Abstract:
Digital image processing apparatus for applying pixel-based colour correction to an input image to generate an output image comprises colour correction logic arranged to provide two or more colour correction processes each having a respective associated locus in a colour space and a respective associated colour mapping operation; the colour correction processes being arranged as a succession of processes so that the results of a colour correction process form the input to a next such process in the succession; each colour correction process being operable to detect whether each pixel lies within the respective locus in colour space and, if so, to apply the colour mapping operation to that pixel; and each colour correction process after the first process in the succession being arranged to inhibit colour mapping in respect of the loci associated with previous processes in the succession.

Description:
BACKGROUND OF THE INVENTION  
         [0001]    1. Field of the Invention  
           [0002]    This invention relates to colour correction.  
           [0003]    2. Description of the Prior Art  
           [0004]    Colour correction is a technique used in the production of image or video material to replace occurrences of certain colours in original material with corresponding replacement colours. Two examples of when this process might be needed are to match the appearance of scenes shot under different lighting conditions, or simply to change the appearance of an image for artistic reasons. Particularly in the context of this second example, it will be understood that the term “correction” does not imply that there was necessarily anything intrinsically wrong with the original colour; the way that the expression “colour correction” is used in the art (and in the present application) is in fact with the more generic meaning of “colour alteration”.  
           [0005]    The colour properties of an image are usually considered in one of the following representations, often referred to as “colour spaces”: as a set of contributions from primary colours (e.g. RGB—red, green and blue), as a luminance value (L) plus two colour difference values (e.g. Cb, Cr) or as a luminance value (L), a hue value (H) and a saturation value (S). In real images (rather than test patterns) what is perceived as a “colour” does not correspond to a single point in colour space and so cannot generally be defined as a precise, single, set of such values. Instead, what the viewer may perceive as a single “colour” would typically occupy a range of values in colour space. For example, an image of, say, a red car would have a range of “red” values depending on the local lighting, angle and even cleanliness of each area of the car. So, in order to apply colour correction to the “red” of the car, in fact a region in colour space is defined to encompass all of the “red” colour exhibited by the car. A processing operation is then applied to map that source region to another similar (target) region elsewhere in colour space. By mapping the whole region in this way, variations in shade are mapped to corresponding variations in shade at the target region.  
           [0006]    The colour correction may thus alter one or more of the colour properties of the image. For example, hue could be altered without changing the saturation and intensity values.  
           [0007]    Colour correction is usually carried out in the digital domain. U.S. Pat. No. 6,434,266 discloses a digital colour correction system in which each pixel value of a source image is converted from an RGB representation into an L,S,H representation. The L,S,H values are compared—pixel by pixel—with a range of L,S,H values defined as a source range of “colours to be corrected”. If a pixel is found to lie within the source range, that pixel is replaced by a pixel value in a “target” colour range.  
         SUMMARY OF THE INVENTION  
         [0008]    This invention provides digital image processing apparatus for applying pixel-based colour correction to an input image to generate an output image, the apparatus comprising:  
           [0009]    colour correction logic arranged to provide two or more colour correction processes each having a respective associated locus in a colour space and a respective associated colour mapping operation;  
           [0010]    the colour correction processes being arranged as a succession of processes so that the results of a colour correction process form the input to a next such process in the succession;  
           [0011]    each colour correction process being operable to detect whether each pixel lies within the respective locus in colour space and, if so, to apply the colour mapping operation to that pixel; and  
           [0012]    each colour correction process after the first process in the succession being arranged to inhibit colour mapping in respect of the loci associated with previous processes in the succession.  
           [0013]    The invention recognises that it is possible, in a colour correction system having a succession of colour correction processes, that conflicting corrections can be applied to regions of colour space, leading to subjectively undesirable results. The invention provides a convenient and elegantly simple technique for alleviating this problem, by each colour correction process after the first process in the succession being arranged to inhibit colour mapping in respect of the loci associated with previous processes in the succession.  
           [0014]    Further respective aspects and features of the invention are defined in the appended claims. 
