Abstract:
A color modification system and method for reducing the number of computations performed on a pixel color. This reduction in computations increases the rate at which color modification may be performed and decreases the effects of rounding errors. Decreasing the effects of rounding errors produces a more accurate color modification, thereby reducing the likelihood of artifacts. The system and method performs color modification on a pixel color, where the color includes a first, second, and third component and each component defines a value of the color. The system includes a chroma lookup table having a plurality of entries. Each entry corresponds to a luma value and contains chroma coefficients. The chroma coefficients define color modifications to be applied to the components of the color. If a luma value is received, the chroma lookup table generates output chroma coefficients at an output. The output coefficients are generated by accessing the entry corresponding to the luma value, and extracting the output coefficients from the entry. The coefficients may include at least four matrix coefficients. The system may include a first matrix multiplier that receives the four matrix coefficients and at least a first and second of the color at an input and generate at least a first modified component and second modified component as output. The first matrix multiplier applies matrix multiplication to the first and second components using the four output chroma coefficients as the coefficients of the matrices. The chroma lookup table may defines a function of luma, and the function may be nonlinear.

Description:
This patent application is a continuation of U.S. Ser. No. 09/293,259, filed on Apr. 16, 1999, U.S. Pat. No. 6,417,891 which is incorporated by reference herein. 
    
    
     BACKGROUND 
     Digital non-linear editing (DNLE) is a process by which digital media may be edited. DNLE, as the name implies, is performed on digital media stored as data in digital media files on a digital random access medium. DNLE may be conducted in a non-linear fashion because the digital media files in which the digital media is stored can be randomly accessed. Thus an editor may access a piece of the digital media without having to proceed sequentially through other pieces of the digital media stored in the same or other digital media files. More than one editor also may be able to access different pieces of the same digital media contemporaneously. The digital media may be a digitized version of a film or videotape or digital media produced through live capture onto a disk of a graphics or animation software application. Example commercial DNLE systems include the Media Composer® or Symphony video production systems or NewsCutter® news editing system available from Avid Technology, Inc. For a more detailed description of DNLE, see  Digital Nonlinear Editing, New Approaches to Editing Film and Video,  1993 , by Thomas Ohanian. 
     Color modification is a class of operations that may be performed to correct color errors due to process errors and to adjust the colors used in the video for artistic expression. Such color modifications may include enhancing contrasts or color in an image to give a program an overall “look,” or applying special effects to selected segments. Other color modifications may be made by an editor during an editing session to correct problems with color or lighting resulting from the source of the media. Such corrections may include color balancing for camera and lighting differences, correcting for film processing differences, matching colors and tones from shot to shot, or adjusting video levels for differences in source tapes, source decks, etc. 
     Digital images are comprised of an array of picture elements called pixels. For a given image, color modifications may be applied to all pixels in the image or pixels comprising a portion of the image. In digital video signal processing, a variety of data formats can be used to represent the color of pixels within a digital image. Formats may be classified into two major categories: composite signals and component signals. Component formats represent a color as multiple components, each component defining a value along a dimension of the color space in which the color being represented is defined. A composite video signal is an analog signal that uses a high frequency subcarrier to encode color information. The subcarrier is a sinewave of which the amplitude is modulated by the saturation of the color represented by the signal, and the hue of the color is encoded as a phase difference from a color burst. Analog composite signals are generally used to broadcast television video signals. 
     There are a variety of component formats used to represent color. RGB (Red, Green, Blue) format represents a color with a red component, a green component and a blue component. CMYK (Cyan, Magenta, Yellow, Black) format represents a color with a cyan component, a magenta component, and a yellow component. CMYK is a format commonly used by printers. The CMYK components are color opposites of RGB components. In a three-dimensional coordinate system, each component of either the RGB or the CMY format represents a value along an axis, the combination of the values defining a cubic color space. 
     The data formats HSL (Hue, Saturation, Lightness or Luminance) and HSV (Hue, Saturation, Value) represent a color with a hue component, a saturation component, and a luma component. In a three-dimensional coordinate system, the luma component represents a value along a luma axis, the hue component represents the angle of a chroma vector with respect to the luma axis and the saturation component represents the magnitude of the chroma vector. The combination of the values defines a hexagonal cone-shaped color space. 
     YCrCb, YUV, and YIQ are three formats that represent a color with a luma component Y, and two chroma components, Cr and Cb, U and V, or I and Q, respectively, that define a chroma vector. In a three-dimensional coordinate system, each component of either the YCrCb, YUV, and YIQ format represents a value along an axis, the combination of the values defining a cylindrical color space around the luma axis. The chroma components define the chroma vector. In data formats with a luma component, the luma component can be used independently to represent a pixel in a black and white image to be displayed, for example, with a black and white monitor. 
     A typical color modification in HSL color space may include increasing a color component or a combination of color components for all pixels in each digital image of a section of digital media. Typically, an editor accesses a segment of a composition that represents the section of media through an editor interface and inputs desired color modifications through the editor interface. Some systems permit an editor to apply color modifications to only portions of a digital image. Portions of a digital image may be specified as one or more pixels or by specifying a region. For example, an editor may select with a mouse, keyboard, or some other editor input device a portion of the image and define color modifications for the selected portion. A suitable commercial system for color modification is Avid Media Illusion™ available from Avid Technology, Inc. The Avid Media Illusion Reference Guide, available from Avid Technology, Inc. is herein incorporated by reference. Other commercial software applications may be used. 
