a plurality of projectors  200  can thus be corrected, whereby the luminance of the entire image displayed on the projection surface  10  can be uniform. 
     In the two-dimensional coordinate system employed by the control apparatus  100  and defined by the axis X parallel to a first side of the first image and the axis Y intersecting with the first side and parallel to a second side of the first image, the coordinate X of the second position is the integer ax that satisfies at least one of
 
0≤ ax≤ 0.1 X  max or 0.9 X  max≤ ax≤X  max
 
where Xmax represents the maximum coordinate of the first image along the axis X.
 
     Since an image displayed on the projection surface  10  is brighter at a position closer to the center of the image and becomes darker toward the periphery thereof, the first luminance value at the first position can be corrected based on the second luminance value at the second position by selecting a position that satisfies the conditions described above as the second position. 
     In the two-dimensional coordinate system employed by the control apparatus  100  and defined by the axis X parallel to the first side of the first image and the axis Y intersecting with the first side and parallel to the second side of the first image, the coordinate Y of the second position is the integer by that satisfies at least one of
 
0≤ by≤ 0.1 Y  max or 0.9 Y  max≤ by≤Y  max
 
where Ymax represents the maximum coordinate of the first image along the axis Y.
 
     Since an image displayed on the projection surface  10  is brighter at a position closer to the center of the image and becomes darker toward the periphery thereof, the first luminance value at the first position can be corrected based on the second luminance value at the second position by selecting a position that satisfies the conditions described above as the second position. 
     The control apparatus  100  selects the second position in the first image in such a way that the second position is located outward from the first position. 
     Since an image displayed on the projection surface  10  is brighter at a position closer to the center of the image and becomes darker toward the periphery thereof, the first luminance value at the first position can be corrected based on the second luminance value at the second position by selecting a position that satisfies the conditions described above as the second position. 
     In the two-dimensional coordinate system employed by the control apparatus  100  and defined by the axis X parallel to the first side of the first image and the axis Y intersecting with the first side and parallel to the second side of the first image, ax, by, cx, and dy are integers that satisfy the following conditions: 
                 ❘   &#34;\[LeftBracketingBar]&#34;         c   ⁢   x     -       X   ⁢   max     2         ❘   &#34;\[RightBracketingBar]&#34;       ≤         ❘   &#34;\[LeftBracketingBar]&#34;         a   ⁢   x     -       X   ⁢   max     2         ❘   &#34;\[RightBracketingBar]&#34;       ⁢        and   ⁢            ❘   &#34;\[LeftBracketingBar]&#34;         d   ⁢   y     -       Y   ⁢   max     2         ❘   &#34;\[RightBracketingBar]&#34;         ≤       ❘   &#34;\[LeftBracketingBar]&#34;         b   ⁢   y     -       Y   ⁢   max     2         ❘   &#34;\[RightBracketingBar]&#34;             
where Xmax represents the maximum coordinate of the first image along the axis X, Ymax represents the maximum coordinate of the first image along the axis Y, (cx, dy) represents the coordinates of the first position, and (ax, by) represents the coordinates of the second position.
 
