Abstract:
An apparatus for scaling an image composed of pixels by a scale factor is described. The apparatus includes a local image analyzer for identifying from among said pixels a target pixel and a set of pixels proximate to said target pixel and determining a type for the target pixel. The apparatus includes a linear interpolation function that is parameterized by a horizontal linear interpolation coefficient and a vertical linear interpolation coefficient. The apparatus includes an interpolation coefficient generator for defining the horizontal and vertical linear interpolation coefficients. The apparatus includes an image scaler for scaling said image in a neighborhood of the target pixel by the scale factor using the linear interpolation function with the horizontal linear interpolation coefficient and the vertical linear interpolation coefficient. A method of scaling a source image. The source image comprised of a first plurality of pixels, by a scale factor said method for scaling comprising the acts of: determining a first type of a target pixel, said target pixel in said plurality of pixels; selecting a first interpolation function for said target pixel from said first type of said target pixel; and scaling said source image using said first interpolation function for scaling said target pixel.

Description:
BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     This invention relates to the field of digital image interpolation and more specifically relates to improved methods of detecting the type of image being interpolated on a pixel by pixel basis to better select interpolation functions. 
     2. Description of the Related Art 
     Images are typically provided at a single size and need to be scaled either up or down for a variety of uses. Image scaling is done in diverse fields such as video production and editing, multimedia content creation, desktop publishing, photography, and photocopying. It is important that the scaled image be a faithful interpretation of the original image. It can not be an exact duplicate because in the process of scaling an image up, interpolating, additional information must be generated, or filled in, to create the enlarged image. Similarly, when scaling an image down, decimating, it is necessary to eliminate some information to create the reduced image. 
     Interpolation functions are functions that can be used to generate the interpolated, or decimated, images. However, these interpolation functions tend to cause either blurring or aliasing of a digital image that is being interpolated. Aliasing is the creation of jagged edges. In images that are composed primarily of text, computer line graphics and other images with hard edges, it is important to select an interpolation function that preserves the edges and avoids blurring the image. Similarly, in images that are composed primarily of graphics, natural images, scanner input, and other images which lack hard edges, it is important to select an interpolation function that will avoid creating jagged edges and instead tends to blur the image slightly. 
     Mr. Muyramatsu teaches, in U.S. Pat. No. 5,553,201, that it may be desirable to use a less computationally expensive interpolation function for images being interpolated by a small :scale factors and a more computationally expensive interpolation function for images being interpolated by a large scale factors. A drawback of this approach is that it is not responsive to image type but rather to the amount of scaling being done. 
     Mr. Tanioka teaches in U.S. Pat. No. 5,018,024, that it may be desirable to compute the number of color transitions in a square block of pixels to select a dithering process for an image. A drawback of this approach is that it is computationally intensive and not capable of responding to localized changes in image type. 
     Accordingly, what is needed is a method for identifying pixel types for interpolation that is computationally simple and that can be used to select the most appropriate interpolation functions for an image on a pixel by pixel basis. 
     SUMMARY OF THE INVENTION 
     A method of scaling a source image is described. The source image has a plurality of pixels and the source image is being scaled by a scale factor. One of the pixels in the source image is selected as a target pixel. A type is determined for that target pixel. Based on the type of the target pixel, an interpolation function is selected and the source image is scaled using the selected interpolation function to scale the target pixel. 
     Determining the type of the target pixel includes examining a neighborhood of pixels surrounding the target pixel and determining whether the target pixel is similar to that neighborhood. If the target pixel is similar to the neighborhood of pixels, the pixel is categorized as an artificial type image. If the pixel is dissimilar to the neighborhood of pixels it is categorized as a natural image type. 
     An apparatus for scaling an image composed of pixels by a scale factor is described. The apparatus includes a local image analyzer for identifying from among said pixels a target pixel and a set of pixels proximate to said target pixel and determining a type for the target pixel. The apparatus includes a linear interpolation function that is parameterized by a horizontal linear interpolation coefficient and a vertical linear interpolation coefficient. The apparatus includes an interpolation coefficient generator for defining the horizontal and vertical linear interpolation coefficients. The apparatus includes an image scaler for scaling said image in a neighborhood of the target pixel by the scale factor using the linear interpolation function with the horizontal linear interpolation coefficient and the vertical linear interpolation coefficient. 
    
    
     BRIEF DESCRIPTION OF THE FIGURES 
     FIG. 1 illustrates an image being interpolated by the present invention. 
     FIG. 2 is a hardware block diagram of an image scaler that dynamically selects scaling functions based on pixel type. 
     FIG. 3 is a logic diagram of a pixel type determiner. 
     FIG. 4 illustrates a source image similar to that shown in FIG.  1 . 
     FIGS. 5A-E show different stages of processing a row of data in the logic circuit of FIG.  3 . 
     FIG. 6 is a process flow diagram illustrating a method of selecting interpolation functions based on image type on a pixel by pixel basis. 
     FIG. 7 is a logic diagram of a color pixel comparator. 
     FIG. 8 is a logic diagram of an optimized pixel type determiner. 
    