     Some systems permit an editor to define a color modification as a function of the luma of a pixel. Some systems also allow a user to define functions of luma that allow an editor to define the effect of a color modification over a range of possible luma values of a pixel. For example, an editor may define a highlight function that primarily affects high luma values, a midtone function that primarily affects mid-range luma values, and a shadow function that primarily affects low luma values. The editor may then associate a color modification with each function. If more than one function is defined over a range of luma values, each function, and thus a color modification associated with the function, may have a weighted effect for a given luma value. This weighted effect is defined by the value of the function for the given luma value normalized with respect to the values of functions for the given luma value. 
     For example, a color modification A is specified for a luma function defined by X=2L−2, and a color modification B is specified for a luma function defined by Y=0.5L+2. For pixel P with a luma value of 16, X=30 and Y=10. Normalizing X and Y, the weighted value of X is 0.75 and the weighted value of Y is 0.25. Thus, the color modification applied to pixel P is Z=0.75A+0.25B. It should be noted that the equation used in this example is linear to simplify the explanation, but for decreasing and increasing the effect of a color modification for different values of luma, the function is usually non-linear. 
     The range of possible luma values may have ranges in which one of the functions has a predominant effect. For the highlight, midtone, and shadow functions described above, a highlight range is the range of luma values for which the highlight function has the strongest effect or the greatest weighted value, a midtone range is the range of luma values for which the midtone function has the strongest effect or the greatest weighted value, and the shadow range is the range of luma values for which the shadow function has the strongest effect or the greatest weighted value. 
     On some DNLE systems, an editor may specify a variety of color modifications to be applied to a digital image or a portion of a digital image. These modifications may be specified in variety of color formats, including RGB, HSL, and composite, and in a variety of units, depending on the interface used by the editor and in a variety of units. Possible units include IRE units in accordance with NTSC standards, millivolts in accordance with PAL standards, percentages, radians, and degrees, and a unit may be represented in integer or real number form. The units and formats for software, hardware, and storage on a color modification may all be different. 
     Types of color modifications may range from simple offsets and linear functions to complex non-linear functions and color effects defined by an editor, and may be applied to all pixels of a digital image or specified for pixels meeting positional or component-based criteria. For a component color, modifications may be specified for less than all of the components. For example, a color modification may specify that all pixels having a luma value within a certain range receive an increase in saturation depending on the luma value of the pixel. Color modifications may also include combining color components of a component color to produce a modified component or color. Color modifications are described in U.S. patent application Ser. No. 09/293,730, entitled “Source Color Modification on a Digital Nonlinear Editing System” (the Gonsalves I application) by Robert Gonsalves and Michael D. Laird filed on Apr. 16, 1999, and in U.S. patent application Ser. No. 09/293,732, entitled “Multi-tone Representation of a Digital Image on a Digital Nonlinear Editing System” (the Gonsalves II application), by Robert Gonsalves, filed on Apr. 16, 1999. 
     SUMMARY 
     Because color modifications may be specified in a variety of ways and in a variety of combinations, performing color modifications on an image may include several computations. These computations may consume considerable resources, such as bandwidth and processor time, slowing down the color modification process, and consequently the processing of a video stream. Also, as the number of computations increases, the concatenation of the rounding errors inherent in these computations reduces the accuracy of the modifications applied to a pixel color. This reduction in accuracy may produce undesired artifacts in a digital image. 
     A color modification system that reduces the number of computations performed for color modifications increases the rate at which color modification may be performed and decreases the effects of rounding errors. Decreasing the effects of rounding errors produces more accurate color modifications, thereby reducing the likelihood of artifacts. 
     In one aspect, a system performs color modification on a color, where the color including a first, second, and third component. Each component of the color defines a value of the color. The system includes a chroma lookup table having a plurality of entries, each entry corresponding to a luma value and containing chroma coefficients. The chroma coefficients define color modifications to be applied to the components of the color. If a luma value is received, the chroma lookup table generates output chroma coefficients at an output. The chroma coefficients are generated by accessing the entry corresponding to the luma value, and extracting the output coefficients from the entry. 
     In one embodiment, the chroma coefficients include at least four matrix coefficients, and the system includes a first matrix multiplier that receives the four matrix coefficients and at least a first and second component of the color at an input. The matrix multiplier generates at least a first modified component and second modified component as output by applying matrix multiplication to the first and second components using the four output chroma coefficients as the coefficients of the matrices. 
     In another embodiment, the chroma lookup table defines a function of luma, where the function may be nonlinear. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     In the drawings, 
     FIG. 1 is a data flow diagram of a color modification system; 
     FIG. 2 is a block diagram illustrating an embodiment of a color modification system; 
     FIG. 3 is a data flow diagram illustrating an embodiment of the color modification system of FIG. 1 in more detail; 
     FIG. 4 is a data flow diagram illustrating an embodiment of the secondary color modifier of FIG. 3; 
     FIG. 5 is a block diagram illustrating an embodiment of a luma look up table; 
     FIG. 6 is a flow chart illustrating an embodiment of a process performed by a luma look up table; 
     FIG. 7 is a dataflow diagram illustrating an embodiment of a process performed by a coefficient generator; 
     FIG. 8 is a block diagram illustrating an embodiment of an upsampler; 
     FIG. 9 a  is a data flow diagram illustrating a portion of an embodiment of a primary color modifier; 
     FIG. 9 b  is a data flow diagram illustrating a portion of an embodiment of a primary color modifier; 
     FIG. 10 is a flow chart illustrating an embodiment of a process performed by a RGB lookup table; 
     FIG. 11 a  is a portion of a flow chart illustrating an embodiment of a process performed by a luma/chroma component restorer; 
     FIG. 11 b  is a portion of a flow chart illustrating an embodiment of a process performed by a luma/chroma component restorer; 
     FIG. 12 a  is a circuit diagram illustrating an embodiment of a downsampler; 
     FIG. 12 b  is a block diagram illustrating an embodiment of an operation performed by a downsampler. 
    
