# Patent

## Title
Method and system for predictive scaling of colour mapped images

## Abstract

A method for determining a scaled color map of a scaled image is described using the transformation of the original color map and the original image only, independently of the scaled image. A number of colors N in the original color map is determined; and provided N>Nmax, all colors in the original color map are reused in the scaled color map. If N<Nmin, the number of colors in the original color map is increased. Otherwise, the scaled color map is formed including: selecting a sub-set of colors in the original color map; increasing a number of colors in the selected sub-set; adding the resulting sub-set with increased number of colors to the original color map; and removing duplicate colors, wherein Nmin and Nmax are respective predetermined minimum and maximum thresholds for a number of colors in the original color map. A corresponding system is also provided.

## Background
CROSS REFERENCE TO RELATED APPLICATIONS
The present application is a Continuation of patent application Ser. No. 12/185,081 filed on Aug. 2, 2008, now issued as a U.S. Pat. No. 8,107,724 on Jan. 31, 2012, entire contents of which being incorporated herein by reference.


FIELD OF THE INVENTION
The present invention relates to scaling of digital images, and in particular, to a method and system for predictive scaling of colour mapped images.
BACKGROUND
Processing of images is a time consuming and CPU intensive procedure because of the shear volume of data to be processed and complexity of algorithms involved.
For this reason, various methods of reducing both the volume of data and the complexity of the image processing algorithms have been developed.
One of the methods relies on reducing the number of distinct colours used to produce an image, even at the expense of the image quality. Instead of storing and managing every primary colour component of every pixel of the image, the most representative colours are grouped into a limited size array of colour elements, in which each element (a colour) is indexed by its position. Such array of colour elements, representing a positive trade off between the number of colours in the set and the image quality, is customarily referred to as a colour map of the image. This way, the pixels of the image contain not the full colour components but merely their index into the colour map and are often referred to as a pixel map of the image. Thus, an image structurally organized into a colour map and a pixel map is called the colour mapped image.
For many applications, colour mapped images are preferred over other types of images, since they are smaller in size and simpler to process, while maintaining an acceptable perceived visual quality.
However, for some applications, such as transformation of images, best known in the art as scaling, benefits provided by colour mapped images are still insufficient. The need for performing scaling may arise, for example, when the size of a high-quality original image exceeds the display or memory capabilities of a mobile device, particularly when a number of images are streamed in a video sequence. In this case, pixels of the image that do not fit into a smaller display must be dropped, which may result in an unacceptable loss of quality of the image because of the lower resolution and no longer adequate colour map. To minimize the damage caused by scaling, prior art suggests to perform a computationally intensive procedures, such as re-generation of the colour map of the scaled image.
However, prior art seems to overlook many opportunities for further minimization of image processing arising during scaling of colour mapped images.
Correspondingly, it is desirable and advantageous to develop an improved method and system for scaling a colour mapped digital image, which would reduce the computational intensity of image processing.
SUMMARY OF THE INVENTION
Accordingly, there is an object of the invention to provide an improved method and system for scaling of colour mapped images, which would avoid or mitigate the shortcomings of the prior art.
According to one aspect of the invention, there is provided a method of scaling an original image, having an original colour map and original pixel map, into a scaled image having a scaled colour map and a scaled pixel map, the method comprising steps of:
(a) transforming the original colour map into the scaled colour map based on the original colour map and the original image independently of the scaled image;
(b) scaling the original image into the scaled image;
(c) for each pixel of the scaled image:


    
    
        (i) determining a set of contributing pixels in the original image, which define a colour of the pixel;
        (ii) determining the colour of the pixel based on colours of the contributing pixels and geometric proximity of the pixel to the contributing pixels; and
        (iii) establishing correspondence between the colour of the pixel and a colour in the scaled colour map; and determining a corresponding colour map index thereof; and
        (iv) setting the determined colour map index in the scaled pixel map.
    
    


The step (a) comprises computing a number of colours N in the original colour map, excluding transparent colours.
In the method described above, the transforming comprises re-using the original colour map as the scaled colour map provided N>Nmax.
In the method described above, the step of transforming comprises:
(v) increasing the number of colours available in the original colour map to produce the scaled colour map provided N<Nmin.
Beneficially, the step of the transforming further comprises:
(vi) selecting a sub-set of colours, available in the original colour map, for colour enhancement;
(vii) increasing the number of colours for the selected sub-set of colours; and
(viii) removing duplicate colours obtained in the step (vii); provided Nmin<N<Nmax.
Conveniently, the step (v) comprises:

    
    
        generating combinations of any two colours from the original colour map;
        for each combination, interpolating between said two colours.
    
    


In the embodiment of the invention, the step (vi) comprises:

    
    
        selecting a number of colours Ms in the sub-set of colours according to the following:
        Ms=N, provided N(N+1)≦2Nmax;
        Ms=M, where M is the smallest number M<N for which M(M−1)≧2(Nmax−N), provided N(N+1)>2Nmax;
        wherein N is a number of colours in the original colour map, and Nmax is a predetermined maximum number of colours.
    
    


In the method described above, the step (vii) comprises:

    
    
        generating combinations of any two colours from the sub-set of colours;
        for each combination, interpolating between said two colours.
    
    


For an image in a video stream, the step (b) comprises scaling only a delta region of the original image, i.e. the region of the original image that has been changed compared to a previous frame in the video stream.
In the method described above, the step (ii) comprises:

    
    
        assigning the colour of the pixel equal to the colours of the contributing pixels provided the colours of the contributing pixels are the same; or
        assigning the colour of the pixel by interpolating colours between the contributing pixels.
    