       
    
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0015]    The above and other objects, features and advantages of the invention will be apparent from the following detailed description of illustrative embodiments which is to be read in connection with the accompanying drawings, in which:  
         [0016]    [0016]FIG. 1 is a schematic diagram of a colour correction system according to an embodiment of the present invention;  
         [0017]    [0017]FIG. 2 schematically illustrates the use of soft regions in colour space;  
         [0018]    [0018]FIG. 3 schematically illustrates a mixing arrangement;  
         [0019]    [0019]FIG. 4 schematically illustrates a key generator arrangement;  
         [0020]    [0020]FIG. 5 is a schematic flow chart showing a key priority process;  
         [0021]    [0021]FIG. 6 schematically illustrates a first embodiment of a key modifier;  
         [0022]    [0022]FIG. 7 schematically illustrates a second embodiment of a key modifier;  
         [0023]    [0023]FIG. 8 schematically illustrates a bypass controller;  
         [0024]    [0024]FIG. 9 is a schematic diagram of a mixing arrangement;  
         [0025]    [0025]FIGS. 10 a  and  10   b  are schematic diagrams illustrating problems with hue rotation in a rectangular domain;  
         [0026]    [0026]FIG. 11 a  and  11   b  are schematic diagrams illustrating hue rotation in a polar domain;  
         [0027]    [0027]FIG. 12 is a schematic diagram illustrating hue rotation in a soft region;  
         [0028]    [0028]FIG. 13 is a schematic diagram illustrating a possible implementation of hue rotation in the rectangular domain;  
         [0029]    [0029]FIG. 14 schematically illustrates hue rotation in the polar domain;  
         [0030]    [0030]FIG. 15 schematically illustrates the derivation of look-up table values; and  
         [0031]    [0031]FIG. 16 schematically illustrates the use of a look-up table for luminance modification. 
     
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS  
       [0032]    The embodiments to be described below may be implemented in hardware, in semi-programmable hardware (e.g. application specific integrated circuits or field programmable gate arrays), in software running on a general purpose data processing apparatus, or as any combination of the above. In the case of software-implemented features, the software may be stored in a storage medium (not shown) such as a disk storage medium, a read only memory or the like, and/or via a transmission medium such as an internet connection (not shown)  
         [0033]    [0033]FIG. 1 is a schematic diagram of a colour correction system according to an embodiment of the present invention.  
         [0034]    The colour correction system comprises an input processor  10 , a pre-processor  20 , a mixer arrangement  30 , a post-processor  40 , an output processor  50 , a bypass buffer  60 , a mixing controller  70  and a bypass controller  80 .  
         [0035]    Input video data is received by the input processor in a 4:2:2 Y,C (luminance, chrominance) format. The input processor routes the video data to the pre-processor  20  and also to the bypass buffer  60 . The input processor also encompasses a stage of up-sampling of the chrominance components of the input video signal to a 4:4:4 Y,C format.  
         [0036]    The pre-processor  20  carries out a rectangular to polar conversion of the chrominance components to give a (luminance, saturation, hue) (LSH) representation of the video. (Of course, the rectangular to polar conversion does not change the luminance, only the representation of the colour information). This is passed to the mixer arrangement  30  and to the mixing controller  70 .  
         [0037]    The mixing controller  70  is responsive to key parameters defining regions in colour space which are to be altered by the colour correction system. The mixing controller  70  detects whether the L,S,H values in respect of a current pixel lie within a region of colour space defined to be altered. The mixing controller generates a key value k defining whether the current pixel is to be altered and, in at least some embodiments, a degree to which alteration is to take place. The key value k is passed to the mixer arrangement  30 .  
         [0038]    The mixing controller  70  also passes information to the bypass controller  80  which, in effect, defines any pixels which have not been altered by the colour correction system. The bypass controller  80  generates a bypass control signal which is used by the output processor  50  to route the input (unaltered) data buffered in the bypass buffer  60  as output data in respect of those pixels where no alteration has been made. This means that the effect of filtering and other processors taking place at the input processor  10 , the pre-processor  20 , the mixer  30  and the post-processor  40  are not applied to any pixels where no alteration is in fact required.  
         [0039]    Returning to the mixer arrangement  30 , this receives the L,S,H values of a current pixel and a key value k in respect of that pixel. The key value controls the degree of alteration or colour correction processing applied to that pixel. An alteration is carried out in proportion to the key value. If k=0, then no alteration is made to that pixel. If k=1 then the full amount of a predetermined alteration is made. If 0&lt;k&lt;1 then a proportion of the predetermined alteration is made.  
         [0040]    In FIG. 1, only a single stage of mixing controller  70  and mixer arrangement  30  is illustrated, but in a preferred embodiment six consecutive such stages are provided.  
         [0041]    The post-processor  40  carries out a polar to rectangular conversion back to a 4:4:4 Y,C format along with a limiting function to remove any so-called “illegal” colours generated by the mixer arrangement  30 . Illegal colours lie outside a range of colours deemed to be legal, which is generally is taken to be a range outside a so-called “colour cube”.  