    
     DETAILED DESCRIPTION 
     The following detailed description should be read in conjunction with the attached drawing in which similar reference numbers indicate similar structures. All references cited herein are hereby expressly incorporated by reference. 
     The following numerical notation is used to represent binary numbers: (C) I.F, where C (optional) indicates a  2 &#39;s complement number requiring a sign bit, and absence of the C indicates a magnitude only number. I is a number of integer bits including the sign for  2 &#39;s complement number, and F is the number of fractional bits. 
     The color modification described herein uses lookup tables and matrices to reduce the number of computations performed on a pixel color. The lookup tables and matrices simplify the implementation of color modification by providing predefined values representing combinations of color modification functions and conversion factors. 
     FIG. 1 is a data flow diagram illustrating an example embodiment of a color modification system  1 . The color modifier  4  receives color modification parameters  6 , control data  5 , and a pixel color  2  as inputs. The color modifier  4  applies the control data  5  and the color modification parameter  6  to produce a modified pixel color  8 . 
     FIG. 2 is a block diagram illustrating an example embodiment of a video production system incorporating the color modification system  1 . During playback, a component signal flows from a code interface  14  through a raster/block converter  3 , to a color modification system  1 , through a color effects generator  15 , through a safe color modifier  7 , through a crop/border logic  9  and finally to a pixel interface  17 . In the digitize direction, the data flows in the reverse direction from the pixel interface  11  to the code interface  14 . The arrows in FIG. 2 indicate the direction of data flow, with dotted lines representing the option to bypass a functional block in the data flow path. A suitable system for the playback and digitization of a digital video signal is described in U.S. patent application Ser. No. 09/054,764, entitled “Multistream Switch-Based Video Editing Architecture,” by Jeffrey D. Kurtze et al., filed Apr. 3, 1998, U.S. patent application Ser. No. 09/055,073, entitled “A Multi Stream Video Editing System Using Uncompressed Video Data for Real-Time Rendering Performance, and for Non Real Time Rendering Acceleration,” by Craig R. Frink et al., filed Apr. 3, 1998, and U.S. patent application Ser. No. 09/054,761, entitled “Computer System and Process for Transferring Multiple High Bandwidth Streams of Data Between Multiple Storage Units and Multiple Applicants in a Scalable and Reliable Manner,” by Eric C. Peters et al., filed Apr. 3, 1998. A suitable commercial system for the playback and digitization of a digital video are AirPlay® and Symphony™ from Avid Technology, Inc. of Tewksbury, Mass. A suitable system for implementing the safe color modifier is described in U.S. patent application Ser. No. 09/293,590, entitled “Safe Color Limiting Of A Color On A Digital Nonlinear Editing System,” by Raymond Cacciatore and Michael Laird filed on Apr. 16, 1999. 
     In an example embodiment of color modification, pixels are received as part of a 4:2:2 YC b C r  video stream. Although YC b C r  is used to illustrate the color modification system of FIG. 1, the color modification system can be used on other three-component signals, with certain modifications made for component conversion as discussed below. 
     FIG. 3 illustrates an embodiment of the color modification system  1  in more detail. A secondary color modifier  16  receives the pixel color  2  as an input. The pixel color  2  includes a luma component  10 , a first chroma component  12 , and a second chroma component  14 . The secondary color modifier  16  also receives secondary modification parameters  44  as an input. The secondary color modifier  16  produces at an output the luma component  10 , a changed first chroma component  20  and a changed second chroma component  22 . The secondary color modifier  16  is described below in connection to FIG.  4 . 
     An upsampler  24  receives the changed first chroma component  20 , and the changed second chroma component  22  as inputs, and produces as output an upsampled first chroma component  26  and an upsampled second chroma component  28 . The upsampler  24  is described below in connection with FIG.  7 . 
     A primary color modifier  30  receives the luma component  10 , the upsampled first chroma component  26 , and the upsampled second chroma component  28  as inputs. The primary color modifier  30  also receives primary modification parameters  46 . The primary color modifier  30  produces at an output a modified luma component  42 , modified 4:4:4 first chroma component  32 , and a modified 4:4:4 second chroma component  34 . The primary color modifier  30  is described below in connection to FIGS. 9 a  and  9   b.    
     A delay buffer  37  receives the modified luma component  42  as an input, and produces the modified luma component  42  delayed at an output. A downsampler  36  receives the modified 4:4:4 first chroma component  32  and the modified 4:4:4 second chroma component  34  as inputs, and produces as outputs a modified first chroma component  40  and a modified second chroma component  38 . The downsampler  36  is described below in connection to FIGS. 11 a  and  11   b.    
     FIG. 4 is a data flow diagram illustrating an embodiment of the secondary color modifier  16 . A chroma coefficient lookup table (cc LUT)  48  is loaded with chroma coefficients. The cc LUT receives the luma component  10  as an input, and produces chroma coefficients  50  as outputs. The chroma coefficients  50  include a first coefficient  52 , a second coefficient  54 , a third coefficient  56 , and a fourth coefficient  58 . A chroma offset subtractor  61  receives the first chroma component  12  and a second chroma component  14  and a chroma offset  51  as inputs, and produces an offset first chroma component  55  and an offset second chroma component  57  as outputs. 
     A secondary matrix multiplier  60  receives the chroma coefficients  50 , the offset first chroma component  55 , and the offset second chroma component  57  as inputs. The secondary matrix multiplier  60  generates a changed first chroma component  62  and a changed second chroma component  64  as an output. 
     FIG. 5 is a block diagram showing the cc LUT  48  in more detail. The cc LUT  48  includes a plurality of entries  59 . Each entry has four coefficients, illustrated in FIG. 5 as columns a, b, c, and d. The number of entries  59  is determined by the number of possibilities of the luma component  10 . The value of the luma component  10  serves as a pointer to the proper entry  59 . The coefficients of the entry pointed to by the luma component value are then output and sent to the secondary matrix multiplier. 
     The function of the cc LUT  48  is to allow color modifications to be performed on the chroma components  12  and  14  based on the value of the luma component  10 . The cc LUT coefficients  53  that are loaded into the cc LUT  48  in columns a, b, c, and d of each entry  59  may be defined by a user through a user interface. An example process for defining cc LUT coefficients  53  as functions of a luma component  10  is described in U.S. patent application Ser. No. 09/293,732, entitled “Multi-Tone Representation of a Digital Image on a Digital Nonlinear Editing System,” by Robert Gonsalves, filed on Apr. 16, 1999, and U.S. patent application Ser. No. 09/293,730, entitled “Source Color Modification on a Digital Nonlinear Editing System,” by Robert Gonsalves and Michael Laird, filed on Apr. 16, 1999. A user may define color modifications to be made to chroma components  12  and  14  of the pixel color  2  for a range of luma values as defined by a plurality of luma functions, for example, shadow, midtone, and highlight functions. A user interface may allow a user to define the shadow, midtone, and highlight functions for a range of luma values. The cc LUT coefficients  53  are defined with respect to the luma functions, and these coefficients are stored in the entries  59  for each possible luma component value. For a 601 pixel format, the value of the luma components may be represented with 8 bits, providing a possible luma value in the range from 0-255. 
     FIG. 6 is a flow chart illustrating an example embodiment of a process performed by the cc LUT  48  or  48 ′. In step  68 , a luma value of a pixel color is received. In steps  70  and  72 , the chroma entry corresponding to the received luma value is accessed, and the four coefficients corresponding to the luma entry are extracted. In step  74 , the four coefficients are sent to an output. 
     In an embodiment, the cc LUT  48  is double-buffered as illustrated in FIG. 4 by cc LUT  48 ′. In another embodiment, both the cc LUTs  48  and  48 ′ have 256 entries, each entry being four coefficients wide, or having 256×8 bytes organized into two side-by-side blocks of RAM, each 256×32. The cc LUTs  48  and  48 ′ may be loaded by an address pointer mechanism, for example, a pointer register. Such a pointer register selects the desired LUT address, and may automatically increment after a write operation occurs to the LUT. This double-buffering of the cc LUT  48  allows cc LUT entries  59  to be changed for an inactive copy  48 ′, for example. The active copy, for example  48 , is used to determine coefficients for the luma component  10 . Thus the cc LUT  48  may process the luma component  10  while the cc LUT  48 ′ is being loaded. Changing LUT entries may be desired, for example, if it is desired to make changes to the coefficients at boundaries of a video field, for example, if a user wants to add a color effect to a single video frame. In an example embodiment where the pixel color  2  is represented in  601  format, the secondary matrix multiplier performs the following matrix operation:            Equation   1:          
     [           C     b   ′                 C     r   ′             ]     =       [         a       b           c       d         ]     ·     [           C   b               C   r           ]                              
     where C b′  is the changed first chroma component  62 , C r′  is the changed second chroma component  64 , a is the first coefficient  52 , b is the second coefficient  54 , c is the third coefficient  56 , and d is the fourth coefficient  58 . The matrix operation of Equation 1 produces the following equation defining the changed chroma components: 
     