    


Beneficially, the interpolating colours between the contributing pixels comprises bi-linear interpolating.
For bi-linear interpolation, the step (i) of the method comprises determining first (Q11), second (Q12), third (Q21) and fourth (Q22) contributing pixels located in vertices of a rectangle surrounding the pixel (P1) and having respective colours f(Q11), f(Q12), f(Q21) and f(Q22); and wherein the step (ii) comprises determining the colour f(P1) of the pixel (P1) as follows:

f(P1)=f(Q11)(x2−x)/(x2−x1)+f(Q21)(x−x1)/(x2−x1)

provided f(Q11)=f(Q12) and f(Q21)=f(Q22) and wherein x is a horizontal coordinate of the pixel P1, x1 is a horizontal coordinate of the pixels Q11 and Q12, and x2 is a horizontal coordinate of the pixels Q21 and Q22.

Alternatively, for the bi-linear interpolation, the step (i) of the method may comprise determining first (Q11), second (Q12), third (Q21) and fourth (Q22) contributing pixels located in vertices of a rectangle surrounding the pixel (Q) and having respective colours f(Q11), f(Q12), f(Q21) and f(Q22); and wherein the step (ii) comprises determining the colour f(Q) of the pixel (P1) as follows:

f(P1)=f(Q11)(y2−y)/(y2−y1)+f(Q12)(y−y1)/(y2−y1)

provided f(Q11)=f(Q21) and f(Q12)=f(Q22) and wherein y is a horizontal coordinate of the pixel P1, y1 is a horizontal coordinate of the pixels Q11 and Q21, and y2 is a horizontal coordinate of the pixels Q12 and Q22.

Conveniently, the step (iii) of the method comprises finding the closest match in the scaled colour map.
According to another aspect of the invention, there is provided a system for scaling an original image, having an original colour map and original pixel map, into a scaled image having a scaled colour map and a scaled pixel map, the system comprising:

    
    
        a computer having a processor and computer readable medium having computer readable instructions stored thereon for execution by the processor for forming the following:
        a colour map transformation module for transforming the original colour map into the scaled colour map based on the original colour map and the original image independently of the scaled image;
        a pixel selection module for scaling the original image into the scaled image;
        a colour interpolation module for determining, for each pixel of the scaled image:
        (i) a set of contributing pixels in the original image, which define a colour of the pixel;
        (ii) the colour of the pixel based on colours of the contributing pixels and geometric proximity of the pixel to the contributing pixels; and

a colour map index generation module for:

        (iii) establishing correspondence between the colour of the pixel and a colour in the scaled colour map; and determining a corresponding colour map index thereof; and
        (iv) setting the determined colour map index in the scaled pixel map.
    
    


In the system described above, the colour map transformation module further comprises a colour map analyzer module for determining a number of colours N in the original colour map, and comparing the number of colours N with a predetermined thresholds Nmin and Nmax.
The colour map transformation module further comprises a colour culling module for selecting a sub-set of colors available in the original color map, which are most beneficial for colour enhancement, provided Nmin<N<Nmax.
The colour map transformation module further comprises a colour map enhancement module for increasing the number of colours available in the original colour map to produce the scaled colour map provided N<Nmax, and for increasing the number of colours in the selected sub-set of colours provided Nmin<N<Nmax, and for removing duplicate colours.
The colour map enhancement module comprises means for generating combinations of any two colours from the original colour map; and for each combination, interpolating between said two colours.
The colour culling module comprises means for selecting a number of colours Ms in the sub-set of colours according to the following:

    
    
        Ms=N, provided N(N+1)≦2Nmax;
        Ms=M, where M is the smallest number M<N for which M(M−1)≧2(Nmax−N), provided N(N+1)>2Nmax;
        wherein N is a number of colours in the original colour map, and Nmax is a predetermined maximum number of colours.
    
    


In the system as described above, the colour culling module further comprises means for:

    
    
        determining a colour usage vector indicating frequency of use of colours in the original colour map;
        generating an octree graph based on the colour usage vector;
        parsing the octree graph to select Ms colours to be included in the sub-set.
    
    


A computer readable medium having computer readable instructions, stored thereon for execution by a processor to perform the steps of the method described above, is also disclosed.
Beneficially, the original and scaled images are Graphical Interchange Format (GIF) images. Alternatively, the images may be encoded with Portable Network Graphics (PNG) formats, Bitmap (BMP), or other image formats using colour maps.
Thus, an improved method and system for scaling colour mapped images have been provided.



BRIEF DESCRIPTION OF THE DRAWINGS
Embodiments of the invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 illustrates the steps of the method for scaling a colour mapped image according to the embodiment of the present invention;
FIG. 2 shows the block 104 (Colour Map Transformation) of the method of FIG. 1 in more detail;
FIG. 3 shows the block 108 (Colour Mapped Image Scaling) of the method of FIG. 1 in more detail;
FIG. 4 is a schematic illustration of bi-linear interpolation performed in block 312 and the analysis of colours of the contributing pixels performed in block 310 of FIG. 3;
FIG. 5 shows the block 310 (Key Decision) of FIG. 3 in more detail; and
FIG. 6 shows a system for scaling a colour mapped image of the embodiment of the invention.