         [0042]    Finally, the output processor  50  provides the bypass mixing function described above and also provides a down sampling function back to 4:2:2 Y,C format.  
         [0043]    It will be seen from FIG. 1 that relative delays are applied to compensate for the processing delay of the up sampling, rectangular to polar conversion, polar to rectangular conversion and down sampling processors.  
         [0044]    [0044]FIG. 2 schematically illustrates the use of a key value k and so-called “soft” key values, to define a colour correction.  
         [0045]    A region or locus  92  in colour space (e.g. a rectangular CrCb space) is defined so as to have a key value equal to a certain amount (e.g. a maximum key value, which in the present embodiment will be taken as being equal to 1). Well away form that region, for example at a position  96 , the key value is set to another predetermined amount, such as zero. A colour alteration  94  is defined in respect of that keyed region. This maps the region  92  onto a corresponding region  92 ′.  
         [0046]    Now, for a current pixel, the colour attributes (Cb, Cr in this case) of that pixel are compared with the keyed region. If the attributes of the current pixel are found to lie within the keyed region, then the alteration  94  is applied to that pixel. If the key value is zero for that current pixel, then no colour correction change is applied.  
         [0047]    However, it is possible to set a key value which represents neither “a full change” nor “no change at all”. In the present embodiment this is achieved by using a key value of greater than zero but less than one. Regions  98  having a key value k where 0&lt;k&lt;1 are referred to as “soft” regions and are shown schematically as shaded regions in FIG. 2.  
         [0048]    In a soft region, a partial colour correction operation is carried out. That is to say, a part of the alteration  94  is applied to a pixel having colour attributes corresponding to a soft region. The amount or proportion of the transition may conveniently be set so as to be proportional to the key value.  
         [0049]    The problem of how to handle a partial colour transition is discussed extensively in the following description.  
         [0050]    [0050]FIG. 3 schematically illustrates a mixing and mixing control arrangement.  
         [0051]    A succession of mixers  31 ,  32 ,  33  . . . are used. In actual fact, six such mixers are used, with the output of a mixer forming the input to a next mixer in the sequence. Each mixer uses a respective key signal k 1 , k 2 , k 3  . . .  
         [0052]    The key signal k 1 , for the first mixer  31  is generated by a first key generator  71 . Similarly, a key signal k v  for the second mixer is generated by a second key generator  72 . The key signal from the first key generator and the key signal from the second key generator are supplied to key modifying logic  73 . This generates two outputs: one is the key k 2  which is actually used to control the second mixer, and another is k f —effectively a “running total” key amount—which is passed to a next stage of key modifying logic in the sequence. The key k 2  is delayed by a delay  74  so as to arrive at the second mixer  32  at the same time as the (potentially modified) pixel data to which it refers.  
         [0053]    Continuing down the chain, a third key generator  75  supplies a key k v  via a compensation delay  76 , to a second key modifying logic  77 , which also receives a running total key value k f  from the key modifying logic of the preceding stage. This outputs a key k 3  which, via delays  78 , is supplied to the third mixer  33 .  
         [0054]    The basic principle underlying the key generation and key modifying logic is that a position in colour space which has been modified by an earlier mixing operation in the sequence of mixing operations should not be modified again. So, if a key value of 1 (complete alteration) has been generated by an earlier key generator in respect of that position in colour space, later key generators are inhibited from generating a non-zero key value in respect of the same colour space position. If a key value representing a partial modification has been generated in respect of a particular position in colour space, then a further partial modification is allowed to be passed to the key modifying logic. The “running total” key, k f , represents the total amount of modification applied to that pixel by preceding key generators in the sequence. So, if the first key generator had generated a key value of, say, 0.2 in respect of a current pixel, and the second key generator had generated a key value of, say, 0.1 in respect of that pixel, then the running total key value k f  passed to the third key generation stage would be 0.3. The maximum key value k 3  which could be passed by the key modifying logic of the third stage would then be (1−0.3)=0.7.  
         [0055]    As mentioned above, it is preferred that a succession of six mixers with corresponding key generation is provided, but for clarity of the diagram, FIG. 3 shows only three stages of the mixing process. Accordingly, in a final stage, the key modifying logic  77  outputs a key k f  which provides an input (via a delay  79 ) to the bypass controller  80 .  
         [0056]    [0056]FIG. 4 schematically illustrates a key generator such as the key generator  71 ,  72  or  75 .  