     Since an image displayed on the projection surface  10  is brighter at a position closer to the center of the image and becomes darker toward the periphery thereof, the first luminance value at the first position can be corrected based on the second luminance value at the second position by selecting a position that satisfies the conditions described above as the second position. 
     In the two-dimensional coordinate system employed by the control apparatus  100  and defined by the axis X parallel to the first side of the first image and the axis Y intersecting with the first side and parallel to the second side of the first image, one of (0, 0), (0, Ymax), (Xmax, 0), or (Xmax, Ymax) is selected as the coordinates of the second position (ax, by), where Xmax represents the maximum coordinate of the first image along the axis X, Ymax represents the maximum coordinate of the first image along the axis Y. 
     A pixel at an end of the first image can therefore be selected as the second position. Since an image displayed on the projection surface  10  is brighter at a position closer to the center of the image and becomes darker toward the periphery thereof, the first luminance value at the first position can be corrected based on the second luminance value at the second position by selecting a position that satisfies the condition described above as the second position. 
     The control apparatus  100  selects a pixel located substantially at the center of the first image as the first position. 
     The luminance value of the central pixel having high luminance can therefore be corrected to the luminance value of a peripheral pixel having low luminance. 
     In the two-dimensional coordinate system employed by the control apparatus  100  and defined by the axis X parallel to the first side of the first image and the axis Y intersecting with the first side and parallel to the second side of the first image, cx=Xmax/2 is selected as the coordinate cx of the first position along the axis X, and dy=Ymax/2 is selected as the coordinate dy of the first position along the Y-axis, where Xmax represents the maximum coordinate of the first image along the axis X, Ymax represents the maximum coordinate of the first image along the axis Y. 
     The luminance value of the central pixel having high luminance can therefore be corrected to the luminance value of a peripheral pixel having low luminance. 
     7. Other Embodiments 
     The embodiment described above is a preferable embodiment of the present disclosure. The present disclosure is, however, not limited to the embodiment described above, and a variety of variations are conceivable to the extent that the variations do not depart from the substance of the present disclosure. 
     For example, the first projector  200 A or the second projector  200 B may perform the actions of the control apparatus  100  according to the embodiment described above to generate the first, second, and third correction values. 
     The first projector  200 A may generate the first correction values, and the second projector  200 B may generate the second correction values. Furthermore, when the first target value is greater than the second target value, the first projector  200 A may generate the third correction value, and when the second target value is greater than the first target value, the second projector  200 B may generate the third correction value. 
     When the first projector  200 A generates the first and third correction values, the first projector  200 A performs the actions below. 
     The first projector  200 A first determines the first target value by correcting the first luminance value representing the luminance at the first position in the first image, which is displayed by the first projector  200 A on the projection surface  10 , based on the second luminance value representing the luminance at the second position in the first image. 
     The first projector  200 A then displays on the projection surface  10  the first corrected image generated by correcting the first image in such a way that the luminance at the first position in the first image becomes the first target value. 
     The first projector  200 A then changes the first target value based on the second target value when the second target value, which is determined by correcting the third luminance value representing the luminance at the third position in the second image, which is displayed by the second projector  200 B on the projection surface  10 , based on the fourth luminance value representing the luminance at the fourth position in the second image, is smaller than the first target value. 
     The first projector  200 A displays the third corrected image generated by using the changed first target value on the projection surface  10 . 
     Also in the configuration described above, when the luminance values of the first image are corrected to the first target value, and the first target value is greater than the second target value, the third corrected image in which the first target value is corrected based on the second target value is displayed on the projection surface  10 . The luminance unevenness of the images displayed by a plurality of projectors  200  can therefore be corrected by causing the second projector  200 B to display on the projection surface  10  the second corrected image in which the luminance values have been corrected to the second target value, whereby the luminance of the entire image displayed on the projection surface  10  can be uniform. 
     In the embodiments described above, the luminance of the image displayed on the projection surface  10  is detected based on the image captured by the imaging section  215 A incorporated in the first projector  200 A, and the luminance may instead be detected with a sensor. The sensor is disposed, for example, between the light source  231 A and the liquid crystal panels  233 A and downstream from the rear end of any of mirrors that separate the light outputted from the light source  231 A into the R light, the G light, and the B light. 
     The luminance values of the images displayed by the projectors  200  may be corrected after the luminance values in the blended area for the tiling projection are set. In this case, the control apparatus  100  sets a pixel at an end of the blended area to be the second position, the pixel set when the luminance values in the blended area are set, and generates the first correction value that corrects the luminance value at the first position to the luminance value at the set second position. 