DETAILED DESCRIPTION OF THE EMBODIMENTS OF THE INVENTION
The preferred embodiment of the present invention takes an advantage of opportunities for minimizing the processing of colour mapped images arising during the transformation of one colour mapped image into another, such as scaling of the image.
FIG. 1 shows a flow-chart 10 illustrating the method for scaling a colour mapped image of the embodiment of the present invention. The method 10 starts at block 100. At block 104 (Colour Map transformation), an original colour map 102 is modified into a scaled colour map 106, based on the analysis of each pixel in the pixel map 110 of the original image against its colour map index to determine the most frequently used colours of the original image. Afterwards, block 108 (Colour Mapped Image Scaling) performs scaling of the original image by using the original pixel map 110 and the scaled colour map 106 as input to the block 108 to produce scaled colour map image 112 having scaled colour map and scaled pixel map (not shown in FIG. 1). The method terminates at block 114.
The purpose of the block Colour Map Transformation 104 is to transform the original colour map so as to make it resemble the colour map of the scaled image without performing a computationally intensive quantization of the scaled image. Instead of the quantization, the method of the embodiment of the present invention performs the steps shown in more detail with regard FIG. 2.
The colour map transformation procedure 20 starts at block 200, followed by determining whether or not the original colour map 102 needs to be transformed. This accomplished by counting the number of colours N, i.e. colours used in the original colour map, excluding a transparent colour (block 204), and analyzing its value (block 206). The transparent colour is handled separately. Our research shows that for N exceeding a predetermined maximum number of colours Nmax, i.e. N>Nmax, the original colour map can be effectively re-used as the scaled colour map without modifications. A reasonable value for Nmax has been determined to be 16, but there may be other circumstances where other values of the Nmax maximum number of colours would be beneficial. If it is determined to be the case (exit “false” from block 206), the scaled colour map 230 is defined in step 228 as a copy of the original colour map 102, and the procedure 20 stops at step 232.
However, if N<Nma, the number of colours N is considered to be insufficient for maintaining an acceptable quality of the scaled image, and therefore the transformation of the original colour map is further required (exit “true” from block 206). Quality of the transformation substantially depends on the choice of colours to be transformed, which, in turn, depends on the number of colours N. Analysis of N is performed in block 208. For N smaller than a predetermined minimum number of colours Nmin, i.e. N<Nmin (exit “false” from block 208), all colours in the original colour map are selected in block 210 for further transformation. A reasonable value for Nmin has been determined to be Nmin=4, however, there may be other circumstances where other values of the minimum number of colours would be beneficial. Otherwise (exit “true” from block 208), i.e. when the number of colours N being greater than Nmin, but smaller than Nmax, only a sub-set of colours is selected, the colours in the sub-set being the most beneficial for the transformation of the original colour map. To determine which colours to select, each pixel of the original image is analyzed (block 212) against its colour map index to determine the most frequently used colours. In this analysis, actual colour values are not processed. Instead, a value of a pixel in the original pixel map (block 110) serves as a direct index for a colour usage vector of N integer values, each value representing the frequency of use of the corresponding colour. Each time the match is determined, the value of the colour usage vector corresponding to the direct index is incremented (block 216).
When all pixels of the original pixel map 110 are processed, the colour usage vector populates an octree graph in block 218. The octree graph includes nodes arranged in levels, and each node holds 8 values, each level corresponding to a colour component bit depth from most to least significant bits. For example, the most significant bits of the red, green and blue components of a color are combined to form a 3 bit index in the first node of the octree graph. Each following bits are indexed the same way into the deeper levels of the tree. This is a very efficient way to classify the colors. Each node must hold a value for the proportion of the whole image. When a colour entry is added to the tree, its usage increments the proportion value of each node it traverses.
Let us consider an exemplary color with the RGB components RGB (13210, 2610, 8710), which is used 21% of the whole input image. The subscript 10 indicates the decimal representation of the corresponding value of the RGB component. In binary representation, the RGB components are RGB (100001002, 000110102, 010101112), correspondingly. The RGB components in binary representation fill the R, G, and B sub-columns of the column “Color” of Table 1 shown below. At each depth, bits of the RGB components form bit patterns that are translated into the indices. For example, at depth 0, the exemplary color bit pattern is 1002, which translates into the index 410. The value of the index determines the number of the sub-column of the column “Octree Indexing” of Table 1, intersection of which with the row of table 1 corresponding to depth 0 indicates the cell to fill in with the value of the exemplary color usage, i.e. 21%.







TABLE 1







Octree indexing











Color

Octree Indexing



















Depth
R
G
B
Index
0
1
2
3
4
5
6
7





0
1
0
0
4




21%





1
0
0
1
1

21%


2
0
0
0
0


3
0
1
1
3



21%


4
0
1
0
2


21%


5
1
0
1
5





21%


6
0
1
1
3



21%


7
0
0
1
1

21%









From a quick overview we see that the branch 4 of the first node holds 21% of all colours in the image.

When all values of the colour usage vector are used to populate the octree graph, the number of colours Ms selected for inclusion in the sub-set of the most beneficial colours is determined in block 220. Ms is chosen according to the following rules:

    Rule 1: If N(N+1)≦2Nmax, then Ms=N.
    Rule 2: If N(N+1)>2Nmax, then Ms=M, where M is the smallest number M<N for which M(M−1)≧2(Nmax−N).


If Rule 2 is applicable, Ms can be easily found in closed form, if desired. Indeed, the following theorem holds true:
Theorem
Let N and Nmax be natural numbers such that N<Nmax and N(N+1)>2Nmax. Let [x] be the integer part of x, and E(x)=[x] if x is a natural number, otherwise E(x)=[x]+1.
The smallest natural number M=m<N for which m(M−1)≧2(Nmax−N) can be determined as




  M
  =
  
    E
    ⁡
    
      (
      
        
          1
          2
        
        +
        
          
            1
            2
          
          ⁢
          
            
              1
              +
              
                8
                ⁢
                
                  (
                  
                    
                      N
                      max
                    
                    -
                    N
                  
                  )
                
              
            
          
        
      
      )
    
  




Proof.

Inequality m(m−1)≧2(Nmax−N) becomes m2−m−2(Nmax−N)≧0 after simple algebra. Solving M2−M−2(Nmax−N)=0 for M, we arrive at two roots




  
    M
    
      1
      ,
      2
    
  
  =
  
    
      1
      2
    
    ±
    
      
        1
        2
      
      ⁢
      
        
          1
          +
          
            8
            ⁢
            
              (
              
                
                  N
                  max
                
                -
                N
              
              )
            
          
        
      
    
  




The inequality m2−m−2(Nmax−N)≧0 can be satisfied only by values of M bigger then the positive root




  
    m
    1
  
  =
  
    
      1
      2
    
    +
    
      
        1
        2
      
      ⁢
      
        
          1
          +
          
            8
            ⁢
            
              (
              
                
                  N
                  max
                
                -
                N
              
              )
            
          
        
      
    
  




M=E(m1), since M must be a natural number.