       
           C   b ′=( a·C   b )+( b·C   r ) 
       
     
     
       
           C   r ′=( c·C   b )+( d·C   r )  Equation 2 
       
     
     The chroma coefficients  50  allow the hue to be changed by changing the angle of a CbCr vector. The chroma saturation may also be adjusted in this matrix, by scaling the magnitude of the CbCr vector. 
     FIG. 7 is a data flow diagram illustrating an embodiment of a coefficient generator. A highlight LUT  302 , a midtone LUT  304  and a shadow LUT  306  receive a luma value  300  and generate a highlight value  308 , a midtone value  310 , and a shadow value  312 , respectively. Each LUT  302 ,  304  and  306  includes a plurality of entries, each entry representing a luma value in a range of luma values, where each LUT represents a luma function. Such functions are described in a U.S. patent application Ser. No. 09/293,732, entitled “Multi-tone Representation of a Digital Image,” by Robert Gonsalves, filed on Apr. 16, 1999. The output values  308 ,  310  and  312  of these LUTs are values that are weighted relative to each other. In an alternative embodiment, each LUT  302 ,  304  and  306  may be replaced by a corresponding function. In this alternative embodiment, a luma value is received by the function, and the function generates a weighted value at an output. 
     For each luma function, a saturation modification and a hue modification are defined. In FIG. 7, these modifications are represented by  316 ,  320 ,  324 ,  328 ,  332 , and  336 . As illustrated in FIG. 7, multipliers  314 ,  318 ,  322 ,  326 ,  330 , and  334  receive the outputs from the LUTs, and the respective luma function modifications. The multipliers produce outputs  315 ,  317 ,  319 ,  321 ,  323 , and  325 , respectively. 
     A hue modification generator  338  receives the hue outputs  315 ,  317 , and  319  and generates at an output a hue modification  342 . A saturation modification generator  340  receives saturation output  321 ,  323 , and  325  and generates a saturation modification  344 . The modification generators  338  and  340  normalize their inputs to produce their outputs  342  and  344 , respectively. For example, the hue modification generator  338  adds the hue modification outputs  315 ,  317 , and  319  and divides them by the sum of the highlight value  308 , the midtone value  310 , and the shadow value  312 . The saturation modification generator  340  performs an analogous operation on the saturation modification outputs  321 ,  323 , and  325  to produce the saturation modification  344 . 
     In an example embodiment, if an editor enters the hue modifications  316 ,  320 , and  324  as radians, the hue modification generator  338  performs the additional function of multiplying by Pi (π) and dividing by  180 , thus converting the hue modifications  315 ,  317 , and  319  from radians to a normalized value between 0 and 1. In another embodiment, if the saturation modifications  328 ,  332 , and  336  are entered as percentages, the saturation modification generator  340  additionally divides the sum of the saturation modifications by 100, thereby normalizing the saturation modification  344  as a value between 0 and 1. 
     The coefficient calculator  346  receives the hue modification  342  and the saturation modification  344  and generates chroma coefficients  348 ,  350 ,  352 , and  354  to be loaded into the cc LUT  48  for an entry corresponding to the luma value  300 . The chroma coefficients are defined by the following equation: 
     
       
           a =cos( hue )· sat   
       
     
     
       
           b =sin( hue )· sat   
       
     
     
       
           c =−sin( hue )· sat   
       
     
     
       
           d =cos( hue )· sat   Equation 3 
       
     
     where hue is the hue modification  342 , sat is the saturation modification  344 , and a, b, c, and d are the luma coefficients  348 ,  350 ,  352 , and  354 , respectively. Substituting equation 3 into equation 2 provides the following: 
       C   b ′=( Cb ·cos( hue )· sat )+( Cr ·(−sin( hue ))· sat ) 
     