     The control apparatus  100  may set the position shifted inward from an end of the image displayed in the first projection area  11  by 10% of the entire horizontal width thereof to be the second position, as described in the aforementioned embodiments. 
     In the embodiments described above, the image processing section  223 A corrects the image data based on the first correction values or the first and third correction values to lower the luminance of the image. Another method for lowering the luminance of the image may be lowering the luminance value of the light from the light source  231 A. In this case, the second control section  250 A controls a light source driver that drives the light source  231 A based on the first correction values or the first and third correction values received from the control apparatus  100  to lower the luminance value of the light from the light source  231 A. The light source driver is not shown in the figures. 
     The functional portions of the control apparatus  100  shown in  FIG.  2    each represent a functional configuration and are each not necessarily implemented in a specific form. That is, hardware corresponding to each of the functional portions is not necessarily implemented, and a single processor that executes a program can, of course, achieve the functions of the plurality of functional portions. Furthermore, in the embodiments described above, part of the functions achieved by software may be achieved by hardware, or part of the functions achieved by hardware may be achieved by software. In addition, the specific detailed configuration of each of the other portions in the control apparatus  100  can be arbitrarily changed to the extent that the change does not depart from the substance of the present disclosure. The same holds true for the configurations of the first projector  200 A and the second projector  200 B. 
     The functional portions of the projectors  200  shown in  FIG.  3    each represent a functional configuration and are each not necessarily implemented in a specific form. That is, hardware corresponding to each of the functional portions is not necessarily implemented, and a single processor that executes a program can, of course, achieve the functions of the plurality of functional portions. Furthermore, in the embodiments described above, part of the functions achieved by software may be achieved by hardware, or part of the functions achieved by hardware may be achieved by software. In addition, the specific detailed configuration of each of the other portions of the projectors  200  can be arbitrarily changed to the extent that the change does not depart from the substance of the present disclosure. 
     The process units in the flowcharts shown in  FIGS.  6  to  9    are process units into which the action of the display system  1  is divided in accordance with the contents of primary processes for easy understanding of the action. How to divide the action into the process units or the names of the process units shown in the flowcharts in  FIGS.  6  to  9    do not limit the present disclosure. The processes carried out by the display system  1  can each be further divided into a larger number of process units, or can each be so divided that one process unit includes a larger number of processes in accordance with the content of the process. Furthermore, the orders in accordance with which the processes are carried out in the flowcharts described above are not limited to those shown in  FIGS.  6  to  9   . 
     In a case where the display method for the display system or the display method for the display apparatus according to the embodiments of the present disclosure is achieved by a computer provided in the control apparatus  100  or a computer provided in any of the projectors  200 , a program executed by the computer can be configured in the form of a recording medium. The program executed by the computer can instead be configured in the form of a transmission medium via which the program is transmitted. The recording medium can be a magnetic or optical recording medium or a semiconductor memory device. Specific examples of the recording medium may include a flexible disk, an HDD, a CD-ROM (compact disk read only memory), a DVD (digital versatile disc), a Blu-ray disc, a magneto-optical disk, a flash memory, and a portable or immobile recording medium such as a card-shaped recording medium. The recording medium described above may instead be a RAM, a ROM, an HDD, or any other nonvolatile storage device that is an internal storage device provided in a server apparatus. Blu-ray is a registered trademark. 
     The aforementioned embodiments have been described with reference to a configuration using the projectors  200  each as the display apparatus, but not necessarily in the present disclosure. For example, the display apparatus may be formed of a self-luminous display apparatus, for example, a monitor or a television, such as a liquid crystal display, an organic EL (electro-luminescence) display, a plasma display, a micro-LED (light emitting diode) display, a CRT (cathode ray tube) display, an SED (surface-conduction electron-emitter display). 
     When any of the display apparatuses described above is employed, the liquid crystal panel, the organic EL panel, the plasma display panel, the LED, or any other image forming portion corresponds to the display section. 
     The embodiments described above have been described with reference to the configuration in which the projectors  200 , which are each the display apparatus, each include three transmissive liquid crystal panels, the liquid crystal panels  233 A(r),  233 A(g), and  233 A(b) corresponding to RGB, as the light modulators, but not necessarily. For example, the projectors  200  may each have a configuration employing three reflective liquid crystal panels or a single liquid crystal panel combined with a color wheel. The projectors  200  may still instead each have a configuration employing, for example, three digital mirror devices (DMDs) or a single digital mirror device combined with a color wheel. In place of a liquid crystal panel or a DMD, a light modulator capable of modulating the light outputted from a light source is employable with no problem.