Hence,




  M
  =
  
    
      E
      ⁡
      
        (
        
          
            1
            2
          
          +
          
            
              1
              2
            
            ⁢
            
              
                1
                +
                
                  8
                  ⁢
                  
                    (
                    
                      
                        N
                        max
                      
                      -
                      N
                    
                    )
                  
                
              
            
          
        
        )
      
    
    .
  




Let us consider two examples illustrating calculation of Ms in case of Nmax=16.
EXAMPLE 1
Let the number of colours used in the original colour map be N=4.
In this case, (1⁄2)N(N+1)=(1⁄2)4(4+1)=10.
Since 10<16, rule 1 is applicable, resulting in Ms=N or Ms=4.
Thus, four colours must be selected for inclusion into the sub-set.
EXAMPLE 2
Let the number of colours used in the original colour map be N=9.
In this case, (1⁄2)N(N+1)=(1⁄2)9(9−1)=36.
Since 36>16, rule 2 is applicable. According to the Theorem above, we will get



  
    
      M
      =
      
        E
        ⁡
        
          (
          
            
              1
              2
            
            +
            
              
                1
                2
              
              ⁢
              
                
                  1
                  +
                  
                    8
                    ⁢
                    
                      (
                      
                        16
                        -
                        9
                      
                      )
                    
                  
                
              
            
          
          )
        
      
    
    ,
    
      

    
    ⁢
    or
  




  
    
      M
      =
      
        E
        ⁡
        
          (
          
            
              1
              2
            
            +
            
              
                1
                2
              
              ⁢
              
                57
              
            
          
          )
        
      
    
    ,
  



which yields M=E(4.27)=5, resulting in Ms=5.

Thus, five colours must be selected for inclusion into the sub-set.
When the number of the colours Ms in the sub-set is determined, the octree graph is parsed from node to node to select the most beneficial colours. For example, if 16 colours are needed, each selected colour is required to be used by at least 6% of all pixels. The octree graph is parsed until we find nodes which meet the requirement. If a node isn't a leaf (full colour), then the resulting colour is calculated by averaging each of the node's child entries by their corresponding proportion.
The selected colours form the sub-set of colours of the original colour map, which are considered to be the most beneficial for performing the transformation of the original colour map.
Since the transformation of the sub-set is performed in block 222 via interpolating selected colours by averaging colours in each pair of neighbouring colours in the sub-set of colours, the resulting




  
    1
    2
  
  ⁢
  
    
      M
      s
    
    ⁡
    
      (
      
        
          M
          s
        
        -
        1
      
      )
    
  




new colours are added to the already present N colours. Red, green, and blue components of each pair are averaged independently of each other. Thus, the total number of colours after the interpolation is determined to be





  
    M
    t
  
  =
  
    N
    +
    
      
        1
        2
      
      ⁢
      
        
          
            M
            s
          
          ⁡
          
            (
            
              
                M
                s
              
              -
              1
            
            )
          
        
        .
      
    
  




The total number of colours after the interpolation Mt may exceed the Nmin number of colours. If that is the case (exit “true” from block 224), the colours after the interpolation are checked for duplicate colours, which are subsequently removed in block 226 to ensure that the remaining colours are unique. The scaled colour map 106 is defined in block 228 as the colours generated in block 226. If the total number of colours after the interpolation Mt in block 222 is smaller than Nmin (exit “false” from block 224), then the scaled colour map 106 includes all colours generated in block 222. The transformation of the original colour map stops in block 232.
FIG. 3 shows a diagram 30 expanding the operation of the block 108 (Colour Mapped Image Scaling) of FIG. 1 in more detail.
It is known that image encoding formats like Graphic Interchange Format (GIF) support region optimization, and most encoded GIF animations are region optimized. We intend to take advantage of the readily available region optimization to reduce the number of pixels processed during scaling of the original image. For this purpose, upon start (block 300), the size of the displayable area of the mobile device is compared with the size of the original image to determine the required scale ratio. This scale ratio is applied to the optimized region parameters to determine the selection of pixels for the scaled image (block 302). Further processing is required to determine which colours from the scaled colour map 106, generated in advance in the step 104 of FIG. 1, should be assigned to each pixel in the selection.
For each pixel (block 304) selected in block 302 (exit “do” from block 304), steps outlined in blocks 308 to 320 are performed, unless all selected pixels are processed (exit “done” from block 304). For each pixel, a set of contributing pixels in the original image is determined (block 308) based on the original pixel map (block 110). The colour of each pixel depends upon colours of the contributing pixels, and is determined either by interpolating Red, Green, Blue (RGB) values of the contributing pixels (exit “true” from block 310), or skipping the interpolation entirely (exit “false” from block 310) depending on the analysis of the colours of the contributing pixels performed in block 310.
In the embodiment of the present invention, the bi-linear interpolation is used (block 312), but it is contemplated that there may be other circumstances where other interpolation techniques would be beneficial.
Before proceeding with further details of the procedure 30 describing the operation of the block 108 (Colour Mapped Image Scaling), we'll make a detour to FIGS. 4 and 5 to illustrate the operation of blocks 312 and 310 in more detail.
Let us denote a pixel of the scaled image as P1, and the corresponding contributing pixels of the original image as Q11, Q12, Q21, and Q22, as shown on diagram 40 of FIG. 4. Each of the P1, Q11, Q12, Q21, and Q22 pixels is characterized by its respective RGB values, which are denoted here collectively as f(P1), f(Q11), f(Q12), f(Q21), and f(Q22), respectively. Pixels Q11, Q12, Q21, and Q22, are gathered in step 308 shown on FIG. 3 and form the list of contributing pixels further analyzed in step 310. The analysis is directed towards determining whether or not f(Q11), f(Q12), f(Q21), and f(Q22) satisfy the following condition:

f(Q11)=f(Q12)=f(Q21)=f(Q22)  (1)

If condition (1) applies, then the interpolation simplifies into the following:

f(P1)=f(Q11)

which means that the common colour of the contributing pixels Q11, Q12, Q21, and Q22, is assigned to the pixel P1 in the selection.

