Abstract:
A method is proposed for reducing the cost of color transformations implemented by multi-dimensional lookup tables, especially in the case where the input space is a luminance-chrominance color space. Multilevel halftoning is applied to the two chrominance coordinates in order to map them to the chrominance node values of the lookup table. Multilevel chrominance halftoning introduces chrominance errors at high spatial frequencies, where the human visual system is insensitive. 1-D interpolation is then applied on the luminance coordinate to obtain the output color value. This method therefore reduces 3-D interpolation to halftoning and 1-D interpolation, thereby saving computational cost without introducing objectionable image error.

Description:
BACKGROUND OF THE PRESENT INVENTION 
     The present invention is directed to the digital imaging arts. It finds particular application to a method of color correction using multi-level halftoning and will be described with particular reference thereto. It is to be appreciated that the present invention can also be applied to any type of color transformation process including color space transformation, device calibration and characterization, color correction, and the like. 
     Computers and other electronic equipment typically depict color in 3-D coordinates such as RGB. Many printers, on the other hand, print in either three-dimensional colorant space, cyan, magenta, yellow (CMY) or four-dimensional colorant space, cyan, magenta, yellow, and black (CMYK) which correspond to the input values, e.g. RGB. Frequently, a device independent color space is used as an intermediate representation of the image. A common choice for such a device independent space is a luminance-chrominance space, denoted generically as LC 1 C 2 . The L component represents luminance or lightness, and C 2  and C 2  are the two chrominance coordinates representing red-green and yellow-blue variations, respectively. An example of such a space is CIELAB. Translations are then derived from input RGB to LC 1 C 2 , and from LC 1 C 2  to printer colorant space. 
     While this invention is applicable to a wide variety of transformations, the discussion will focus on transforms from a luminance chrominance space LC 1 C 2  to printer colorant space CMYK. Such transformations are typically implemented by a 3-D look-up table (LUT), which converts each digital LC 1 C 2  input to the corresponding output CMYK value before being received by the printer. 
     A printer which has an ideal colorant behavior has a one-to-one correspondence of cyan-to-red, magenta-to-green, and yellow-to-blue. This means that when printed, the cyan colorant will only absorb red light, the magenta colorant will only absorb green light, and the yellow colorant will only absorb blue light. However, typical printer colorants deviate from this ideal behavior, and in fact absorb light in bands of the electromagnetic spectrum other than the intended absorption band. These so called unwanted absorptions lead to interactions between the colorants that result in a complex nonlinear relationship between digital values that drive the printer, and the resulting colorimetric response. A response, or other value, labeled as “colorimetric” refers to a measurement of the printed color, as seen by an average human observer, and represented in a device independent color coordinate system such as CIELAB. Modeling the calorimetric response across the entire range of CMYK values therefore cannot usually be achieved by a simple function, and in fact requires many parameters and measurements. The number of measurements required to characterize the printer adequately, can easily number 1,000 or more. Usually, in order to represent such a complex function at reasonable computational cost, a color correction LUT is built which approximates the mapping between colorimetric space and CMYK values. More specifically, the color correction LUT corrects for non-linearities and unwanted absorptions of colorants. For every input color specified in some luminance-chrominance space LC 1 C 2 , the LUT retrieves the corresponding CMYK which, when printed and measured, will yield the requested LC 1 C 2  color, provided that this color is within the reproducible gamut of the device. 
     To build the LUT, a predefined set of CMYK digital values are sent to the printer. The printer prints a corresponding set of color patches. The calibration color patches are measured and a colorimetric LC 1 C 2 coordinate is determined for each patch, i.e. for each of the predefined CMYK values. Each of the measured LC 1 C 2 coordinates then, identifies a three-dimensional vector location within the three-dimensional space. Each LC 1 C 2  coordinate is typically represented by 8-bit values for each of the L, C 1 , and C 2  components. Although such an 24-bit LC 1 C 2  coordinate is capable of addressing 256 3  locations, the look-up table is typically partitioned into a smaller size, such as 16×16×16 (4096) table locations, each node of which stores a CMYK value. CMYK values at intermediate LC 1 C 2  points are determined by some form of interpolation among the LUT nodes. The size of the look-up table is a compromise between the desired accuracy of the look-up table (i.e. the fidelity of the output) and the expense of storing a large number of values. Thus after the calibration patches are produced, each measured LC 1 C 2  coordinate has a corresponding known CMYK value. Unfortunately, the LC 1 C 2  coordinates do not, in general, perfectly coincide with the node locations (i.e. the three dimensional intersection points) of the look-up table. Hence, the CMYK values placed at the nodes are estimated by some multidimensional data fitting technique such as Shepard&#39;s algorithm. 
