Abstract:
Methods and circuits can be provided to correct crosstalk artifacts by generating image data correction matrices for respective pixel locations in an image sensor, based on pre-calibration matrices associated with the respective pixel locations. The image data correction matrices can be applied to the respective pixel locations to reduce imaging crosstalk artifacts associated with at least one of disparity, luminance, and chrominance.

Description:
FIELD OF THE INVENTION 
     The inventive concept relates to digital image signal processing in general, and more particularly to devices and methods for correcting crosstalk artifacts. 
     BACKGROUND 
     An image sensor is a device that converts an optical signal into an electrical signal. As the size of each pixel in the image sensor decreases, an undesired effect can be created, which is referred to as crosstalk. Crosstalk can be a major cause of artifacts in images taken by the image sensor. 
     SUMMARY 
     Embodiments can provide methods for correcting crosstalk artifacts in an image signal processor circuit. In some embodiments according to the inventive concept, methods and circuits can be provided to correct crosstalk artifacts by generating image data correction matrices for respective pixel locations in an image sensor, based on pre-calibration matrices associated with the respective pixel locations. The image data correction matrices can be applied to the respective pixel locations to reduce imaging crosstalk artifacts associated with at least one of disparity, luminance, and chrominance. 
     In some embodiments the method includes: performing an interpolation operation using color values of neighbor pixels to obtain interpolated color values at a current pixel; determining first matrix coefficients; and performing a first multiplication operation between the interpolated color values and the first matrix to correct disparity between the current pixel and the neighbor pixels. 
     According to at least some example embodiments, the first matrix is expressed as follows: 
     
       
         
           
             
               ( 
               
                 
                   
                     1 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     
                       
                         d 
                         1 
                       
                       2 
                     
                   
                   
                     
                       1 
                       + 
                       
                         
                           d 
                           2 
                         
                         2 
                       
                     
                   
                   
                     
                       
                         d 
                         2 
                       
                       2 
                     
                   
                   
                     
                       
                         d 
                         3 
                       
                       2 
                     
                   
                 
                 
                   
                     
                       - 
                       
                         
                           d 
                           1 
                         
                         2 
                       
                     
                   
                   
                     
                       - 
                       
                         
                           d 
                           2 
                         
                         2 
                       
                     
                   
                   
                     
                       1 
                       - 
                       
                         
                           d 
                           2 
                         
                         2 
                       
                     
                   
                   
                     
                       - 
                       
                         
                           d 
                           3 
                         
                         2 
                       
                     
                   
                 
                 
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     1 
                   
                 
               
               ) 
             
               
           
         
       
         
         
           
             wherein d1, d2, and d3 are the first matrix coefficients. 
           
         
       
    
     According to at least some example embodiments, the method for correcting crosstalk artifacts in an image signal processor may further include determining second matrix coefficients; and performing a second multiplication operation between the interpolated color values and the second matrix to correct chromaticity. 
     According to at least some example embodiments, the second matrix is expressed as follows: 
     
       
         
           
             
               ( 
               
                 
                   
                     
                       a 
                       11 
                     
                   
                   
                     
                       a 
                       12 
                     
                   
                   
                     
                       a 
                       13 
                     
                   
                 
                 
                   
                     
                       a 
                       21 
                     
                   
                   
                     
                       a 
                       22 
                     
                   
                   
                     
                       a 
                       23 
                     
                   
                 
                 
                   
                     
                       a 
                       31 
                     
                   
                   
                     
                       a 
                       32 
                     
                   
                   
                     
                       a 
                       33 
                     
                   
                 
               
               ) 
             
               
           
         
       
         
         
           
             wherein a 11 , a 12 , a 13 , a 31 , a 32 , and a 33  are coefficients. 
           
         
       
    
     According to at least some example embodiments, the method for correcting crosstalk artifacts in an image signal processor may further include determining a third matrix coefficient; and performing a third multiplication operation between the interpolated color values and the third matrix to correct Luma. 
     According to at least some example embodiments, the third matrix is expressed as follows: 
     
       
         
           
             
               ( 
               
                 
                   
                     C 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     C 
                   
                   
                     0 
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     0 
                   
                   
                     C 
                   
                   
                     0 
                   
                 
                 
                   
                     0 
                   
                   
                     0 
                   
                   
                     0 
                   
                   
                     C 
                   
                 
               
               ) 
             
               
           