    
     DETAILED DESCRIPTION 
     A. Overview 
     A first type of image is an artificial image. Examples of artificial images include computer text and computer generated graphics. Because this type of image is computer created, for any pixel in an artificial image, there are generally neighboring pixels with the same pixel value or color. A second type of image is a natural image. Examples of natural images include scanned images and images captured using a digital camera. Natural images have atmospheric and electronic noise; therefore, for any pixel in a natural image, it is hard to find neighboring pixels with the same pixel value, or color. In order to produce the best results, the interpolation function should be selected based on the type of image being interpolated. 
     Because a single image can consist of both artificial and natural images interspersed together, the present invention teaches a method and apparatus for determining pixel type on a pixel by pixel basis. Different interpolation functions can then be applied to scale each pixel of the image based on the pixel type. 
     Furthermore, it is desirable for the interpolation function to be adjusted based on the scaling factor. This is especially true when artificial images are being interpolated. This is to find a balance between two factors: intensity variation and instantaneous contrast. Take for example an image composed of equal width vertical stripes. If the image is being interpolated by a non-integer scale factor, each stripe can not have equal width in the resulting image. Either the intensity variation or the contrast will be sacrificed depending on the interpolation function. If nearest neighbor interpolation is used, contrast will be preserved, but intensity variation will be high. However, smoother interpolation functions will have less intensity variation as well as less contrast. Depending on the scaling factor, the resulting image will be more or less aesthetically tolerable. For small scaling factors, the lower contrast is typically acceptable, for larger scaling factors, higher contrast is more desirable. 
     Consequently, it is helpful to design an adjustable interpolation function for artificial images that can vary with the scaling factors. Equation 1 is a formula for the value of the resulting pixel q(m+Δ m ,n+Δ n ) derived by linear interpolation of a source pixel p(m,n) with a linear interpolation coefficient of a i  in the horizontal direction and b j  in the vertical direction.                  q        (       m   +     Δ   m       ,     n   +     Δ   n         )       =         ∑     j   =   0     1            b   j            ∑     i   =   0     1              a   i     ·     p        (       m   +   i     ,     n   +   j       )                       0           ≤     Δ   m         ,       Δ   n     ≤   1             (   1   )                                
     This can be further refined by limiting the linear interpolation coefficients as shown by Equation 2.                  ∑     i   =   0     1          a   i       =         ∑     j   =   0     1          b   j       =   1             (   2   )                                
     Despite these limitations on the interpolation function, adjustments can be made by making the linear interpolation coefficients dependent on Δ m  and Δ n . Considering only the horizontal coefficient, a i  which depends on Δ m , the bilinear interpolation is given by using the linear interpolation coefficients shown by Equation 3.                a   0     =     {               1   -     λ                   Δ   m   2                 for                   Δ   m       ≤   0.5               λ                   Δ   m   2           otherwise              
          a   1       =     1   -     a   0                   (   4   )                                
     A class of parameterized interpolation functions can be generated using these basic formulae and the linear interpolation coefficients shown by Equation 4, in which the type of edge weighting (EW) in this example is determined by the coefficient λ.                      a   0     =     1   -     Δ   m                     a   1     =     1   -     a   0                     (   3   )                                
     The linear interpolation coefficients must both be positive and less than one, accordingly, λ will range from 0 to 2. Two members of this class are EW1, λ=1, and EW2, λ=2. 
     The performance of the λ-parameterized interpolation functions in terms of intensity variation and instantaneous contrast can then be considered. The intensity variation, V, for a scale factor s, can be approximated by the polynomial shown in Equation 5.                    V   ^     λ          (   s   )       =       1   s          (       0.054                   λ   2       -     0.23                 λ     +   0.25     )               (   5   )                                
     The imaging system designer will select an acceptable level of variation and the interpolation function can be selected from the class of interpolation functions by computing λ from the scale factor and the acceptable variation level. 
     The instantaneous contrast C, for a scale factor s, can be approximated by Equation 6.                    C   ^     λ          (   s   )       =     1   -     0.5                   λ     -     2.1   s                     (   6   )                                
     The imaging system designer will select an acceptable level of instantaneous contrast and the interpolation function can be selected from the class of interpolation functions by computing λ from the scale factor and the acceptable contrast level. 
     Typically, the variation level is more important for image appearance than the instantaneous contrast when the scaling factor is less than a certain value, for example 2.0. For larger scaling factors, the instantaneous contrast is more important than intensity variation. Therefore, the system designer has a range of choices based on the scaling factor and the desired level of variation and instantaneous contrast. The functions EW1 and EW2 are two examples from this class that might be used in a system. However, more generally, the functions might be used in their general parameterized form. 
     B. An Interpolated Image 
     FIG. 1 illustrates an image being interpolated by the present invention. The invention allows the artificial and natural image portions of the image to be discriminated so that different interpolation functions can be used to scale the different portions appropriately. 
     FIG. 1 illustrates an image being interpolated by the present invention comprising an input  100 , an input row  100 , a letter G  112 A, grayscale photograph  114 A, a scaled letter G  112 B, a scaled grayscale photograph  114 B, an output  150 , and an output row  160 . 
     The input  100  includes the input row  110 . The output  150  includes the output row  160 . The input  100  is comprised of two distinct images, the letter G  112 A and the grayscale photograph  114 A. The output  150  is comprised of two distinct images, the scaled letter G  112 B and the scaled grayscale photograph  114 B. 
     The input  100  is a digital image. Digital images are comprised of pixels. The pixels of the digital image are arranged in a matrix with columns and rows. The location of a pixel p can be designated by its column and row: p(m,n). The pixel p(m,n) is in column m and row n. 
     The input row  110  is a row of pixels in the input  100 . Many computer graphics algorithms operate in row order because memory devices are typically designed to be read and written in row order. In one embodiment, the invention works on rows of pixels. In another embodiment, the invention works on both rows and columns of pixels. In this example, the row based operation of the invention will be considered. The designation p(m) can be used to designate the m th  pixel in the current row. 
     The output  150  is a digital image. The output  150  will contain more or fewer pixels then the input  100  depending on the scale factor. In this example, the scale factor is 2.0 in the horizontal direction and 1.0 in the vertical direction. That means that the output  150  has twice as many pixels in the horizontal direction as the input  100  and an equal number of pixels in the vertical direction as the input  100 . If the scale factor had been 0.5 in the horizontal direction, the output  150  would have had half as many pixels in the horizontal direction as the input  100 . 
     The output row  160  is the row of pixels in the output  150  that corresponds to the input row  110  after it has been scaled by the scale factor. Because the scale factor was 2.0 in the horizontal direction, the output row  160  has twice as many pixels as the input row  110 . The pixels that were added to the output row  160  have been interpolated based on the contents of the input row  110 . Table 1 demonstrates that the output row  160  is composed of two types of pixels, those from the input row  110  and those that have been interpolated in. 
     