     An illustration of the operation of a look-up table is instructive. Referring to FIG. 1, an input LC 1 C 2  value  10  is sent into the table  12  for conversion into a printer specific CMYK value. The conversion is accomplished by interpolating the known CMYK values corresponding to the nodes  14  nearest the input LC 1 C 2  coordinate location  10 . Because the color is defined in three dimensions, the interpolation is similarly done in three dimensions. Common examples of 3-D interpolation techniques include trilinear, tetrahedral, and prism interpolation. Of these, tetrahedral interpolation is the fastest method, requiring interpolation only among 4 nodes. (The trilinear and prism schemes utilize 8 and 6 nodes, respectively.) All these techniques require several multiplication, addition, shift, and comparison operations for each output signal at each pixel; and are often implemented with special purpose hardware. This interpolated CMYK value is then output by a printer. Unfortunately, three-dimensional interpolation presents a significant computational burden for many applications. 
     The present invention provides a new and improved method of color correction which overcomes the above-referenced problems and others. 
     BRIEF SUMMARY OF THE INVENTION 
     In accordance with the present invention an improved method is proposed for lookup table based color transformations that combines multilevel halftoning with interpolation Specifically, if the input color space to the lookup table is in luminance-chrominance coordinates, multilevel halftoning is applied to each of the chrominance coordinates to achieve coincidence with the nodes of the lookup table along these two coordinates. The multilevel halftoning step introduces errors at high spatial frequencies in the chrominance channels. However, these errors are not easily perceptible by the human visual system. Finally, 1-dimensional interpolation is performed on the luminance component to obtain the output color values. 
     In accordance with an aspect of the present invention, a method of color transforming an input color value to an output color value includes a multi-dimensional color transformation table having an arrangement of nodes. Each node defines an output color value. The method includes receiving the input color value and applying multilevel halftoning to a predetermined subset of the input color components to select a plurality of nodes constrained to a selected number of dimensions. Remaining others of the input color components are then used to interpolate among the selected plurality of nodes to obtain the output color value. 
     In accordance with another aspect of the present invention, the halftoning step includes independently halftoning certain ones of the predetermined subset of input color components to select the plurality of nodes constrained to the selected number of dimensions. 
     In accordance with another aspect of the present invention, the halftoning includes applying a halftone screen function to ones of the predetermined subset of input colors to select the plurality of nodes. 
     In accordance with another aspect of the present invention, input color components are defined by L*a*b* components. The halftoning includes halftoning the a* and the b* components to select a plurality of nodes constrained to the L* dimension. 
     In accordance with another aspect of the present invention, the arrangement of nodes within the color transformation table is nonrectangular. 
     In accordance with the present invention, an electronic imaging system including a receiver and a conversion processor are provided. The conversion processor includes a multi-dimensional table having a plurality of nodes each containing predefined output color data. A first quantizer receives a predetermined subset of the input color components and identifies nodes constrained to a selected number of dimensions. An interpolator calculates an output color from the predefined color data contained at the nodes identified based on remaining ones of the input color components. 
     In accordance with another aspect of the present invention, the quantizer comprises a multilevel halftoner applying a halftone screen function to ones of the predetermined subset of input color components, and identifies the nodes constrained to the selected number of dimensions. 
     In accordance with another aspect of the present invention, the electronic imaging system further includes a second quantizer depending on the nodes identified by the first quantizer to identify the nodes constrained to the selected number of dimensions. 
     One advantage of the present invention is that the expensive 3-D interpolation is reduced to a much simpler process of halftoning and 1-D interpolation, which brings substantially savings in computation, with minimal loss in visual quality. Another advantage of the present invention is that the halftoning and 1-D interpolation steps require less storage and memory for precomputed quantities in the lookup table. This allows alternative grid structures to be employed for the lookup table. 
     Still further advantages of the present invention will become apparent to those of ordinary skill in the art upon reading and understanding the following detailed description of the preferred embodiments. 
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The invention may take physical form in certain parts and arrangements of parts, and in various steps and arrangements of steps. The drawings, then, must be presented for illustrative purposes only and should not be construed as limiting the scope of the present invention, wherein: 
     FIG. 1 is a graphic depiction of the prior art three-dimensional interpolation look up table; 