       
           C   r ′=( Cb ·cos(hue)·sat)+( Cr ·sin( hue )· sat )  Equation 4 
       
     
     Hue defines the angle, e.g., in degrees by which to rotate the C b C r  vector. In the hardware embodiment of the color modification system, 13 bits of fraction are specified in the matrix coefficients, allowing the vector angle to be changed in increments of one degree. The saturation component of the matrix coefficients scales the magnitude of the YC b C r  vector. Three bits of integer, plus 13 bits of fraction, allow a range of coefficients of +3.999877929 to −4.0. The output of the secondary matrix multiplier in this example embodiment are in C 12.13 format. 
     In an embodiment of the color modification system, video data is input to the color modifier  4  in 4:2:2 sampling format, for example, the 4:2:2 YC b C r  format. Before 4:2:2 pixel data can be converted to RGB, it is converted to 4:4:4 sampling space, which includes generation of the odd chroma components. This conversions may be performed by a simple linear interpolation as described below in connection to FIG.  8 . The upsampler  24  of FIG. 3 may apply linear interpolation using the following equation to produce the odd luma components:        Equation   5:             C   n     =         C     n   -   1       +     C     n   +   1         2                            
     where C n  is an odd chroma component, C n−1  is the preceding even chroma component, and C n+1  is the next even chroma component. Either of these even chroma components may be one of the changed chroma components  21  of FIG.  3 . 
     FIG. 8 is a circuit diagram illustrating an example embodiment of the upsampler  24 . The even chroma components C b0 C r0 C b2  . . . are received as an input of the upsampler  24 . The luma component  10  (not shown) may be delayed through pipeline registers, which may serve as the delay buffer  11  of FIG.  3 . An adder  75  alternately adds C bn +C b(n+2)  and C m +C r(n+2)  after the chroma components have passed through shift registers  47  and  49 . The shift registers  47  and  49  may be clocked by a 3.5 megahertz clock, which is the standard sampling frequency of a YC b C r  signal. The inputs to the adder  75  may be two C12.13-bit values and the output of the adder  75  may be in C13.13 format. The output of the adder  75  is received as an input of the divide-by-2 circuit  77 . The divide-by-2 circuit  77  produces a C12.14 bit output. The output of the divide-by-2 circuit  77  is connected to the input of shift register  45  and multiplexer  43 . 
     The output of shift register  47  is connected to the input of shift register  49  and the input of align circuit  71 . The output of shift register  49  is connected to an input of align circuit  73 . Each of the align circuits  71  and  73  adds a zero as a least significant fractional bit to the C12.13 input that it receives to produce a C12.14 formatted output. Multiplexer  43  is connected at an input to the output of the align circuit  71  and the output of the divide by 2 circuit  77 . The multiplexer  43  also receives a select input S and outputs data in C12.14 format. The multiplexer  41  is connected at an input to align circuit  73  and the output of shift register  45 . The multiplexer  41  is also controlled by the select input S, and outputs data in C12.14 format. A round and clamp circuit  39  is connected at a first input to the output of multiplexer  43  and at second input to the output of multiplexer  41 . The round and clamp circuit  39  produces the outputs of the upsampler  24 , the upsampled chroma components  23 , in C9.5 format. The select input S controls both the multiplexers  41  and  43  to each alternate between selecting even chroma components or the interpolated value produced by the combination of the adder  75  and the divide-by-2 circuit  77 . Although in the embodiment of the upsampler  24  described above, linear interpolation is used to upsample the components, other types of interpolation may be used. 
     The round and clamp circuit  39  rounds its input values from C12.14 format to C12.5 format and clips these values to C9.5 format. The round and clamp circuit  39  uses even rounding. In even rounding, if the value to the right of the rounding point is greater than 0.5 or equal to 0.5, the value to the left of the rounding point is rounded up only if the rounding up will result in an even valve to the left of the rounding point. If rounding up will result in an odd value to the left of the rounding point, the rounding up will not be performed. This even rounding function causes the rounding error distribution to be symmetric about zero. 
     FIGS. 9 a  and  9   b  are a data flow diagram illustrating an embodiment of the primary color modifier  30 . An RGB matrix multiplier  76  receives the luma component  10 , the upsampled first chroma component  26  and the upsampled second chroma component  28  as inputs. The RGB multiplier also receives RGB matrix coefficients  122 . The RGB matrix coefficients  122  are applied to the inputs of the RGB multiplier  76  to produce a red component  78 , a green component  80  and a blue component  82 . An RGB clipper  84  receives the red component  78 , the green component  80 , and the blue component  82  as inputs. The RGB clipper clips the red, green, or blue component if the component represents a chroma value outside a predefined chroma range, and outputs a checked red component  86 , a checked green component  88 , and a checked blue component  90 . 
     RGB LUTs  94 , including red LUT  100 , green LUT  98 , and blue LUT  96  are loaded with RGB lookup table values  124 . The RGB LUTs  94  receive the checked red component  86 , the checked green component  88 , and the checked blue component  90 , access the corresponding entries in the red LUT  100 , the green LUT  98 , and the blue LUT  96 , respectively, and generate a modified red component  104 , a modified green component  106 , and a modified blue component  108  respectively. 
     A red adder  110  receives the modified red component  104  and a red offset  112 , and produces as an output an offset red component  128 . A green adder  114  receives the modified green component  106  and a green offset  116  and produces an offset green component  130  as an output. A blue adder  118  receives the modified blue component  108  and a blue offset  120  at an input and produces an offset blue component  132  as an output. 
     LC (Luma/Chroma) matrix multiplier  134  receives the offset red component  128 , the offset green component  130 , and the offset blue component  132  as inputs. The LC matrix multiplier  134  also receives LC matrix coefficients  148  which it applies to the inputs to produce as outputs a raw modified luma component  136 , a raw modified first chroma component  138  and a raw modified second chroma component  140 . 
     A chroma inverse offset adder  141  receives the raw modified first chroma component  138  and the raw modified second chroma component  140 , and applies a chroma offset  51 ′ to produce as outputs an offset modified first chroma component  142  and an offset modified second chroma component  144 . The chroma offset  51 ′ is the mathematical negative of the chroma offset  51  in FIG.  4 . 
     An LC component restorer  146  receives the offset modified first chroma component  142  and the offset modified second chroma component  144  as inputs. The LC component restorer  146  also receives clipping threshold values  150  and applies these threshold values to the inputs to produce as outputs the modified luma component  42 , the modified first chroma component  40 , and the modified second chroma component  38 . 
     The RGB matrix multiplier  76  operates on the luma and chroma components that it receives and transforms these values into RGB color space, and performs a number of other color operations. In another embodiment, the inputs are already in RGB color space and, therefore, the RGB matrix multiplier  76  performs the color operations, but does not transform the values into RGB color space. 
     The operation performed by the RGB matrix multiplier  76  on its inputs is defined by the following equation 6:            Equation   6:          
     [         R           G           B         ]     =       [         a       b       c       d           e       f       g       h           i       j       k       l         ]     ·     [         Y           Cb           Cr           1         ]                              
     where R is the red component  78 , G is the green component  80 , B is the blue component  82 , a-l are the RGB matrix coefficients  122 , Y is the luma component  10 , C b  is the upsampled first chroma component  26 , and C r  is the upsampled second chroma component  28 . The values from the application of the matrices of Equation 6 for the red component  78 , the green component  80 , and the blue component  82  are defined by the following equation: 
     
       
         
           R=aY+bC 
           b 
           +cC 
           r 
           +d 
         
       
     
     
       
         
           G=eY+fC 
           b 
           +gC 
           r 
           +h 
         
       
     
     
       