         
       
     
     wherein C is a coefficient. 
     According to at least some example embodiments, the first, second, and third multiplication operations are performed sequentially. 
     According to at least some example embodiments, the first, second, and third multiplication operations are performed simultaneously. 
     According to at least some example embodiments, the first, second, and third multiplication operations do not affect each other. 
     At least one other example embodiment provides an image signal processor. 
     According to at least some example embodiments, the image signal processor includes: a current pixel selector configured to select a current pixel in an image data output from an image sensor; an interpolator configured to obtain interpolated color values at the current pixel; and a disparity filter configured to perform a first multiplication operation between the interpolated color values and a first matrix for correcting disparity between the current pixel and neighbor pixels. 
     According to at least some example embodiments, the image signal processor may further include a Chroma filter configured to perform a second multiplication operation between the interpolated color values and a second matrix for correcting chromaticity. 
     According to at least some example embodiments, the image signal processor may further include a Luma filter configured to perform a third multiplication operation between the interpolated color values and a third matrix for correcting Luma. 
     According to at least some example embodiments, the first, second, and third multiplication operations are performed sequentially. 
     According to at least some example embodiments, the first, second, and third multiplication operations are performed simultaneously. 
     According to at least some example embodiments, the first, second, and third multiplication operations do not affect each other. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic block diagram of an image processing system in some embodiments of the inventive concept; 
         FIG. 2  is a cross-sectional view of a pixel region included in the pixel array of an image sensor illustrated in  FIG. 1 , according to some embodiments of the inventive concept; 
         FIG. 3  is a schematic block diagram of an image signal processor circuit illustrated in  FIG. 1 , according to embodiments of the inventive concept; 
         FIG. 4A  is a diagram illustrating disparity correcting operations according to embodiments of the inventive concept; 
         FIG. 4B  is a diagram illustrating disparity correcting operations according to embodiments of the inventive concept; 
         FIG. 5A  is a diagram illustrating chromaticity correcting operations according to embodiments of the inventive concept; 
         FIG. 5B  is a diagram illustrating chromaticity correcting operations according to embodiments of the inventive concept; 
         FIG. 5C  is a diagram illustrating chromaticity correcting operations according to embodiments of the inventive concept; 
         FIG. 5D  is a diagram illustrating chromaticity correcting operations according to embodiments of the inventive concept; 
         FIG. 6  is a flowchart illustrating methods of correcting crosstalk artifacts according to embodiments of the inventive concept; and 
         FIG. 7  is a schematic block diagram of an image processing system including an image sensor according to embodiments of the inventive concept. 
     
    
    