     FIG. 2 an illustration of one C 1  C 2  plane and an off-node arrival of an input color; 
     FIG. 3 is a graphical depiction of a logical flow diagram in accordance with an embodiment of the present invention; and 
     FIG. 4 is an illustration of interpolation along a remaining dimension following multilevel halftoning on the other dimensions; 
     FIG. 5 is graphical depiction of a sequential grid according to the present invention; and 
     FIG. 6 is a graphical depiction of a logical flow diagram in accordance with an alternate embodiment of the present invention. 
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A method is provided for reducing the cost of interpolation operations required in 3-D lookup table (LUT) based color correction. The input color value will be described in luminance-chrominance (LC 1 C 2 ) coordinates, however, the present invention is equally applicable to other input formats with no loss of functionality. Multilevel halftoning is used to restrict C 1  and C 2  to a limited set of levels; namely those levels that coincide with the LUT node locations along C 1  and C 2 . The LUT calculation then reduces from 3-D interpolation in LC 1 C 2  to 1-D interpolation only along L. Testing shows that acceptable images can be obtained, with significant gains in computational cost as compared to the prior art 3D interpolation. 
     The present invention recognizes that reducing color correction from a 3-D interpolation problem to a one-dimensional problem will significantly reduce the cost and speed of color correction. Typically, device independent image values are stored as luminance-chrominance coordinates, for example the CIELAB color space. Generally, the human visual system is less sensitive to chrominance errors than it is to distortions in luminance at high spatial frequencies. In other words, an observer is more likely to detect small errors in luminance than in chrominance at high spatial frequencies. It is this recognition that is the basis of the present invention. 
     For clarity, a single C 1 -C 2  plane  20  is shown in FIG.  2 . Input color  22  comprises input color components L in , C 1in  and C 2in . To reduce the computational cost of the ensuing color correction operation, some distortion in the C 1  and C 2  channels is accepted. Accordingly, the C 1  component is limited to a finite set of dimensions or levels  24 ,  25 ,  26 ,  27 ,  28  each coinciding with a plurality of nodes (i.e. along the C 2  and L axes). Similarly, the C 2  component is constrained to match levels  31 ,  32 ,  33 ,  34 ,  35 . One skilled in the art can appreciate that if an input color value is forced to always coincide with a level or a predefined dimension in the LUT, then there is no need to perform interpolation along that dimension. In other words, of the three input components, two (C 1  and C 2 ) have been determined through multilevel halftoning. Hence, the color correction reduces to 1-D interpolation along the remaining axis (e.g. luminance or L) as will be shown below. 
     Reducing the precision of a signal to a small set of levels or dimensions is a quantization problem. A typical color correction LUT would assign 16 node locations along each of the L, C 1  and C 2  dimensions (from FIG. 1) resulting in a total of 16 3 =4096 node entries. Thus, for a typical 8-bit input, the present invention requires for each chrominance channel, a quantization mapping from 256 possible input levels to the 16 output node locations. Straightforward quantization involves mapping each input value to the closest node. However, experiments show that this approach can result in objectionable contouring artifacts. 
     A method of minimizing such artifacts in the quantized image is through dithering, or more generally, multilevel halftoning. This effectively pushes quantization errors into high spatial frequencies, exploiting another insensitivity in the human visual system. Preferably then, halftoning is applied to the chrominance channels C 1  and C 2  at high spatial frequencies thus, exploiting the greatly reduced sensitivity of the human visual system to high frequency chrominance errors. There are two known methods of multilevel halftoning: screening and error diffusion. The present invention preferably employs a blue noise stochastic screen, as it enjoys the computational ease of any screening technique, and borrows some of the more desirable qualitative behavior from error diffusion. An equally viable alternative is to use a dispersed dot screen. Still referring to FIG. 2, the halftoning operation can be envisioned as an input color  22  entering the LUT. As is typical, the input color  22  lies between the predefined levels  24 - 28  and  31 - 35  on both the C 1  and C 2  axes. Starting with C 1 , a determination is made whether to place the input color  22  on either a slightly lower level  25  or a slightly higher level  26 . No interpolation is performed, the input color is “forced” onto one of the levels, thus inducing an error. A similar determination is made for C 2  forcing the input color  22  onto either the lower level  33  or the higher level  34 . Assume for illustration purposes, the thresholding placed the input color on node  40 . 
     As seen in FIG. 3, a conversion processor  50  receives the input color  22  comprising three components i.e. L  22   L , C 1    22   A  and C 2    22   B . In the illustrated embodiment, C 1    22   A  and C 2    22   B  are quantized independent of each other. The first step in multilevel halftoning is to normalize the coordinate C 1 (x, y)  22   A  at pixel (x, y) within the interval formed by the two neighboring nodes (e.g. levels  22  and  23  from FIG. 2) in the LUT along the C 1 . The normalized coordinate C 1 ′ is obtained by 
     