Let us prove this statement.
Indeed, in its most general form, bi-linear interpolation is performed according to the following expression:




  
    
      
        
          f
          ⁡
          
            (
            
              P
              1
            
            )
          
        
        =
        
          
            
              f
              ⁡
              
                (
                
                  Q
                  11
                
                )
              
            
            ·
            
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    x
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    y
                  
                  )
                
              
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
            
          
          +
          
            
              f
              ⁡
              
                (
                
                  Q
                  21
                
                )
              
            
            ·
            
              
                
                  (
                  
                    x
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    y
                  
                  )
                
              
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
            
          
          +
          
            
              f
              ⁡
              
                (
                
                  Q
                  12
                
                )
              
            
            ·
            
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    x
                  
                  )
                
                ⁢
                
                  (
                  
                    y
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
            
          
          +
          
            
              f
              ⁡
              
                (
                
                  Q
                  22
                
                )
              
            
            ·
            
              
                
                  (
                  
                    x
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    y
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
              
                
                  (
                  
                    
                      x
                      2
                    
                    -
                    
                      x
                      1
                    
                  
                  )
                
                ⁢
                
                  (
                  
                    
                      y
                      2
                    
                    -
                    
                      y
                      1
                    
                  
                  )
                
              
            
          
        
      
    
    
      
        (
        2
        )
      
    
  




where x, y are the coordinates of P1, and xi, yj are coordinates of Qij (i=1, 2; j=1, 2).

Since f(Q11)=f(Q12)=f(Q21)=f(Q22), we can factor the common multiple f(Q11) out of the brackets




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      f
      ⁡
      
        (
        
          Q
          11
        
        )
      
    
    ·
    
      {
      
        
          
            
              (
              
                
                  x
                  2
                
                -
                x
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                y
              
              )
            
          
          
            
              (
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
              )
            
          
        
        +
        
          
            
              (
              
                x
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                y
              
              )
            
          
          
            
              (
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
              )
            
          
        
        +
        
          
            
              (
              
                
                  x
                  2
                
                -
                x
              
              )
            
            ⁢
            
              (
              
                y
                -
                
                  y
                  1
                
              
              )
            
          
          
            
              (
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
              )
            
          
        
        +
        
          
            
              (
              
                x
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                y
                -
                
                  y
                  1
                
              
              )
            
          
          
            
              (
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
              )
            
            ⁢
            
              (
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
              )
            
          
        
      
      }
    
  




Adding fractions in the curly brackets and simplifying the resulting expression, we will arrive finally to

f(P1)=f(Q11)  (3)

A schematic illustration of the steps of analyzing the list of contributing pixels is shown with the reference to diagram 50 of FIG. 5. Upon start (block 500), it is assumed that condition (1) is satisfied, which results in setting a special “interpolate” indicator to “false” (block 502). The entries in the list of contributing pixels are checked to find the first non-transparent entry, which is saved in block 504 as a reference entry for other conditions. The entries in the list of the contributing pixels are also checked in block 506 to find the last entry. If the last entry has been found (exit “done from block 506), processing of the list of contributing pixels is stopped in block 516. Otherwise (exit “do” from block 506), the processing of the list proceeds to block 510. If colour is the contributing pixel is transparent (exit “True” from block 510), the entry contribution is removed from the list in block 508, since the transparent colour is handled separately. Otherwise (exit “False” from block 510), the current entry is compared in block 512 with the reference entry saved in block 504. If both entries are the same (exit “True” from block 512), the steps 506 to 512 are repeated. Otherwise (exit “False” from block 512), the “interpolate” indicator is set to “true” in block 514, and the analysis of the remaining entries is stopped (block 516), since condition (1) is clearly not satisfied.
Referring back to FIG. 3, we'll continue describing the procedure 30 with block 310, resuming the analysis of the colours of the contributing pixels.
In the most favorable case, the list of contributing pixels is exhausted without changing the default value of the “interpolate” indicator, which allows the image processing to skip the interpolation block 312 (exit “false from block 310) and proceed directly to block 320 for setting the colour of the pixel P1 according to the expression (3) shown above.
However, if the default value of the “interpolate” indicator has been changed to “true” (exit “true” from block 310), the step of interpolation 312 is performed. The list of contributing pixels is again analyzed (block 312) to determine whether or not f(Q11), f(Q12), f(Q21), and f(Q22) satisfy one of the following conditions:

f(Q11)=f(Q12) and f(Q21)=f(Q22)  (4)

f(Q11)=f(Q21) and f(Q12)=f(Q22)  (5)

If condition (4) applies, then the interpolation expression (2) simplifies into the




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        
          
            x
            2
          
          -
          x
        
        
          
            x
            2
          
          -
          
            x
            1
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        
          x
          -
          
            x
            1
          
        
        
          
            x
            2
          
          -
          
            x
            1
          
        
      
    
  




Let us prove this statement.
Indeed, substituting f(Q11) instead of f(Q12) and f(Q21) instead of f(Q22) into (2), we will get




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        
          
            (
            
              
                x
                2
              
              -
              x
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              y
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        
          
            (
            
              x
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              y
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        
          
            (
            
              
                x
                2
              
              -
              x
            
            )
          
          ⁢
          
            (
            
              y
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        
          
            (
            
              x
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              y
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
  