           B=iY+jC   b   +kC   r   +l   Equation 7 
       
     
     Each of the RGB matrix coefficients  122 , a-l, can be identified with the color modification functions that they affect. Matrix 1 below represents how each RGB matrix coefficients  122 , may be identified with a specific function.          Matrix   1                     
     [           contrast   ,   cs         cs       cs         tint   ,   brightness               contrast   ,   cs           saturation   ,   hue   ,   cs           saturation   ,   hue   ,   cs           tint   ,   brightness               contrast   ,   cs           saturation   ,   hue   ,   cs           saturation   ,   hue   ,   cs           tint   ,   brightness           ]                          
     where cs refers to color space conversion. Similar to the secondary matrix multiplier  60 , the RGB matrix multiplier can provide saturation and hue adjustments, but as a “master” control, as opposed to defining color changes to be applied for specific luminance values. 
     In an example embodiment, the first three columns of coefficients in the RGB matrix are in C5.10 format, and the last column of RGB matrix coefficients are in C10.0 format. The reasons for the C5.10 format of the coefficients of the first three columns in the example embodiment are as follows. The largest input value represented by the bits of the luma component  10  and the upsampled chroma components  26  and  28  is  255 . The smallest fraction that causes a 1-bit change when multiplied by the largest input is {fraction (1/256)}, which can be represented with 8 bits. Since the matrix operation uses three such multiplication products to be added together, using an additional 2 bits of fraction avoids rounding errors in the final result. Therefore, a total of 10 fraction bits are used. For the sole purpose of color space conversion, the coefficient values are less than 2.0. However, four bits of integer allow saturation to be multiplied by a factor of greater than 8 and contrast to be multiplied by factors up to 16. 
     In the example embodiments, the reasons for the data format of the fourth column of the RGB matrix, which deals with tint and brightness, are as follows. Nine bits of integer allow an offset of +/−512 to be added to the luma and chroma components  10 ,  26 , and  28  in order to adjust the tint and brightness of the pixel. These fourth column coefficients also may be used to add an offset to the data used by the RGB LUTs  94 . The offset may be used for the following purposes. The input values of the RGB LUTs  94 , for example, the red component  78 , the green component  80 , and the blue component  82 , are positive values because these input values are used as addresses into the memory. The RGB conversion matrix, the possible negative values of the chroma components  26  and  28 , and hue rotation all may cause one of the RGB values,  78 ,  80  and  82 , to become negative. For RGB conversion alone, the red range is −175-431, the green range is −133-388, and blue is −221-478. These ranges are outside the normal 0-255 range for 8-bit components; however, clipping the values here would truncate the range of the modified components  38 ,  40 ,  42  resulting from the final conversion to YC b C r . Therefore, if the range of a component extends into negative values, an offset is incorporated into the fourth column of the RGB matrix such that each component has a range greater than 0. 
     Furthermore, as contrast, saturation, hue, tint, and brightness effects are defined through a user interface, the range of each of the RGB matrix coefficients  122  is re-computed such that the offset is properly adjusted. For example, if YCbCr values are converted to RGB using the standard ITU-R BT.601 conversion matrix, allowing for a full 0-255 range for the YC b C r  component, the resulting red component may have any value in the range −175-431. In order to preserve the full range of red components, an offset of 175 is added to the red, shifting its range to 0-606. This range now fits entirely within the range of 0-1023 that can be handled by the 10-bit LUTs. 
     In an embodiment, the RGB matrix multiplier  76  yields a 31-bit result: 15-bits integer, 15-bits fraction, and a sign bit. The final value is rounded off to an integer value, using even rounding. As described above, in the absence of contrast, saturation, tint, and brightness effects, the overall output range of the RGB components is 0-700, and the conversion back to Yc b C r  maps the components back to within the 0-255 range. However, saturation and contrast multiplication factors may bring the component outside of the legal ranges. For this reason, the RGB clipper  84  may always clip the RGB components  78 ,  80 ,  82  to within the 0-1023 range that can be accepted by the LUTs. Further clipping can be performed by programming the RGB LUTs  94 . 
     In an example embodiment, further resolution can be gained in the RGB LUT operations where the component range is less than 1024. The color components  78 ,  80 , and  82  may be scaled by adjusting the RGB matrix coefficients  122  such that the component range extends from 0-1023. The inverse operation may be applied by the LC matrix multiplier  134  to de-scale the RGB components. 
     Generally, the RGB LUTs  96 ,  98  and  100  operate in similar fashion to the luma LUT engine  53 . For example, the red LUT  100  receives checked red component  86  instead of a luma component  10 , and produces a modified red component  104  instead of coefficients  50 . 
     The three RGB LUTs  96 ,  98 , and  100  allow non-linear functions to be performed on the checked red component  86 , the checked green component  88 , and the checked blue component  90 , respectively. Performing the color space conversion function alone through the RGB matrix multiplier  76  can result in RGB components  86 ,  88  and  90  with values greater than the 0-255 range usually expected, without even considering modifications to the contrast, saturation, tint, and brightness. 
     In an example embodiment of the RGB LUTs  94 , to encompass the full range of value for the RGB components  86 ,  88 , and  90 , each LUT comprises 1024 locations, each with a width of 10 bits. As with the cc LUT  48 , each of the RGB LUTs,  100 ,  98 , and  96  is double-buffered so that one copy of each LUT may be updated while the other copy is in use. The RGB LUTs  94  may be loaded using an address pointing mechanism such as that described with respect to the luma LUT. In an example embodiment of the primary color modifier, the address pointer is a register whose value is used to select a specific address within one of the LUTs  94 . Similar to the luma LUT tables  48  and  48 ′, a status bit is maintained in a register to indicate which copy of an RGB LUT,  100  or  100 ′,  98  or  98 ′, or  96  or  96 ′ respectively, is the current active copy. After a write operation to a LUT has been performed, the pointer register is incremented. When accessing the RGB LUTs  94 , the 30 least-significant bits are valid. 
     It is possible for the modified RGB components  104 ,  106 , and  108 , to have color values and RGB space that exceed the normal 8-bit component range. In an embodiment, an RGB gamut checker  109  identifies components  104 ,  106 , and  108  that exceed the 8-bit component range, or a range defined by RGB gamut values  125 , and may warn a system user that video components are present which exceed specified range. Although components that exceed a specified range may eventually produce valid YC b C r  values after passing through the remaining data path of the primary color modifier, the RGB gamut checker provides a mechanism by which a user can be warned that certain RGB components before being converted back to YC r C b  format are out of the RGB gamut range. Thus, the RGB gamut checker receives the modified RGB components  104 ,  106 , and  108  and the RGB gamut values that define the upper and lower limit for the RGB values. The RGB gamut checker then may produce a gamut interrupt or event if one of the components  104 ,  106 , or  108  falls outside of the RGB gamut region. 
     After the RGB data is modified by the RGB LUT engine  94 , the offset that was applied as part of the fourth column of the RGB matrix coefficients  122  is removed by the red, green, and blue adders  110 ,  114 , and  118 , respectively. The adders  110 ,  114 , and  118  receive a red offset  112 , a green offset  116 , and a blue offset  120 , which are offset values defined to remove the offset applied by the fourth column of the RGB matrix coefficients  122 . In another embodiment, the red, green and blue offsets  112 ,  116 , and  120  respectively, can be a value other than a value defined to remove the offset applied by the RGB matrix coefficients  122 . 
     In an embodiment, the RGB offsets  126  may be incorporated into the RGB LUT values  124 . However, applying the RGB offsets  126  as a separate operation, as opposed to factoring the RGB offsets  126  into the RGB lookup table values  124 , saves a bit in each of the LUT memories, and simplifies computations by keeping the LUT range adjustments. In an embodiment of the primary color modifier  30 , the RGB offsets  126  are a 2s complement integer of the form C9.0. 
     The LC matrix multiplier  134  is similar to the RGB matrix multiplier  76 . The values of the LC matrix coefficients  148 , however, incorporate contrast, hue, saturation, tint, and brightness color modifications. The LC matrix multiplier  134  applies matrix multiplication defined by equation 8:            Equation   8:          
     [         Y           Cb           Cr         ]     =       [         a       b       c       d           e       f       g       h           i       j       k       l         ]     ·     [         R           G           B           1         ]                              
     where Y is the raw modified luma component  136 , C b  is the raw modified first chroma component  138 , C r  is the raw modified second chroma component  140 , R is the offset red component  128 , G is the offset green component  130 , B is the offset blue component  132 , and a-l are the LC matrix coefficients  148 . The matrix multiplication defined by equation 7 results in the following equation defining the values of the raw modified luma component  136 , the raw modified first chroma component  138 , and the raw modified second chroma second component  140 : 
     