     DETAILED DESCRIPTION 
     The invention now will be described more fully hereinafter with reference to the accompanying drawings. The invention may, however, be embodied in many different forms and should not be construed as limited to the embodiments set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the invention to those skilled in the art. Like numbers refer to like elements throughout. 
     The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used herein, the singular forms “a”, “an” and “the” are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms “comprises” and/or “comprising,” when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. 
     It will be understood that when an element is referred to as being “connected” or “coupled” to another element, it can be directly connected or coupled to the other element or intervening elements may be present. In contrast, if an element is referred to as being “directly connected” or “directly coupled” to another element, there are no intervening elements present. 
     It will be understood that, although the terms first, second, etc. may be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. Thus, a first element could be termed a second element without departing from the teachings of the present invention. 
     Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein. 
     As will be appreciated by one skilled in the art, aspects of the present disclosure may be illustrated and described herein in any of a number of patentable classes or contexts including any new and useful process, machine, manufacture, or composition of matter, or any new and useful improvement thereof. Accordingly, aspects of the present disclosure may be implemented entirely hardware, entirely software (including firmware, resident software, micro-code, etc.) or combining software and hardware implementation that may all generally be referred to herein as a “circuit,” “module,” “component,” or “system.” Furthermore, aspects of the present disclosure may take the form of a computer program product comprising one or more computer readable media having computer readable program code embodied thereon. 
     Any combination of one or more computer readable media may be used. The computer readable media may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an appropriate optical fiber with a repeater, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device. 
     A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device. Program code embodied on a computer readable signal medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing. 
     Aspects of the present disclosure are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the disclosure. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable instruction execution apparatus, create a mechanism for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     These computer program instructions may also be stored in a computer readable medium that when executed can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions when stored in the computer readable medium produce an article of manufacture including instructions which when executed, cause a computer to implement the function/act specified in the flowchart and/or block diagram block or blocks. The computer program instructions may also be loaded onto a computer, other programmable instruction execution apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatuses or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     As described herein, in some embodiments according to the inventive concept, an artificial grid construct can be arranged to overlie some physical pixel locations included in an image sensor. In some embodiments, each of the locations in the grid can correspond to a subset of the physical pixels in the sensor, in other embodiments, however, the locations in the grid can be in a one-to-one correspondence with the physical pixels in the sensor. 
     A calibration process can be employed to determine correction matrices for pixels that are associated with locations in the grid. For example, during calibration, a known target can be sampled using the image sensor. The values for the physical pixels that correspond to the grid locations can be analyzed to determine how the sample values should be corrected to more closely correspond to the known values of the target. 
     Correction matrices for the remaining physical pixels (that do not correspond to the grid locations) can be determined based on correction matrices determined during calibration by, for example, interpolation. Accordingly, if an physical pixel is located between four adjacent grid locations, a correction matrix for the actual pixel can be determined by interpolating from the correction matrices associated with each of the adjacent grid locations. It will be understood, however, that in embodiments where each of the physical pixels in the image sensor corresponds to a grid location, no interpolation may be necessary to determine the correction matrices for the physical pixels. Rather, the correction matrices for each of the physical pixels could be determined during calibration. 
     In some embodiments, the interpolated correction matrices can be used to correct disparity, Luma, and Chroma between physical pixels. Furthermore, each of these corrections can be separable from one another such that any of the corrections can be performed without affecting the remaining corrections. Furthermore, the corrections may be carried out in any order without any impact on the outcome of each of the corrections. 
       FIG. 1  is a schematic block diagram of an image processing system  10  according to embodiments of the inventive concept. Referring to  FIG. 1 , the image sensing system  10  includes an image sensor  100 , a digital signal processor (DSP)  200 , and a display unit  300 . 
     The image sensor  100  includes a pixel array or an active pixel sensor (APS) array  110 , a row driver  120 , an analog-to-digital converter (ADC)  130 , a ramp generator  160 , a timing generator  170 , a control register block  180 , and a buffer  190 . 
     The image sensor  100  is controlled by the DSP  200  to sense an object  400  photographed through a lens  500  and output electrical image data. In other words, the image sensor  100  converts a sensed optical image into image data and outputs the image data. 
     The pixel array  110  includes a plurality of photo sensitive devices such as photo diodes or pinned photo diodes. The pixel array  110  senses light using the photo sensitive devices and converts the light into an electrical signal to generate an image signal. 
     The timing generator  170  may output a control signal to the row driver  120 , the ADC  143 , and the ramp generator  160  to control the operations of the row driver  120 , the ADC  130 , and the ramp generator  160 . The control register block  180  may output respect control signals to the ramp generator  160 , the timing generator  170 , and the buffer  190  to control the operations thereof. The control register block  180  is controlled by a camera control  210 . 
     The row driver  120  drives the pixel array  110  in units of rows. For instance, the row driver  120  may generate a row selection signal. That is, the row driver  120  decodes a row control signal (e.g. an address signal) generated by the timing generator  170 , and selects at least one of rows in the pixel array  110  in response to the decoded row control signal. The pixel array  110  outputs to the ADC  130  pixel signals from the row selected by the row selection signal provided from the row driver  120 . 
     The ADC  130  converts the pixel signals from the pixel array  110  to digital pixel signals and outputs the digital pixel signals to the buffer  190 . The buffer  190  temporarily stores the digital pixel signals output from the ADC  130  and outputs the buffered digital pixel signals to the DSP  200 . 
     The DSP  200  may output image data, which has been sensed and output by the image sensor  100 , to the display unit  300 . At this time, the display unit  300  may be any device that can display an image for viewing. For instance, the display unit  300  may be a computer, a mobile phone, or any type of image display terminal. The DSP  200  includes the camera control  210 , an image signal processor circuit  220 , and a personal computer (PC) interface (I/F)  230 . The camera control  210  controls the control register block  180 . The camera control  210  may control the image sensor  100  according to the I 2 C protocol. Other protocols can be used. 
     The image signal processor circuit  220  receives image data, i.e., the buffered digital pixel signals from the buffer  190 , performs a processing operation on an image corresponding to the image data, and outputs the image to the display unit  300  through PC I/F  230 . The image data may be called an “image”. 
       FIG. 2  is a cross-sectional view of a pixel region included in the pixel array of an image sensor illustrated in  FIG. 1 , according to embodiments of the inventive concept. Referring to  FIGS. 1 and 2 , the pixel region  111  includes microlenses  113 , a color filter  115 - 1 ,  115 - 2  or  115 - 3 , an inter-metal dielectric layer  117  and a carrier substrate  121 . 
     Each of the microlenses  113  focuses light incident from an external source. In some embodiments, the pixel region  111  may be implemented without including the microlenses  113 . 
     The color filter  115 - 1 ,  115 - 2  or  115 - 3  transmits wavelengths in a visible region. For example, the color filter  115 - 1 ,  115 - 2  or  115 - 3  may be a red filter, a green filter, or a blue filter respectively. The red filter transmits light having wavelengths in a red region from among the wavelengths in the visible region. The green filter transmits light having wavelengths in a green region from among the wavelengths in the visible region. The blue filter transmits light having wavelengths in a blue region from among the wavelengths in visible region. In some embodiments, the color filter  115 - 1 ,  115 - 2 , or  115 - 3  may be a cyan filer, a magenta filter, or a yellow filter, respectively. The cyan filter transmits light having wavelengths in a 450-550 nm region from among the wavelengths in the visible region. The magenta filter transmits light having wavelengths in a 400-480 nm region from among the wavelengths in the visible region. The yellow filter transmits light having wavelengths in a 500-600 nm region from among the wavelengths in the visible region. Other filters can be used. 
     The inter-metal dielectric layer  117  may be formed of an oxide layer, or a composite layer of an oxide layer and a nitride layer. The oxide layer may be a silicon oxide layer. The inter-metal dielectric layer  117  may include metals  119 . Electrical wiring for sensing operations of the pixel region  111  may be provided by the metals  119 . The metals  119  may include copper, titanium, or titanium nitride. Other metals can be used. The carrier substrate  121  may be a silicon substrate. Other substrates can be used. The photodetectors  123 - 1 ,  123 - 2 , and  123 - 3  are in the carrier substrate  121 . Each of the photodetectors  123 - 1 ,  123 - 2 , and  123 - 3  may generate photoelectrons in response to light incident from an external source. Each of the photodetectors  123 - 1 ,  123 - 2 , and  123 - 3  is a photosensitive element and may be implemented by using a photodiode, a phototransistor, a photogate, or a pinned photodiode (PPD). 
     As appreciated by the present inventors, as the pixel size  112  decreases, the light passed through the filter  115 - 2 , for example, can be transmitted to the photodetector  123 - 1  rather than the photodetector  123 - 2 . This phenomenon is called the optical crosstalk. In addition, part of the photoelectrons generated by the photodetector  123 - 2  can flow to the photodetector  123 - 3 . This phenomenon is called electrical crosstalk. The optical or electrical crosstalk can cause artifacts in images taken by the image sensor  100 . The artifacts are related to Luma, Chroma, and disparity. 
     Luma represents the brightness in an image. Luma may be called luminance. Luma can be expressed as shown below in Equation 1.
 