After rearranging the order of the second and third terms, we will arrive to




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        (
        
          
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  x
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  y
                
                )
              
            
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  
                    y
                    1
                  
                
                )
              
            
          
          +
          
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  x
                
                )
              
              ⁢
              
                (
                
                  y
                  -
                  
                    y
                    1
                  
                
                )
              
            
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  
                    y
                    1
                  
                
                )
              
            
          
        
        )
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        (
        
          
            
              
                (
                
                  x
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  y
                
                )
              
            
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  
                    y
                    1
                  
                
                )
              
            
          
          +
          
            
              
                (
                
                  x
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  y
                  -
                  
                    y
                    1
                  
                
                )
              
            
            
              
                (
                
                  
                    x
                    2
                  
                  -
                  
                    x
                    1
                  
                
                )
              
              ⁢
              
                (
                
                  
                    y
                    2
                  
                  -
                  
                    y
                    1
                  
                
                )
              
            
          
        
        )
      
    
  




Adding fractions in the brackets and simplifying the resulting expressions, we will get




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        
          
            (
            
              
                x
                2
              
              -
              x
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              y
              +
              y
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        
          
            (
            
              x
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              y
              +
              y
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
  




Canceling “y” yields




  
    f
    ⁡
    
      (
      
        P
        1
      
      )
    
  
  =
  
    
      
        f
        ⁡
        
          (
          
            Q
            11
          
          )
        
      
      ·
      
        
          
            (
            
              
                x
                2
              
              -
              x
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
    +
    
      
        f
        ⁡
        
          (
          
            Q
            21
          
          )
        
      
      ·
      
        
          
            (
            
              x
              -
              
                x
                2
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
        
          
            (
            
              
                x
                2
              
              -
              
                x
                1
              
            
            )
          
          ⁢
          
            (
            
              
                y
                2
              
              -
              
                y
                1
              
            
            )
          
        
      
    
  




and simplifying both fractions, we'll obtain





  
    
      
        
          f
          ⁡
          
            (
            
              P
              1
            
            )
          
        
        =
        
          
            
              f
              ⁡
              
                (
                
                  Q
                  11
                
                )
              
            
            ·
            
              
                
                  x
                  2
                
                -
                x
              
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
            
          
          +
          
            
              f
              ⁡
              
                (
                
                  Q
                  21
                
                )
              
            
            ·
            
              
                x
                -
                
                  x
                  1
                
              
              
                
                  x
                  2
                
                -
                
                  x
                  1
                
              
            
          
        
      
    
    
      
        (
        6
        )
      
    
  




Similarly, if condition (5) applies, then the interpolation expression (2) simplifies into the




  
    
      
        
          f
          ⁡
          
            (
            
              P
              1
            
            )
          
        
        =
        
          
            
              f
              ⁡
              
                (
                
                  Q
                  11
                
                )
              
            
            ·
            
              
                
                  y
                  2
                
                -
                y
              
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
            
          
          +
          
            
              f
              ⁡
              
                (
                
                  Q
                  12
                
                )
              
            
            ·
            
              
                y
                -
                
                  y
                  1
                
              
              
                
                  y
                  2
                
                -
                
                  y
                  1
                
              
            
          
        
      
    
    
      
        (
        7
        )
      
    
  




The proof is similar in all respects to the proof of the previous statement and therefore is not presented here.
The interpolation based on expressions (6) or (7) is much simpler than the interpolation based on general expression (1), it requires less memory and fewer processor cycles to compute, and therefore, when applicable, allows speeding up the process of interpolation considerably. For contributing pixels that do not satisfy either of conditions (4) and (5), interpolation is performed by using the expression (2). However, for GIF images, it is anticipated that the majority of pixels to be interpolated will fall within the category of pixels satisfying the condition (1), and therefore little interpolation needs to occur.
As a result of interpolation performed in block 312, the RGB values of the pixel P1 are determined by using the original colour map 102, and we proceed to determining the colour map index of the resulting colour. Colour mapping is known to be computationally intensive procedure, since it involves computing the euclidean distance between the resulting colour and all colours in the colour map with the goal to find the closest match. In the embodiment of the invention, the number of pixels, for which colour mapping is actually performed, is minimized. It is achieved by comparing, in block 314, the resulting RGB values with those of the previous pixel either from the current frame or from the previous frame, if appropriate. If the RGB values match (exit “false” from block 314), the index of the previous pixel is applied directly to the pixel P1 (block 320) without performing the colour map search. Otherwise (exit “true” from block 314), the colour map search is performed in block 318 to find the closest match by using the scaled colour map 106, and apply the corresponding index to the pixel P1.
As soon as the colour map index of the pixel is determined, it is recorded in block 320 in the colour map of the scaled image. All steps are repeated for the next pixel of the scaled image starting from step 304 until all pixels are processed to form the scaled pixel map (block 322). The procedure 30 terminates in block 324.
A schematic illustration of a system that implements the scaling method of the present invention is shown with the reference to FIG. 6.
FIG. 6 shows a diagram 60 illustrating a system for scaling a colour mapped image of the embodiment of the invention. It comprises a computer having a processor and computer readable medium, such as memory, having computer readable instructions stored thereon for execution by the processor to perform the steps of the method describe above, and to form modules 601-612, including various means for performing certain operations, of the system 60 as will be described in detail below.
The system 60 comprises a Colour Map Transformation Module 601, including a Colour Map Analyzer Module (CMA) 602, a Colour Culling Module 604, and a Colour Map Enhancement Module 606. The Colour Map Enhancement Module 606 comprises means for generating combinations of any two colours from the original colour map; and for each combination, interpolating between said two colours, the means for generating being implemented as a computer readable program code stored in a computer readable medium for execution by a processor.
The Colour Map Analyzer Module 602 determines the number of colours N used in the original colour map, excluding a transparent colour, as described above. The Colour Map Analyzer Module 602 is connected to a Pixel Selection Module 608, the Colour Map Enhancement Module 606, and the Colour Culling Module 604. The Colour Culling Module 604 comprises means for selecting a number of Colours Ms as described above, and means for determining a colour usage vector indicating frequency of use of colours in the original colour map;

    
    
        generating an octree graph based on the colour usage vector;
        parsing the octree graph to select Ms colours to be included in the sub-set.
    