       
           C   1 ′( x,y )=[ C   1 ( x,y )− C   1L ( x,y )]/[ C   1G ( x,y )− C   1L ( x,y )]  Equation (1) 
       
     
     where C 1 (x, y) is the original input coordinate; C 1L (x, y) is the nearest LUT node less than C 1 (x, y); and C 1G (X, y) is the nearest LUT node greater than C 1 (x, y). The normalized coordinate C 1 ′(x, y) therefore always lies between 0 and 1. Note that the normalization operation can alternately be carried out ahead of time and stored in a 1-D lookup table array. The normalized value C 1 ′(x, y) is then compared with the halftone screen threshold value, otherwise termed the dither signal D(x, y)  52 , which is also normalized between 0 and 1. If C 1 ′(x, y) is less than or equal to D(x, y), then C 1L (x, y) is picked as the output halftoned level, otherwise C 1G (x, y) is chosen. This output level is denoted CC 1q . An identical operation is performed for C 2 (x, y)  22   B . 
     At this point, and with cross-reference to FIG. 4, the quantized values or dimensions  25  and  33  enter a 2-D lookup able  54  (FIG. 3) to determine a luminance line  60  defined by the intersection of the quantized C 1  chrominance level or plane, e.g.  25  and the C 2  chrominance level or plane  33 . The result passes to the 1-D lookup and interpolation device  56  so that the L component of the input color  22   L  can be interpolated (in 1-D) based on the remaining dimension (i.e. L) between the two nodes  64 ,  66  surrounding the input color value  22 , thus determining the output color. 
     Referring now to FIG. 5, an alternative embodiment employs a sequential grid  70  to be used as an alternative to that shown in FIG. 2 for the 2-D chrominance plane in the 3-D LUT. The sequential grid  70  allows for a more flexible placement of nodes in the C 1 -C 2  plane, than the strictly rectangular grid placement as seen in FIG.  2 . It allows nodes to be placed where the LUT transformation has greatest variation or visual importance, and in general, will result in a better trade-off between LUT accuracy and LUT size. In this embodiment, multilevel halftoning is applied to the first chrominance coordinate of the input color  72 . This maps the C 1  value or component to one of the levels  74  or  75 . In the given example, the halftoning process constrains the possible nodes to the two-dimensional space defined by level  74 . In the next step, multilevel halftoning is applied in the C 2  dimension along the level  74  between nodes  76  and  77 . In the given example, this results in the input color being mapped to node  77 . Finally, as with the original embodiment, a 2-D lookup, followed by 1-D interpolation along the L axis is applied to obtain the output color. 
     A diagram of a conversion processor  80  according to this alternate embodiment process is given in FIG.  6 . The flow processor  80  is identical in all essential respects to that of the original embodiment processor  50  (illustrated in FIG. 3) except that the halftoned output C 1q  along the first dimension is used to determine the set of LUT nodes along the second axis C 2 , which may be different for different node values along C 1 . Hence, the halftoning is carried out sequentially, rather than independently along the two chrominance axes. 
     In Table 1, three methods, trilinear interpolation, tetrahedral interpolation, and the original embodiment of the present invention, are compared in terms of the computations required to perform the color correction operation at each pixel, for N output colors. This operation includes 1) retrieving the nodes of the sub-cell enclosing the input color; and 2) performing the actual interpolation. Note that for the present invention, the comparison step in the multilevel halftoning operation has been included in the cost analysis. In all three cases, any quantities that do not depend on the input color are assumed to be precomputed and stored. These quantities include differences between output values at adjacent nodes, and the normalization of input values given by Equation (1). The last row of Table 1 shows the savings achieved by applying the present invention over tetrahedral interpolation. The savings would be even larger in comparison to trilinear interpolation. 
     
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Cost analysis for trilinear, tetrahedral, and proposed interpolation 
               
               
                 schemes, for N output signals. 
               
             
          
           
               
                   
                 Multiplications 
                 Additions 
                 Comparisons 
                 Shifts 
               
               
                   
                   
               
             
          
           
               
                 1) Trilinear 
                 7N 
                 7N + 2 
                 0 
                 2 
               
               
                 2) Tetrahedral 
                 3N 
                 3N + 2 
                 2.5 
                 2 
               
               
                 3) Proposed Method 
                 N 
                  N + 2 
                 2 
                 2 
               
               
                 4) Savings from (2) 
                 67% 
                 57% 
                 20% 
                 0% 
               
               
                 to (3) for N = 4 
               
               
                   
               
             
          
         
       
     
     The invention has been described with reference to the preferred embodiment. Obviously, modifications and alterations will occur to others upon a reading and understanding of this specification. It is intended to include all such modifications and alterations insofar as they come within the scope of the appended claims or the equivalents thereof.