 Y=R+G+B   [Equation 1]
 
In Equation 1, Y is Luma, R is a red pixel signal having the red value, G is a green pixel signal having the green value, and B is a blue pixel signal having the blue value.
 
     Chroma represents the color information in an image. Chroma may be called chromaticity. Chroma can be expressed as shown below in Equation 2.
 
 Rn=R /( R+G+B ), Bn=B /( R+G+B )  [Equation 2]
 
In Equation 2, Rn is a first component, Bn is a second component, R is a red pixel signal having the red value, G is a green pixel signal having the green value, and B is a blue pixel signal having the blue value. That is the Chroma is represented as the first and second components.
 
       FIG. 3  is a schematic block diagram of an image signal processor circuit  220  illustrated in  FIG. 1 , in some embodiments of the inventive concept. Referring to  FIGS. 1 and 3 , the image signal processor circuit  220  includes a current pixel selector  221 , an interpolator  223 , a disparity filter  225 , a Chroma filter  227 , and a Luma filter  229 . Each component  221 ,  223 ,  225 ,  227  and  229  can be configured as software or hardware or a combination thereof. 
     The current pixel selector  221  selects the current pixel in the image data output from the image sensor  100 . Hereafter the pixel indicates a sample of the image data. The interpolator  223  is used to obtain the interpolated color values at the current pixel selected by the current pixel selector  221 , as illustrated, for example, in  FIG. 4A . The disparity filter  225  is used to improve color disparity between the current pixel and the neighboring pixels, as illustrated, for example, in  FIGS. 4A and 4B . The Chroma filter  227  is used to correct chromaticity, as illustrated, for example, in  FIGS. 5A to 5D . The Luma filter  229  is used to correct Luma, as illustrated, for example, in  FIG. 6 . 
     In some embodiments, operations of the disparity filter  225 , the Chroma filter  227 , and the Luma filter  229  may be performed sequentially. In some embodiments, the operations of the disparity filter  225 , the Chroma filter  227 , and the Luma filter  229  may be performed simultaneously, as the disparity filter  225 , the Chroma filter  227 , and the Luma filter  229  are orthogonal to each other. 
       FIG. 4A  is a diagram illustrating disparity correcting operations in some embodiments of the inventive concept. Referring to  FIGS. 1 to 3 , and  4 A, the current pixel  401  has the color value (e.g. the green value GR 22 ). The color value GR 22  is different from the color values (e.g. GB 11 , GB 13 , GB 31 , and GB 33 ) of the neighbor pixels ( 402 ,  404 ,  407  and  409 ). The color value GR 22  is the green value close to red, and each of the color values GB 11 , GB 13 , GB 31 , and GB 33  is the green value close to blue. 
     The difference between the color value GR 22  at current pixel  401  and the color value GB 11 , GB 13 , GB 31 , or GB 33  at neighbor pixel  402 ,  404 ,  407 , or  409  is defined as disparity. The disparity is expressed as shown below in Equation 3.
 