         [0057]    The key generator receives luminance (Y) chrominance (C b , C r ) and saturation (S) data in respect of a current pixel. A key value k v  is generated in dependence on these attributes of the current pixel and on  13  constants C 1  . . . C 13 . Considering the operation of FIG. 4 in terms of some intermediate values I 1  . . . I 8 , it can be seen that: 
           I   1 =C 12 +(C 1 *Cb)+(C 2 *Cr) 
           I   2 =C 13 +(C 3 *Cb)+(C 4 *Cr) 
         [0058]    The outputs I 1  and I 2  represent a rotation of the hue of the pixel.  
         [0059]    An operation referred to as “NEGNAM” (negative non additive multiplexing) signifies that the numerically lower of the inputs to the NEGNAM is passed as its output. So: 
         I 3 =the lower of I 1  and I 2 , subject to a limiting operation to prevent overflow. 
         [0060]    I 4 =1−(C 5 +{square root}( 1   2 +I 2   3 )), subject to a shift operation and a limiting operation. The reason for the shift operation is as follows. To avoid unnecessary processing overheads, the gain that needs to be applied using C 1  to C 4  is split into two parts, a fractional component and a power-of-two component. The fractional component is applied by the multiplication by C 1  . . . C 4 , and the power-of-two component is applied as a bit shift. 
           I   5 =C 8 *(ABS(Y+C 6 )+C 7 ) subject to a limiting operation to prevent overflow 
           I   6 =C 11 *(ABS(S+C 9 )+C 10 ) again subject to a limiting operation to prevent overflow 
         [0061]    Here, I 5  may be considered as a luminance key and I 6  as a saturation key.  
         [0062]    I 7 =either I 3  or I 4 , depending on whether operation is in a “sector mode”, so that the keyed region represents a sector in colour space, or “ellipse mode” in which the keyed region represents an elliptical region in colour space. I 3  is selected in sector mode and I 4  is selected in ellipse mode. 
         I 8 =the lower of (I 7  and the lower of (I 5  and I 6 )) 
         [0063]    The value I 8  is then “shifted and softened” to form the key value k v . The shifting and softening operation allows modification of the key edges to better align them to the boundary of the region being corrected.  
         [0064]    [0064]FIG. 5 schematically illustrates the process used to handle the running total key values kf and the newly generated key values k v . In the present embodiment the process is carried out in hardware, but the flowchart of FIG. 5 schematically illustrates how the process may be carried out if the key modifying logic referred to above is implemented as programmable data processing apparatus, running a program stored on a storage medium such as a read only memory or a disk storage medium, or received via a network connection such as an internet connection.  
         [0065]    At a start  100 , the running total key value, k f , for a current pixel is set to zero. At a step  110 , the first key generator  71  generates the first key value kv. At a step  120 , a comparison is made between kv and ( 1 -k f ). If k v &gt;( 1 -k f ) then ( 1 -k f )—the remaining amount of key available at that pixel—is passed  140  to the mixer  31 . Otherwise (as would be the case for the first key generation stage) if ( 1 -k f )&gt;=k v , then k v  is passed  130  in full to the mixer  31 .  
         [0066]    At a step  150  the running total key k f  is increased by the amount of k v , subject to a maximum value for k f  of 1.  
         [0067]    If at a step  160 , it is found that the sequence of mixing operations is complete, the process ends. Otherwise, at a step  170 , the process returns to operate in respect of the next key generation step.  
         [0068]    The following table illustrates the operation in respect of the running total key k f  and a newly generated key value k v .  
                                                                                                       Input       Output               to key modifying logic       from key modifying logic                K f     K v     K f     K v                              1   1   1   0           0   1   1   1           1   0   1   0           0   0   0   0           0.5   1   1   0.5           0.2   0.3   0.5   0.3           0.7   0.9   1   0.3                      
 
         [0069]    [0069]FIG. 6 schematically illustrates a hardware implementation of the key modifying logic  73 ,  77  . . . .  
         [0070]    The value k f  is supplied in parallel to a subtractor  200 , which generates a value ( 1 -k f ), and an adder  220 .  
         [0071]    The value ( 1 -k f ) is passed from the subtractor  200  to a NEGNAM  210 , which receives as a second input the newly generated key value kv. The NEGNAM  210  outputs the lower of k v  and ( 1 -k f ) as the current key to be used by the current mixing arrangement. The output of the NEGNAM  210  is also passed to the adder  220 , where it is added to the existing k f  to form the new running total key value k f .  
         [0072]    [0072]FIG. 7 schematically illustrates a second embodiment of the key modifying logic which also handles a “running total” bypass value E xf .  