       
         
           Y=aR+bG+cB+d 
         
       
     
     
       
         
           C 
           b 
           =eR+fG+gB+h 
         
       
     
     
       
           C   r   iR+jG+kB+l   Equation 9 
       
     
     The matrix coefficients  148 , a-l affect the color modification functions of contrast, hue, saturation, tint, and brightness controls as represented by the following matrix 2.          Matrix   2          
     [           contrast   ,                                   tint   ,         brightness             contrast   ,                        saturation   ,   hue   ,               saturation   ,              hue   ,                        tint   ,         brightness             contrast   ,           saturation   ,   hue   ,           saturation   ,   hue   ,           tint   ,         brightness         ]                          
     In an embodiment of the primary color modifier  30 , the offset components  128 ,  130 , and  132  are 10-bits in width with a sign bit. The LC matrix coefficients a-l have more bits of fractional precision than the RGB matrix coefficients  122  because of the greater range of the offset components  128 ,  130 , and  132 . These two more bits result in the first three columns of the LC matrix being defined by coefficients with the data format C4.12, with the coefficients of the fourth column having the data format C11.0. 
     The chroma inverse offset adder  141  reverses the effect of the chroma offset adder  59  of the secondary color modifier  16 , by adding a chroma offset  51 ′, which is the mathematical negative of the chroma offset  51 . For an example embodiment where the pixel color is in YC b C r  format, the chroma offset  51  is 128, and therefore the chroma offset  51 ′ is 128 also, except it is added by the chroma inverse offset adder to the raw modified chroma components  138  and  140 , as opposed to the subtraction produced by the chroma offset subtractor  61 . 
     In an example embodiment of the primary color modifier  30 , the final outputs from the matrix multiplier, numbers of the form C17.12, are rounded, again using even rounding, and are then clamped to 8-bits. For example, the C17.12 value is rounded to a C17.0 value, and then clamped to an 8.0 data format. 
     FIGS. 11A and 11B are flowcharts illustrating an example embodiment of a process performed by the LC component restorer  146 . In step  162 , luma and chroma components  136 ,  142 , and  144  are received. Next in step  164 , even rounding is used to round the luma and chroma components to the nearest integer value. Next in the step  166 , the luma and chroma components are clamped to be within the 8-bit component range. In step  168 , the clipping threshold value  50 , luma high and luma low threshold values, are accessed. 
     In step  170 , the luma component value is compared to the luma high threshold value. In step  172 , if it is determined that the component luma value is greater than the luma high threshold value, then the luma values is clipped to the luma high threshold value in step  180 . If it is determined in step  172  that the component luma value is not greater than the luma high threshold value, then in step  174  the luma component value is compared to the luma low threshold value. If it is determined that the luma value is less than the luma low threshold value in step  176 , then the luma value is clipped to the luma low threshold value. 
     After steps  176 ,  178  or  180  are processed, in the step  182  a first chroma value is compared to a chroma high threshold value. If it is determined in  184  that the first chroma value is greater than the chroma high threshold value, then in step  192  the first chroma value is clipped to the chroma high threshold value. If it is determined in step  184  that the first chroma value is not greater than the chroma high threshold value, then in step  186  the first chroma value is compared to the chroma low threshold value. If in step  188  it is determined that the first chroma value is less than the chroma low threshold value, then in step  194  the first chroma value is clipped to the chroma low threshold value. 
     After steps  188 ,  192  or  194 , steps  162  through  194  are repeated for the second chroma component (Step  190 ). It should be understood that steps  162 - 194  may be performed on the first and second chroma components in any order or in parallel. 
     For an example embodiment, where the final video output is to be in 4:2:2 sampling format, the modified chroma components,  38  and  40 , are downsampled. For properly bandlimited video, downsampling involves dropping the chroma components of the odd pixels. However, the secondary and primary color modifier  16  and  30 , respectively, and the non-linear color effects implemented through the RGB LUT engine  94 , performed in 4:4:4 sampling format, can introduce out-of-band components into the video stream. A downsampler  36  may be used to apply a filter to the modified 4:4:4 chroma components  32  and  34 . Filtering may be accomplished for each chroma component of an even pixel by generating a weighted average combining the even component and its adjacent odd chroma components. 
     FIG. 12A is a circuit diagram illustrating an embodiment of the downsampler  36 . A first shift register  196  receives a 4:4:4 chroma component  32  or  34 . The first shift register  196  is connected at an output to the input of a second shift register  198  and a first input of a first multiplier  202 . The second register  198  is connected at an output to an input of the third register  200  and a first input of the second multiplier  204 . The third shift register  200  is connected at an output to a first input of a third multiplier  206 . 
     The first multiplier  202  receives at a second input the value of 0.25 and is connected at an output to the input of a first adder  210 . The second input of the second adder  204  receives the value 0.50, and is connected at an output to a second adder  208 . The third multiplication circuit  206  receives at a second input the value 0.250, and is connected at an output to a second input of the second adder  208 , which is connected at an output to a second input of the first adder  210 . 
     The first adder  210  is connected at an output to the input of a multiplexer  212 . The multiplexer  212  receives at a second input a 4:4:4 chroma component  32  or  34 . The multiplexer  212  also has a bypass control input and is connected at an output to a fourth shift register  214 . The fourth shift register  214  is controlled by a pixel clock input, and produces at an output a 4:2:2 chroma component signal. The downsampler  36  may execute the following equation: 
     