    


Both means are implemented as a computer readable program code stored in a computer readable medium for execution by a processor.
Only one of the connections 607, 609 or 611 at a time is activated depending on the value of N. If the Colour Map Analyzer Module 602 determines that the number of colours is sufficiently large, i.e. N>Nmax, then the original image colour map is inputted directly to the Pixel Selection Module 608. Otherwise, i.e. when N<Nmax, the number of available colours is insufficient for maintaining an acceptable quality of the scaled image, and the original image colour map is inputted to the Colour Map Enhancement Module 606 either directly (if N<Nmin) or through the Colour Culling Module 604 (if N>Nmin) for the transformation of the original colour map. The purpose of the Colour Culling Module 604 is to reduce the number of colours available in the original colour map by trimming out colours that have little influence on the quality of the scaled image, but may considerably slow down the transformation to be performed by the Colour Map Enhancement Module 606. The reduction of colours is performed according to the steps 212, 110, 216, 218 and 220 of FIG. 2. As a result, the Colour Culling Module 604 provides the Colour Map Enhancement Module 606 with the set of colours that is most beneficial for performing the transformation.
The transformation is performed by interpolating the set of colours according to steps 222, 224, and 226 of FIG. 2. The resulting enhanced colour map is considered to be a reasonably good approximation of the ideal colour map for the scaled image.
Pixel Selection Module 608 determines the selection of pixels of the original image that will be included in the scaled image according to the step 302 of FIG. 3 of the method described above.
Colour Interpolation Module 610 allows to determine RGB values of pixels in the selection, based on collecting and analyzing pixels of the original image contributing to each pixel in the selection, according to the steps of analyzing the list of contributing pixels as described with the reference to FIG. 5.
Colour Map Index Generation Module 612 takes, as its input, RGB values produced by the Colour interpolation Module 610 and colours available in the scaled colour map 106, compares them, picks the closest match and applies its index to the corresponding pixel.
Thus, an improved method and system for scaling a colour mapped image have been provided.
While the embodiments of the invention have been illustrated with reference to Graphical Interchange Format (GIF) images, its principles are also applicable to the scaling of digital images encoded with other formats, for example PNG (Portable Network Graphics), BMP (Bitmap), or other formats using colour maps. The system of the embodiments of the invention includes a general purpose or specialized computer having a CPU and a computer readable medium, e.g., memory, DVD, CD-ROM, storing computer readable instructions for executing the methods of the embodiments of the invention described above and forming various modules of the system shown in FIG. 6. Alternatively, the system of the embodiment of the invention can be implemented in firmware, or combination of firmware and a specialized computer.
The method for scaling a colour mapped image described above may be applicable to still images, or alternatively, it my be applicable to scaling images in a video stream. In the latter case, it would be beneficial to determine a delta region of the image, which has been changed compared to a previous video frame containing the image, and to perform the steps of the method only on the delta region, i.e., to use the delta region as the original image.
The computer readable medium, storing instructions thereon for performing the steps of the methods of the embodiments of the invention is also provided, comprising a memory, DVD, CD-ROM, floppy or other medium.
Although the invention has been described with respect to a preferred embodiment, it will be understood by those skilled in the art that the foregoing and various other changes, omissions and deviations in the form and detail thereof may be made without departing from the scope of the invention.

## Claims

1. A method for determining a scaled colour map of a scaled image obtained by scaling an original image, implemented by a computing device having a processor, the method comprising:
obtaining an original colour map of the original image; and
transforming the original colour map into the scaled colour map using the original colour map and the original image only, comprising:
provided Nmin<N<Nmax, forming the scaled colour map, comprising:
(iv-1) selecting a sub-set of colours in the original colour map;
(iv-2) increasing a number of colours in the selected sub-set, thus forming a resulting sub-set of colours; and
(iv-3) adding the resulting sub-set with increased number of colours to the original colour map, comprising determining the increased number of colours in the resulting sub-set of colours as






  
    
      1
      2
    
    ⁢
    
      
        M
        s
      
      ⁡
      
        (
        
          
            M
            s
          
          -
          1
        
        )
      
    
  
  ,




wherein N is a number of colours in the original colour map, Nmin and Nmax are respective predetermined minimum and maximum thresholds for respective numbers of colours in the original colour map, and Ms is a number of colours in the selected subset of colours.

2. The method of claim 1, wherein the transforming further comprises:
(ii) provided N>Nmax, reusing all colours in the original colour map in the scaled colour map; and
(iii) provided N<Nmin, increasing the number of colours in the original colour map to produce the scaled colour map.

3. The method of claim 2, comprising selecting one or more of the following:
Nmin−4;
Nmax=16;
N=4;
N=9;
N≦16;
Ms=4;
Ms=5;

wherein Ms is a number of colours in the subset of colours.

4. The method as described in claim 1, wherein the original and scaled images are selected from Graphical Interchange Format (GIF), Portable Network Graphic (PNG), and Bitmap (BMP) images.

5. The method as described in claim 2, wherein the steps (iii) and (iv-2) further comprise:
generating combinations of any two colours from the original colour map; and
for each combination, interpolating between said two colours.

6. The method as described in claim 2, wherein the step (iv-1) further comprises:
determining a colour usage vector indicating frequency of use of colours in the original colour map;
generating an octree graph based on the colour usage vector;
parsing the octree graph to select colours to be included in the sub-set.