         [0073]    As mentioned above, to ensure that the colour corrector is transparent to pixels for which no change is made, the final running total key value, k f , may be used to derive a control signal for the bypass function. So, if a pixel has been modified to any extent by any of the mixing stages (i.e. if k f &gt;0 for that pixel) then the output of the sequence of mixing arrangements is used as the output pixel. If, however, k f =0 for that pixel, this shows that the pixel has not been modified by the colour correction process, and so the bypass (buffered) value of the original pixel is used as the output pixel.  
         [0074]    An exception can occur in the following circumstances. It is possible to use one of the earlier stages in the sequence of mixing arrangements to exclude certain regions of colour space from any modification at all. This is done by deriving a key in respect of that region but setting the parameters controlling the corresponding mixing arrangement to provide a zero change. Because of the use of key modifying logic and the running total key, k f , as described above, this will have the effect of inhibiting any subsequent change at that region of colour space by following mixing arrangements in the sequence.  
         [0075]    Using the basic “bypass” method based on k f  alone, such “excluded” pixels corresponding to the excluded region of colour space will be output from the chain of mixing arrangements rather than from the bypass buffer. But as the pixels corresponding to that region of colour space will not have been modified, it would be more appropriate to use the buffered pixels as output.  
         [0076]    Referring to FIG. 7, a running total exclude flag E xf  is derived, at each stage, by an OR operation between the previous value of E xf  and an AND combination of k v  (the key value output by the current key modifying logic and used to control the current mixing arrangement) and a flag E xv  (a flag set high when the current key generator is in an “exclude” mode of operation).  
         [0077]    Using this arrangement, a key generator set to exclude mode will set E xf  high if the current pixel has its key value&#39;s MSB set to 1 by that key generator. The logic implies that Exf, once set high, cannot be set low by a subsequent key modifying logic stage.  
         [0078]    [0078]FIG. 8 schematically illustrates a bypass controller. The bypass controller receives as inputs the running total key value k f  and the running total exclude flag E xf . A bypass control output is generated as: 
         nbypass=(k f doesn&#39;t equal zero) AND (NOT E xf ) 
         [0079]    If the key is non-zero and the exclude flag has not been set, then the bypass (buffered) pixel is not to be selected.  
         [0080]    [0080]FIG. 9 is a detailed schematic diagram of part of the mixing arrangement  30  shown in FIG. 1. The mixing arrangement  30  comprises colour correction logic operable to effect desired additive changes to hue, saturation and luminance and multiplicative changes to saturation and luminance. The mixing arrangement logic operates in the polar domain.  
         [0081]    The mixing arrangement has as its inputs initial values for hue, saturation and luminance from the pre-processor  20 , as well as a key value k from the mixing controller  70  (which defines whether the current pixel is colour corrected, and if so, by how much) and also desired modifiers including additive deltas for hue, saturation and luminance, and gain for saturation and luminance.  
         [0082]    Hue modification is carried out by logic  502 . The logic  502  relates only to additive changes (shifts) in hue. The logic  502  comprises a look-up table (LUT)  520  which tabulates the equations required in providing a smooth colour transition in soft regions of colour space (regions for which 0&lt;k&lt;1). It is noted that a smooth colour transition between initial and desired hue through soft areas of colour space requires a change in saturation as well as hue in the polar domain. This is discussed later with reference to FIGS. 10 a ,  10   b ,  11   a ,  11   b  and  12 . The contents of the look-up table  520  are described later with reference to FIGS. 14 and 15. The look-up table  520  takes the key value k as an input and produces an output to be summed with the input hue by an associated adder  522 . This generates an output hue.  
         [0083]    Saturation modification is carried out by logic  504 . The saturation logic relates to both additive (shift) changes and multiplicative (gain) changes. As noted above, smooth transitions between input and desired hues also require modification to saturation in soft regions, and so these changes are implemented also within the saturation logic  504 .  
         [0084]    The logic  504  comprises a look-up table  540  which provides multiplicative changes to saturation, to operate with the hue changes described above to provide a smooth alteration in soft regions. The look-up table  540  takes the key value k as an input and produces an output to be passed to a multiplier  542  to be multiplied by the input saturation. The result of the multiplicative operation is then passed to an adder  546  to be summed with the result of any desired additive modifications. The desired additive saturation change δSat is taken as an input to multiplier  544 . The second input to the multiplier  544  is key value k. δSat and k are multiplied together by multiplier  544  and the result is passed as an input to the adder  546  to be summed with the output of the multiplier  542 . The sum of the additive and multiplicative modifications to saturation results in an output saturation.  