 D =( GR−GB )/( GR+GB )  [Equation 3]
 
     In Equation 3, D is disparity, GR is the color value at the current pixel  401 , and GB is the color value at the neighbor pixel  402 ,  404 ,  407 , or  409 . In some embodiments, GB may be the color value at the current pixel  401 , and GR may be color value at the neighbor pixel  402 ,  404 ,  407 , or  409 . Therefore the disparity should be corrected. 
     The interpolator  223  performs an interpolation operation by using the color values of neighbor pixels  402 ,  404 ,  407 , and  409  to obtain the interpolated color values. For example, the red value R 22  at the current pixel  401  can be interpolated as shown below in Equation 4.
 
 R   22 =( R   21   +R   23 )/2  [Equation 4]
 
In Equation 4, R 21  and R 23  are the red value at pixels  405  and  406 , respectively. R 22  is the interpolated red value at the current pixel  401 .
 
     The blue value B 22  at the current pixel  401  can be interpolated as shown below in Equation 5.
 
 B   22 =( B   12   +B   32 )/2  [Equation 5]
 
In Equation 5, B 12  and B 32  are the blue value at pixels  403  and  408 . B 22  is the interpolated blue value at the current pixel  401 .
 
     The green value GB 22  close to blue at the current pixel  401  can be interpolated as shown below in Equation 6.
 
 GB   22 =( GB   11   +GB   13   +GB   31   +GB   33 )/4  [Equation 6]
 
In Equation 6, GB 11 , GB 13 , GB 31  and GB 33  are the respective green values GB at the pixels  402 ,  404 ,  407  and  409 . GB 22  is the interpolated green value at the current pixel  401 .
 
     The disparity filter  225  determines the first matrix coefficients. The first matrix is expressed as follows: 
               (         1       0       0       0               d   1     2           1   +       d   2     2               d   2     2             d   3     2               -       d   1     2             -       d   2     2             1   -       d   2     2             -       d   3     2               0       0       0       1         )               
where, d 1 , d 2 , and d 3  are coefficients.
 
     The disparity filter  225  performs the first multiplication operation between the interpolated color value and the first matrix to correct disparity between the color value GR 22  at the current pixel  401  and the color value GB 11 , GB 13 , GB 31 , or GB 33  at the neighbor pixel  402 ,  404 ,  407 , or  409 . The first multiplication operation is expressed as shown below in Equation 7. 
                     (           R   xy   ′               GR   xy   ′               GB   xy   ′               B   xy   ′           )     =       (         1       0       0       0               d   1     2           1   +       d   2     2               d   2     2             d   3     2               -       d   1     2             -       d   2     2             1   -       d   2     2             -       d   3     2               0       0       0       1         )     ⁢           (           R   xy               GR   xy               GB   xy               B   xy           )                 [     Equation   ⁢           ⁢   7     ]               
In Equation 7, R′ xy , GR′ xy , GB′ xy , and B′ xy  are the color values after the first multiplication operation, and R xy , GR xy , GB xy , and B xy  are the color values before the first multiplication operation. xy are the pixel location. For example, the color value GR′ 22  at the current pixel  401  after the first multiplication operation is expressed as shown below in Equation 8.
 
                     GR   22   ′     =           d   1     2     ⁢       (       R   21     +     R   23       )     2       +       (     1   +       d   2     2       )     ⁢     GR   22       +       (       d   2     2     )     ⁢       (       GB   11     +     GB   13     +     GB   31     +     GB   33       )     4       +         d   3     2     ⁢       (       B   12     +     B   32       )     2                 [     Equation   ⁢           ⁢   8     ]               
By calculating the color value GR′ 22  at the current value  401 , the disparity filter  225  corrects disparity between the color value GR 22  at the current pixel  401  and the color value GB 11 , GB 13 , GB 31 , or GB 33  at the neighbor pixel  402 ,  404 ,  407 , or  409 .
 
       FIG. 4B  is a diagram for explaining disparity correcting operation according to some example embodiments of the inventive concept. Referring to  FIGS. 1 to 3 ,  4 A, and  4 B, the interpolator  223  performs an interpolation operation by using the color values of neighbor pixels  402 ,  404 ,  407 , and  409  to obtain the interpolated color values. 
     The color value GB′ 22  at the current pixel  411  after the first multiplication operation is expressed as shown below in Equation 9. 
     