7. A method for determining a scaled colour map of a scaled image obtained by scaling an original image, implemented by a computing device having a processor, the method comprising:
obtaining an original colour map of the original image; and
transforming the original colour map into the scaled colour map using the original colour map and the original image only, comprising:
provided Nmin<N<Nmax, forming the scaled colour map, comprising:
(iv-1) selecting a sub-set of colours in the original colour map, comprising determining a number of colours Ms in the selected subset of colours as follows






  
    M
    s
  
  =
  
    E
    ⁡
    
      (
      
        
          1
          2
        
        +
        
          
            1
            2
          
          ⁢
          
            
              1
              +
              
                8
                ⁢
                
                  (
                  
                    
                      N
                      max
                    
                    -
                    N
                  
                  )
                
              
            
          
        
      
      )
    
  




provided N(N+1)>2Nmax, wherein E(x)=[x] provided “x” is a natural number, otherwise E(x)=[x]+1;

(iv-2) increasing a number of colours in the selected sub-set, thus forming a resulting sub-set of colours; and
(iv-3) adding the resulting sub-set with increased number of colours to the original colour map;


wherein N is a number of colours in the original colour map, Nmin and Nmax are respective predetermined minimum and maximum thresholds for respective numbers of colours in the original colour map, and Ms is a number of colours in the selected subset of colours.

8. The method of claim 1, further comprising:
for each pixel in the scaled image, assigning a colour index, comprising finding a colour in the scaled color map, which is the closest match to a colour of said each pixel, and assigning an index of the colour in the scaled colour map having the closest match as the colour index for said each pixel.

9. The method of claim 2, wherein the step (iv-1) further comprises determining a number of colours Ms in the selected sub-set of colours as follows:
Ms=N, provided N(N+1)≦2Nmax; and
Ms=M, where M is the smallest number M<N for which
M(M−1)≧2(Nmax−N), provided N(N+1)>2Nmax.

10. A method for scaling an image in a video stream, implemented by a computing device having a processor, the method comprising:
selecting a video frame comprising an image;
determining a delta region of the image, which has been changed compared to a previous video frame; and
determining the scaled colour map of the scaled image as described in the method of claim 1, wherein the original image is the delta region.

11. A method for scaling the original image, implemented by a computing device having a processor, the method comprising:
scaling the original image into the scaled image; and
determining the scaled colour map of the scaled image as described in the method of claim 1.

12. A system for determining a scaled colour map of a scaled image obtained by scaling an original image, the system comprising:
a processor and a non-transitory computer readable storage medium having computer readable instructions stored thereon for execution by the processor, causing the processor to:
obtain an original colour map of the original image; and
transform the original colour map into the scaled colour map using the original colour map and the original image only, comprising:
provided Nmin<N<Nmax, forming the scaled colour map:
(iv-1) select a sub-set of colours in the original colour map;
(iv-2) increase a number of colours in the selected sub-set, thus forming a resulting sub-set of colours; and
(iv-3) add the resulting sub-set with increased number of colours to the original colour map, comprising determining the increased number of colours in the resulting sub-set of colours as






  
    
      1
      2
    
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        M
        s
      
      ⁡
      
        (
        
          
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  ,




wherein N is a number of colours in the original colour map, Nmin and Nmax are respective predetermined minimum and maximum thresholds for respective numbers of colours in the original colour map, and Ms is a number of colours in the selected subset of colours.

13. The system of claim 12, wherein the computer readable instructions further cause the processor to:
(ii) provided N>Nmax, reuse all colours in the original colour map in the scaled colour map; and
(iii) provided N<Nmin, increase the number of colours in the original colour map to produce the scaled colour map.

14. The system of claim 13, wherein the computer readable instructions further cause the processor to select one or more of the following:
Nmin=4;
Nmax=16;
N=4;
N=9;
N≦16;
Ms=4;
Ms=5;

wherein Ms is a number of colours in the subset of colours.

15. The system of claim 12, wherein the original and scaled images are selected from Graphical Interchange Format (GIF), Portable Network Graphic (PNG), and Bitmap (BMP) images.

16. The system of claim 13, wherein the computer readable instructions further cause the processor to increase the number of colours in the original colour map or in the selected sub-set of colours as follows:
to generate combinations of any two colours from the original colour map; and
for each combination, to interpolate between said two colours.

17. The method as described in claim 13, wherein the computer readable instructions further cause the processor to select the sub-set of colours in the original colour map as follows:
to determine a colour usage vector indicating frequency of use of colours in the original colour map;
to generate an octree graph based on the colour usage vector;
to parse the octree graph to select colours to be included in the sub-set.

18. A system for determining a scaled colour map of a scaled image obtained by scaling an original image, the system comprising:
a processor and a non-transitory computer readable storage medium having computer readable instructions stored thereon for execution by the processor, causing the processor to:
obtain an original colour map of the original image; and
transform the original colour map into the scaled colour map using the original colour map and the original image only, comprising:
provided Nmin<N<Nmax, form the scaled colour map, comprising causing the computer readable instructions to select a sub-set of colours in the original colour map and to determine a number of colours Ms in the selected subset of colours as





  
    M
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              +
              
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                ⁢
                
                  (
                  
                    
                      N
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provided N(N+1)>2Nmax, wherein E(x)=[x] provided “x” is a natural number, otherwise E(x)=[x]+1;
increasing a number of colours in the selected sub-set, thus forming a resulting sub-set of colours; and
adding the resulting sub-set with increased number of colours to the original colour map.

19. The system of claim 13, wherein the computer readable instructions further cause the processor to determine a number of colours Ms in the selected sub-set of colours as follows:
Ms=N, provided N(N+1)≦2Nmax; and
Ms=M, where M is the smallest number M<N for which
M(M−1)≧2(Nmax−N), provided N(N+1)>2Nmax.