         [0085]    Luminance modification is carried out by logic  506 . The luminance logic relates to both additive (shift) changes and multiplicative (gain) changes. The logic  506  operates in a similar way to the saturation logic  504 , apart from different look-up table data.  
         [0086]    The logic  506  comprises a look-up table  560 , which provides multiplicative changes to luminance, to operate with the hue changes described above to provide a smooth alteration in soft regions. The content of the table is considered later with reference to FIG. 16. The look-up table  560  takes the key value k as an input and produces an output to be passed to a multiplier  562  to be multiplied with the input luminance. The result of the multiplicative operation is then passed to an adder  566  to be summed with the result of any desired additive modifications. The desired additive luminance change δY is taken as an input to multiplier  564 . The second input to multiplier  564  is key value k. δY and k are multiplied together by the multiplier  564  and the product is passed as an input to an adder  566  to be summed with the result of the above described multiplicative modifications. The summation of the additive and multiplicative modifiers results in an output luminance.  
         [0087]    The output hue, saturation and luminance are then passed on to the next mixing arrangement in the sequence or, in the case of the last mixing arrangement, to the post processor  40 .  
         [0088]    The look-up tables may be supplied with data once per field, once per frame etc. The data may be supplied by data generating means (not shown) within the mixing arrangement or by an external data processing apparatus (not shown)  
         [0089]    Part of the reason for using the look-up tables for hue modification will now be described. In basic terms, it has been recognised that it is not possible to simply apply a hue change in the Cb,Cr domain using a deltaCb and deltaCr additive vector translation. The reasons behind this will now be explained.  
         [0090]    Simple additive logic works well to create additive delta changes in Luminance and Saturation, but hue is more complicated. Hue can be considered in either the polar or the rectangular (Cb,Cr) domains.  
         [0091]    [0091]FIG. 10 a  schematically shows a simple additive logic applied to try to create a hue shift in the rectangular domain. Though this works for spot colour correction, that is, correction or alteration of colours represented by single points in colour space, it can result in the wrong output value of saturation when larger regions of colour space are corrected. (Here, it is noted that what a viewer may perceive as a single “colour” would normally occupy a region in colour space). Referring to FIG. 10 b , it can be seen that if an additive correction amount is set up in the rectangular domain which is correct for, say, a spot colour  620  (mapping it to a corresponding colour  620 ′), such a correction will normally be quite inappropriate for other spot colours in the same colour region, such as a colour  610  (mapped to a corrected colour  610 ′) and a colour  630  (mapped to a corrected colour  630 ′). The saturation of the colours  610 ′ and  630 ′ will be very different to the saturation of the input colours  610  and  630 .  
         [0092]    This problem can be alleviated by operating in the hue (polar) domain. FIG. 11 a  schematically shows a simple additive logic applied to hue shift in the polar domain. Here, a change in hue represents a rotation in the rectangular domain. This maintains the correct saturation for different positions within a region of colour space—for example, the colour  610  is correctly mapped to the colour  610 ″, and the colour  630  is now correctly mapped to the colour  630 ″.  
         [0093]    However, operating in the polar domain can introduce other problems. In particular, in “soft” regions (where 0&lt;k&lt;1) of colour correction, which typically are set up so as to occur around the edges of regions to be corrected, undesirable colour “rainbow” effects may be experienced. The reason for this will now be explained with reference to FIG. 12.  
         [0094]    [0094]FIG. 12 schematically shows a hue shift represented in the polar domain. The hue shift can be most easily described as a hue rotation by an angle  720 , so that (for example) an input colour  710  is altered to a corrected colour  710 ′.  
         [0095]    In a basic arrangement using a hue rotation implemented in the polar domain, a correction in a “soft” region (where 0&lt;k&lt;1) would result in a partial rotation by an angle given by: 
         hue rotation=k. (angle  720 ) 
         [0096]    So, for a key value k of, say, 0.3, a rotation of the colour  710  to a corrected colour  710 ″ would occur. This represents a rotation by an angle equal to 30% of the angle  720 .  
         [0097]    However, in soft areas it is more subjectively desirable for the partial correction to describe a straight line  740  on the Cb,Cr plane between the original and corrected colour. So, for a key value k of 0.3, it is more subjectively desirable for the colour  710  to be altered to give a corrected colour  710 ′″.  
         [0098]    This means however, that in softness areas saturation will change as well as hue (saturation being represented by the distance from the origin to the line  740 ).  