       
         
           
             
               
                 
                   
                     GB 
                     22 
                     ′ 
                   
                   = 
                   
                     
                       
                         - 
                         
                           
                             d 
                             1 
                           
                           2 
                         
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               R 
                               12 
                             
                             + 
                             
                               R 
                               32 
                             
                           
                           ) 
                         
                         2 
                       
                     
                     - 
                     
                       
                         
                           d 
                           2 
                         
                         2 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               GR 
                               11 
                             
                             + 
                             
                               GR 
                               13 
                             
                             + 
                             
                               GR 
                               31 
                             
                             + 
                             
                               GR 
                               33 
                             
                           
                           ) 
                         
                         4 
                       
                     
                     + 
                     
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               d 
                               2 
                             
                             2 
                           
                         
                         ) 
                       
                       ⁢ 
                       
                         GB 
                         22 
                       
                     
                     - 
                     
                       
                         
                           d 
                           3 
                         
                         2 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               B 
                               21 
                             
                             + 
                             
                               B 
                               23 
                             
                           
                           ) 
                         
                         2 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     9 
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 5A  is a diagram illustrating chromaticity correcting operations in some embodiments of the inventive concept. Referring to  FIGS. 1 to 3  and  5 A, the Chroma filter  227  determines second matrix coefficients. The Chroma filter  227  performs a second multiplication operation between the interpolated color values and a second matrix for correcting chromaticity. The green value G 22  at the current pixel  501  can be interpolated as shown below in Equation 10.
 
 G   22 =( GB   12   +GR   21   +GR   23   +GB   32 )/4  [Equation 10]
     GB 12 , GR 21 , GR 23  and GB 32  are the pixel values at the neighboring pixels  503 ,  505 ,  506 , and  508 .
 
The blue value B 22  at the current pixel  501  can be interpolated as shown below in Equation 11.
 
 B   22 =( B   11   +B   13   +B   31   +B   33 )/4  [Equation 11]
 
B 11 , B 13 , B 31  and B 33  are the pixel values at the neighboring pixels  502 ,  504 ,  507 , and  509 . The second matrix is expressed as follows:
   

                   (           a   11           a   12           a   13               a   21           a   22           a   23               a   31           a   32           a     33   ⁢                     )           
where, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , and a 33  are the second matrix coefficients. The second multiplication operation is expressed shown below in Equation 12.
 
                     (           R   xy   ′               G   xy   ′               B   xy   ′           )     =       (           a   11           a   12           a   13               a   21           a   22           a   23               a   31           a   32           a   33           )     ⁢     (           R   xy               G   xy               B   xy           )               [     Equation   ⁢           ⁢   12     ]               
In Equation 12, R′ xy , G′ xy , and B′ xy  are the color values after the second multiplication operation and R xy , G xy , and B xy  are the color values before the second multiplication operation, xy is the pixel location.
 
For example, the color value R′ 22  after the second multiplication operation is expressed in Equation 13.
 
     
       
         
           
             
               
                 
                   
                     R 
                     2 
                     ′ 
                   
                   = 
                   
                     
                       
                         a 
                         11 
                       
                       ⁢ 
                       
                         R 
                         22 
                       
                     
                     + 
                     
                       
                         a 
                         12 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               GB 
                               12 
                             
                             + 
                             
                               GR 
                               21 
                             
                             + 
                             
                               GR 
                               23 
                             
                             + 
                             
                               GB 
                               32 
                             
                           
                           ) 
                         
                         4 
                       
                     
                     + 
                     
                       
                         a 
                         13 
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               B 
                               11 
                             
                             + 
                             
                               B 
                               13 
                             
                             + 
                             
                               B 
                               31 
                             
                             + 
                             
                               B 
                               33 
                             
                           
                           ) 
                         
                         4 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     13 
                   
                   ] 
                 
               
             
           
         
       
     
     In some embodiments, the second matrix is expressed as follows: 
                   (           a   11           a   12           a   13               1   -     a   11     -     a   31             1   -     a   12     -     a   32             1   -     a   13     -     a   33                 a   31           a   32           a   33           )           
where, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , and a 33  are the second matrix coefficients.
 
     In some embodiments, the second multiplication operation is expressed shown below in Equation 14 by substituting the second matrix into Equation 12: 
                     (           R   xy   ′               G   xy   ′               B   xy   ′           )     =       (           a   11           a   12           a   13               1   -     a   11     -     a   31             1   -     a   12     -     a   32             1   -     a   13     -     a   33                 a   31           a   32           a   33           )     ⁢     (           R   xy               G   xy               B   xy           )               [     Equation   ⁢           ⁢   14     ]               
In Equation 14, R′ xy , G′ xy , and B′ xy  are the color values after the second multiplication operation and R xy , G xy , and B xy  are the color values before the second multiplication operation, xy is the pixel location.
 