       
           C   n ′=¼ C   n−1 +½ C   n +¼ C   n+1   Equation 10 
       
     
     where C n  is a component of a pixel. 
     FIG. 12B illustrates how the downsampler  36  takes a 4:4:4 input signal C 0 , C 1 , C 2 , C 3 , C 4 , C 5 , C 6 , C 7 , C 8 , C 9  and produces a 4:2:2 output signal C 0 , C 2 , C 4 , C 6 , C 8 . In FIG. 12B, a first chroma component of a line of a video field is passed directly to the output, unfiltered. In the example embodiment of the downsampler described in connection with FIG. 12A, this direct passing, of C 0  for example, is controlled by the bypass control signal controlling the multiplexer  212 . The first chroma component of a line of a video field, for example C 0 , is bypassed because there is no preceding chroma component of an odd pixel to use to produce a weighted average. Although in the embodiment of the downsampler  36  described above, a linear 3-tap filter is used to downsample the components, other forms of filtering may be used. 
     Color modification may be performed on a general purpose computer system but is not limited by the specific computer described herein. Many other different machines may be used to implement the invention. Although the foregoing description sets forth an example of a circuit for implementing color modification, one alternative implementation is a computer program executed on a general purpose computer system. Such a suitable computer system includes a processing unit which performs a variety of functions and a manner well-known in the art in response to instructions provided from an application program. The processing unit functions according to a program known as the operating system, of which many types are known in the art. The steps of an application program are typically provided in random access memory (RAM) in machine-readable form because programs are typically stored on a non-volatile memory, such as a hard disk or floppy disk. When an editor selects an application program, it is loaded from the hard disk to the RAM, and the processing unit proceeds through the sequence of instructions of the application program. 
     The computer system also includes an editor input/output (I/O) interface. The editor interface typically includes a display apparatus (not shown), such as a cathode-ray-tube (CRT) display in an input device (not shown), such as a keyboard or mouse. A variety of other known input and output devices may be used, such as speech generation and recognition units, audio output devices, etc. 
     The computer system also may include a video and audio data I/O subsystem. Such a subsystem is well-known in the art and the present invention is not limited to the specific subsystem described herein. The audio portion of such a subsystem includes an analog-to-digital (A/D) converter (not shown), which receives analog audio information and converts it to digital information. The digital information may be compressed using known compression systems, for storage on the hard disk to use at another time. A typical video portion of such a subsystem includes a video image compressor/decompressor (not shown) of which many are known in the art. Such compressor/decompressors convert analog video information into compressed digital information. The compressed digital information may be stored on hard disk for use at a later time. An example of such a compressor/decompressor is described in U.S. Pat. No. 5,355,450. Video data also may remain uncompressed. 
     It should be understood that one or more output devices may be connected to the computer system. Example output devices include a cathode ray tube (CRT) display, liquid crystal displays (LCD) and other video output devices, printers, communication devices such as a modem, storage devices such as disk or tape, and audio output. It should also be understood that one or more input devices may be connected to the computer system. Example input devices include a keyboard, keypad, track ball, mouse, pen and tablet, communication device, and data input devices such as audio and video capture devices and sensors. It should be understood that color modification is not limited to the particular input or output devices used in combination with the computer system or to those described herein. 
     The computer system may be a general purpose computer system which is programmable using a computer programming language, such as “C++,” JAVA or other language, such as a scripting language or even assembly language. The computer system may also be specially programmed with special purpose hardware such as an application specific integrated circuit (ASIC). In a general purpose computer system, the processor is typically a commercially available processor, such as the series x86 and Pentium processors, available from Intel, similar devices from AMD and Cyrix, the 680X0 series microprocessors available from Motorola, and the PowerPC microprocessor from IBM. Many other processors are available. Such a microprocessor executes a program called an operating system, of which WindowsNT, Windows95 or 98, UNIX, Linux, DOS, VMS, MacOS and OS8 are examples, which controls the execution of other computer programs and provides scheduling, debugging, input/output control, accounting, compilation, storage assignment, data management and memory management, and communication control and related services. The processor and operating system define a computer platform for which application programs in high-level programming languages are written. 
     A memory system typically includes a computer readable and writeable nonvolatile recording medium, of which a magnetic disk, a flash memory and tape are examples. The disk may be removable, known as a floppy disk, or permanent, known as a hard drive. A disk has a number of tracks in which signals are stored, typically in binary form, i.e., a form interpreted as a sequence of one and zeros. Such signals may define an application program to be executed by the microprocessor, or information stored on the disk to be processed by the application program. Typically, in operation, the processor causes data to be read from the nonvolatile recording medium into an integrated circuit memory element, which is typically a volatile, random access memory such as a dynamic random access memory (DRAM) or static memory (SRAM). The integrated circuit memory element allows for faster access to the information by the processor than does the disk. The processor generally manipulates the data within the integrated circuit memory and then copies the data to the disk after processing is completed. A variety of mechanisms are known for managing data movement between the disk and the integrated circuit memory element, and the invention is not limited thereto. It should also be understood that the invention is not limited to a particular memory system. 
     Such a system may be implemented in software or hardware or firmware, or a combination of the three. The various elements of the system, either individually or in combination may be implemented as a computer program product tangibly embodied in a machine-readable storage device for execution by a computer processor. Various steps of the process may be performed by a computer processor executing a program tangibly embodied on a computer-readable medium to perform functions by operating on input and generating output. Computer programming languages suitable for implementing such a system include procedural programming languages, object-oriented programming languages, and combinations of the two. 
     It should be understood that the computer system is not limited to a particular computer platform, particular processor, or particular programming language. Additionally, the computer system may be a multi-processor computer system or may include multiple computers connected over a computer network. It should be understood that each step of FIGS. 6,  10 ,  11   a , and  11   b  may be separate modules of a computer program, or may be separate computer programs. Such modules may be operable on separate computers. 
     Having now described some embodiments, it should be apparent to those skilled in the art that the foregoing is merely illustrative and not limiting, having been presented by way of example only. Numerous modifications and other embodiments are within the scope of one of ordinary skill in the art and are contemplated as falling within the scope of the invention.