         [0099]    It is possible to implement this by producing the hardware needed to create a rotation, but operating in the rectangular (Cb,Cr) domain, but this is undesirable because a lot of hardware is required. A possible logic arrangement suitable for carrying out this rotation in the rectangular domain is shown schematically in FIG. 13. This involves the calculation of sines and cosines of the desired hue change, and generally is very expensive in terms of hardware or processing operations. In contrast, the present embodiment provides an elegantly simpler technique which is much less expensive of hardware or processing operations.  
         [0100]    As described above, when hue alterations are implemented in the polar domain, it is subjectively desirable to change saturation as well as hue, when a hue change is being applied and 0&lt;k&lt;1. This can conveniently be realised using look-up tables, because the equations that describe the hue and saturation deltas in soft areas are complex.  
         [0101]    [0101]FIG. 14 schematically illustrates those parts of the arrangement of FIG. 9 which are relevant to hue modification in soft regions. The look-up tables  520  provides alteration values required for a shift in hue, and the look-up table  540  provides alteration values required for a change in saturation. Both look-up tables take the key value key as an input. The equations from which the look-up table values (for both saturation and hue) are generated are considered below with reference to FIG. 15. Note that the modified saturation shown in FIG. 14 is not necessarily the final output saturation, as it may still be modified by any desired direct changes to the gain or delta of the original saturation.  
         [0102]    The hue look-up table is used to alter the hue in a fashion to ensure that there is a linear transition along the line  740  with respect to the changing key value.  
         [0103]    The contents of the two look-up tables of FIG. 14 can be generated using the geometry shown in FIG. 15 and known trigonometrical identities. FIG. 15 schematically illustrates a colour correction operation in the rectangular (Cb,Cr) domain. In FIG. 15:  
         [0104]    The variable “I” represents the total change that is caused by the colour correction operation, i.e. when k=1.  
         [0105]    The variable “Δhue” represents the total hue rotation that is caused by the colour correction operation, i.e. when k=1.  
         [0106]    The variable “i” represents an incremental (vector) change caused by a partial value of k, i.e. a value for which 0&lt;k&lt;1.  
         [0107]    The variable “s” represents the desired saturation in the situation that 0&lt;k&lt;1.  
         [0108]    The variable “θ” represents the hue change (rotation) which is required when 0&lt;k&lt;1.  
         [0109]    The variable “Sat” represents the saturation of a current pixel.  
         [0110]    To ensure that as the key value increases a straight-line transition will be made from the initial colour to the corrected colour in the rectangular domain, it is necessary to use: 
         i=I.k 
         [0111]    To obtain the saturation look-up table  840 , the following equations are required:  
         s     Sin        (     90   -     Δ                   hue   /   2         )         =         Sat     Sin        (     180   -   θ   -     (     90   -     Δ                   hue   /   2         )       )         .     
        s     =     Sat   *         Cos        (     Δ                   hue   /   2       )         Cos        (       Δ                   hue   /   2       -   θ     )         .                               
 
         [0112]    So, the contents of the saturation look-up table are defined by:  
           Cos        (     Δ                   hue   /   2       )         Cos        (       Δ                   hue   /   2       -   θ     )         .                         
 
         [0113]    and this value is multiplied by the current pixel&#39;s saturation, Sat. The input to the look-up table appears to be the angle θ, but this is in fact a function of the incoming key value k, which will now be shown in relation to the generation of the hue look-up table  820 .  
         [0114]    For the hue look-up table  820 , the following equations are required:  
               I     Sin        (     Δ                 hue     )         =       Sat     Sin        (     90   -     Δ                   hue   /   2         )         .             (   1   )                 i     Sin        (   θ   )         =       Sat     Sin        (     180   -   θ   -   90   +     Δ                   hue   /   2         )         .             (   2   )                               
 
         [0115]    Substituting  1  and  2  into the above, and solving for tan(θ), gives:  
           1       1     k   *     Sin        (     Δ                 hue     )           -     tan        (     Δ                   hue   /   2       )           .     =     tan        (   θ   )                             
 
         [0116]    This means that the angle θ is the arctangent of the left hand side of the equation above. It is this that is used in the hue look-up table  820 , with key value k as the input and the angle θ as the output. This output angle θ is then added into the input hue angle to create the modified hue.  
         [0117]    This equation is also used to relate k to the angle θ for use with the saturation look-up table  840 . This means that the input for the saturation look-up table can be k.  