     In some embodiments, the second matrix can be expressed as a 4×4 matrix as follows: 
                   (           a   11             a   12     2             a   12     2           a   13               1   -     a   11     -     a   31             1   -     a   12     -     a   32           0         1   -     a   13     -     a   33                 1   -     a   11     -     a   31           0         1   -     a   12     -     a   32             1   -     a   13     -     a   33                 a   31             a   32     2             a   32     2           a     33   ⁢                     )           
where, a 11 , a 12 , a 13 , a 21 , a 22 , a 23 , a 31 , a 32 , and a 33  are the second matrix coefficients.
 
     In some embodiments, the second multiplication operation is expressed shown below in Equation 15. 
                     (           R   xy   ′               GR   xy   ′               GB   xy   ′               B   xy   ′           )     =       (           a   11             a   12     2             a   12     2           a   13               1   -     a   11     -     a   31             1   -     a   12     -     a   32           0         1   -     a   13     -     a   33                 1   -     a   11     -     a   31           0         1   -     a   12     -     a   32             1   -     a   13     -     a   33                 a   31             a   32     2             a   32     2           a     33   ⁢                     )     ⁢     (           R   xy               GR   xy               GB   xy               B   xy           )               [     Equation   ⁢           ⁢   15     ]               
In Equation 15, R′ xy , GR′ xy , GB′ xy  and B′ xy  are the color values after the second multiplication operation and R xy , GR xy , GB xy  and B xy  are the color values before the second multiplication operation, and xy is the pixel location.
 
 FIG. 5B  is a diagram illustrating chromaticity correcting operations in some embodiments of the inventive concept. Referring to  FIGS. 1 to 3 ,  5 A and  5 B, the red value R 22  at the current pixel  511  can be interpolated as shown below in Equation 16.
 
 R   22 =( R   21   +R   23 )/2  [Equation 16]
 
The blue value B 22  at the current pixel  511  can be interpolated as shown below in Equation 17.
 
 B   22 =( B   12   +B   32 )/2  [Equation 17]
 
     The color value GR 22 ′ at the current pixel  511  after the second multiplication operation is expressed shown below in Equation 18. 
                     GR   22   ′     =         a   21     ⁢       (       R   21     +     R   23       )     2       +       a   22     ⁢     GR   22       +       a   32     ⁢           ⁢       (       B   12     +     B   32       )     2                 [     Equation   ⁢           ⁢   18     ]                 FIG. 5C  is a diagram for explaining chromaticity correcting operation according to still another example embodiment. Referring to  FIGS. 1 to 3 ,  5 A and  5 C, the red value R 22  at the current pixel  521  can be interpolated as shown below in Equation 19.
 
 R   22 =( R   12   +R   32 )/2  [Equation 19]
 
The blue value B 22  at the current pixel  521  can be interpolated as shown below in Equation 20.
 
 B   22 =( B   21   +B   23 )/2  [Equation 20]
 
     The color value GB 22 ′ at the current pixel  521  after the second multiplication operation is expressed shown below in Equation 21. 
                     GB   22   ′     =         a   21     ⁢       (       R   12     +     R   32       )     2       +       a   22     ⁢     GB   22       +       a   32     ⁢           ⁢       (       B   21     +     B   23       )     2                 [     Equation   ⁢           ⁢   21     ]                 FIG. 5D  is a diagram for explaining chromaticity correcting operation according to still another example embodiment. Referring to  FIGS. 1 to 3 ,  5 A and  5 D, the blue value R 22  at the current pixel  531  can be interpolated as shown below in Equation 22.
 
 R   22 =( R   11   +R   13   +R   31   +R   33 )/4  [Equation 22]
 
The green value G 22  at the current pixel  531  can be interpolated as shown below in Equation 23.
 
 G   22 =( GR   12   +GB   21   +GB   23   +GR   32 )/4  [Equation 23]
 
     The color value B22′ at the current pixel  531  after the second multiplication operation is expressed as shown below in Equation 24. 
     
       
         
           
             
               
                 
                   
                     B 
                     22 
                     ′ 
                   
                   = 
                   
                     
                       
                         a 
                         31 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               R 
                               11 
                             
                             + 
                             
                               R 
                               13 
                             
                             + 
                             
                               R 
                               31 
                             
                             + 
                             
                               R 
                               33 
                             
                           
                           ) 
                         
                         4 
                       
                     
                     + 
                     
                       
                         a 
                         32 
                       
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         
                           ( 
                           
                             
                               GR 
                               12 
                             
                             + 
                             
                               GB 
                               21 
                             
                             + 
                             
                               GB 
                               23 
                             
                             + 
                             
                               GR 
                               32 
                             
                           
                           ) 
                         
                         4 
                       
                     
                     + 
                     
                       
                         a 
                         32 
                       
                       ⁢ 
                       
                         B 
                         22 
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     24 
                   
                   ] 
                 
               
             
           
         
       
     
       FIG. 6  is a flowchart illustrating methods for correcting crosstalk artifacts in some embodiments of the inventive concept. Referring to  FIGS. 1 to 6 , the current pixel selector  221  selects the current pixel in the image data output from the image sensor  100  in operation S 10 . 
     The interpolator  223  performs an interpolation operation using color values of neighbor pixels to obtain interpolated color values at a current pixel selected by the current pixel selector  221  in operation S 20 . 
     The disparity filter  225  corrects color disparity between the current pixel and the neighboring pixels in operation S 30 . That is, the disparity filter  225  performs a multiplication operation between the interpolated color values and the first matrix. 
     The Chroma filter  227  corrects chromaticity in operation S 40 . That is, the Chroma filter  227  performs a multiplication operation between the interpolated color values and the second matrix. 
     The Luma filter  229  corrects Luma in operation S 50 . The Luma filter  229  performs a multiplication operation between the interpolated color values and a third matrix, The Luma filter  229  determines the matrix coefficient for Luma correction. The third matrix can be expressed as follows: 
                   (         C       0       0       0           0       C       0       0           0       0       C       0           0       0       0       C         )           
where, C is the third matrix coefficient.
 
     The multiplication operation for Luma correction can be expressed as shown below in Equation 25. 
                     (           R   xy   ′               GR   xy   ′               GB   xy   ′               B   xy   ′           )     =             (         C       0       0       0           0       C       0       0           0       0       C       0           0       0       0       C         )     ⁢     (           R   xy               GR   xy               GB   xy               B   xy           )                 [     Equation   ⁢           ⁢   25     ]               
In Equation 25, R′ xy , GR′ xy , GB′ xy , and B′ xy  indicate the Luma corrected color values after the multiplication operation and R xy , GR xy , GB xy , and B xy  indicate the color values before the multiplication operation.
 
     In some embodiments, the multiplication operations described above can be performed sequentially as shown. In some embodiments, the multiplication operations can be performed in any order without affecting the corrections provided by any of the multiplications. In some embodiments, the multiplication operations are performed simultaneously. Further, in some embodiments, the multiplication operations do not affect each other. In some embodiments, any of the multiplication operations can be eliminated. 
     The first, second and third matrix coefficients can be determined based on a calibration procedure that involves taking images in several illuminations and a color calibration target (e.g. Gretag-Macbeth Color Checker). The results provided by the calibration procedure can be used to interpolate the coefficients for each of the pixels on which correction to be performed. 
       FIG. 7  is a schematic block diagram of an image processing system  1000  including an image sensor  1040  in some embodiments of the inventive concept. 
     The image processing system  1000  may be implemented as a data processing device, such as a personal digital assistant (PDA), a portable media player (PMP), or a mobile communication device such as a mobile phone or a smart phone, which can use or support mobile industry processor interface (MIPI®). The image processing system  1000  may be also implemented as a portable device such as a tablet computer. 
     The image processing system  1000  includes an application processor  1010 , the image sensor  1040 , and a display  1050 . 
     A camera serial interface (CSI) host  1012  implemented in the application processor  1010  may perform serial communications with a CSI device  1041  included in the image sensor  1040  through CSI. A display serial interface (DSI) host  1011  implemented in the application processor  1010  may perform serial communication with a DSI device  1051  included in the display  1050  through DSI. 
     The image processing system  1000  may also include a radio frequency (RF) chip  1060  communicating with the application processor  1010 . A physical layer (PHY)  1013  of the application processor  1010  and a PHY  1061  of the RF chip  1060  may communicate data with each other according to Mobile Industry Processor Interface (MIPI) DigRF. 
     The image processing system  1000  may further include a global positioning system (GPS)  1020 , a data storage device  1070 , a microphone (MIC)  1080 , a memory  1085  (such as a dynamic random access memory (DRAM)), and a speaker  1090 . The image processing system  1000  may communicate using a worldwide interoperability for microwave access (Wimax)  1030 , a wireless local area network (WLAN)  1100 , and ultra-wideband (UWB)  1160 . 
     While some example embodiments of the inventive concept have been particularly shown and described, it will be understood by those of ordinary skill in the art that various changes in form and details may be made therein without departing from the spirit and scope of the present invention as defined by the following claims.