         [0118]    Because tangent is not a continuous function, and because it is important to prevent divide-by-zero errors, some exceptions are needed in the firmware that calculates the look-up table contents. These exceptions are:  
         [0119]    (a) k=0  
         [0120]    (b) k=1 
                 1     k   *     Sin        (     Δ                 hue     )           -     tan        (     Δ                   hue   /   2       )         =   0           (   c   )                               
 
         [0121]    (d) Δhue&gt;=180 degrees  
         [0122]    These exceptions can be handled using the following procedures:  
         [0123]    (i) if Δhue&lt;−180 degrees, add 360 degrees to Δhue  
         [0124]    (ii) if Δhue&gt;180 degrees, subtract 360 degrees from Δhue  
         [0125]    (iii) if the absolute value of Δhue&gt;179.9 degrees (i.e. nearly 180 degrees) then: 
         if k&lt;0.5, set the look-up table (LUT) value of hue change to zero and the saturation LUT value to (1-2k); 
         otherwise (i.e. if k&gt;=0.5) set the LUT value of hue change to Δhue and the saturation LUT value to (2k-1) 
         [0126]    (iv) if k =0 then set the LUT value of hue change to 0 and the saturation LUT value to 1; else if k is exactly equal to 1, set the LUT value of hue change to Δhue and the saturation LUT value to 1.  
                 when                                    1                  K   *     Sin        (     Δ                 hue     )             -     tan        (     Δ                   hue   /   2       )         =     x   =   0             (   v   )                               
 
         [0127]    the hue LUT value should be set to 90°. However, when x, above, is nearly equal to zero (i.e. within a predetermined amount, SMALLNUMBER, of zero), the hue look-up table should also be set to 90°.  
         [0128]    The present embodiment uses a 10-bit hue value. This implies that 360 degrees of hue rotation corresponds to a hue change of decimal 1024. So, the smallest number of degrees of hue change is represented by 1/1024.  
         [0129]    This means that the closest distinction that can be made between 90 degrees and the next number of degrees is:  90 -(360/1024)=89.6484375.  
         [0130]    The tangent of this is 162.9726164.  
         [0131]    Finally, 1/x is required to give: x=0.00613600158=SMALLNUMBER.  
         [0132]    Using the above criteria and exceptions, it is possible to construct look-up tables for hue and saturation which provide accurate values for a linear transition across the rectangular domain, allowing the operation of the logic itself to take place in the polar domain.  
         [0133]    The previous logic works to provide an additive change. However, it is also advantageous to create a multiplicative delta, as implemented in the logic of FIG. 9.  
         [0134]    [0134]FIG. 16 illustrates the logic required to provide a multiplicative change to saturation and luminance. This is only applicable to saturation and luminance—as discussed above multiplicative changes are not relevant to hue. To save on multipliers these changes are implemented using a look-up table  920  and a multiplier  940 . From FIG. 16 it can be seen that the appropriate value of the look-up table  920  is applied to the multiplier  940  to be multiplied together with the input to provide the appropriate output. The gain in both cases is embodied in the values of the look-up table. In the case of saturation, the gain is applied by multiplying the contents of the look-up table  920  with the desired gain (except for K=0 which is left with unity gain for when the key is off) and applying the appropriate look-up table value to multiplier  940  to be multiplied together with the input saturation. The output of the multiplier  940  being the modified saturation. Note that in this case of saturation, the look-up table  920  and the multiplier  940  are embodied in FIG. 9 as look-up table  540  and multiplier  542 . The look-up table for saturation has the dual purpose of providing for desired saturation gain and hue-related saturation modification.  
         [0135]    In the case of luminance, the content of the look-up table  920  is described by the equation: 
         1 +k *(Desired luminance gain−1) 
         [0136]    The look-up table  920  then takes key value k as an input and produces an output to be applied to the multiplier  940  and thus multiplied together with the input luminance to provide the modified luminance. For luminance, the look-up table  920  and the multiplier  940  are embodied in FIG. 9 as look-up table  560  and multiplier  562 .  
         [0137]    In so far as the embodiments of the invention described above are implemented, at least in part, using software-controlled data processing apparatus, it will be appreciated that a computer program providing such software control and a storage or transmission medium by which such a computer program is provided are envisaged as aspects of the present invention.  
         [0138]    Although illustrative embodiments of the invention have been described in detail herein with reference to the accompanying drawings, it is to be understood that the invention is not limited to those precise embodiments, and that various changes and modifications can be effected therein by one skilled in the art without departing from the scope and spirit of the invention as defined by the appended claims.