       
         
               
             
           
               
                 TABLE 1 
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
     The pixels that were part of the input row  110  are solid circles in Table 1 and the pixels that needed to be interpolated in to scale the image are shown as hollow circles in Table 1. 
     Different interpolation functions take different approaches to compute pixel values for the added pixels, the hollow circles, in the output row  160 . Better interpolation functions will produce results that will fill in pixel values for the output row  160  so that that the output  150  is of a higher quality. 
     In the case of decimation, scale factors less than 1.0, pixels must be removed. The output row  160  would be comprised of fewer pixels than the input row  110  and thus all of the pixel values must be computed. 
     The input  100  contains two different image types, the left hand side of the image is the letter G  112 A and the right hand side of the image is the grayscale photograph  114 A. The letter G  112 A is an artificial image while the grayscale photograph  114 A is a natural image. When scaling the letter G  112 A, the sharp pixel value discontinuity between the black pixels that comprise the letter G  112 A and the surrounding white background should be preserved. If the edge of the letter G  112 A is allowed to blur, it will be hard to discriminate its shape. The grayscale photograph  114 A, in contrast, has continuous pixel values and when scaling it, the creation of sharp discontinuous edges, or aliasing the photograph, should be avoided. If aliasing occurs, the false edges introduced into the grayscale photograph  114 A by: the interpolation process will make it uncomfortable to view the image. 
     The input  100  has the artificial image and natural image portions separated by a large number of pixels, however it is possible for the two type of images to overlap or be positioned very closely in the input  100 . Therefore it is desirable to adopt an image type determination scheme that works in a highly localized fashion. 
     C. Image Scaler with Pixel Type Determiner 
     FIG. 2 is a hardware block diagram of an image scaler that dynamically selects scaling functions based on pixel type. 
     FIG. 2 includes a pixel type determiner  210 , a scaler  250 , and a memory  270 . The pixel type determiner  210  outputs the pixel type of a pixel to the scaler  250  so that an appropriate interpolation function from the memory  270  can be chosen to scale the pixel. 
     The pixel type determiner  210  receives as inputs the input row  200 . The input row  200  is a collection of pixel values. The input row  200  could be the input row  110  or any other row of pixels. The pixel values can be stored as single bytes, with each byte representing the grayscale intensity of the pixel from 0 to 255. In other embodiments, the pixel values might be several bytes comprising all of the color values for the pixel. The pixel type determiner  210  examines the input row  200  and determines a pixel type for the pixels in the input row  200 . The pixel type determiner  210  outputs the pixel types  220 . The pixel types  220  is a row of values corresponding to the pixels in the input row  200 . Each value in the pixel types  220  row indicates either artificial or natural. In one embodiment, a 1 is used to represent artificial image pixels and a 0 to represent natural image pixels. The type of a pixel p(m,n) may be designated e(m,n). Since n is fixed in the input row  200 , the pixel types  220  is a row of e(m) values for the pixels p(m) in row n. 
     The scaler  250  receives as inputs the input row  200 , the pixel types  220 , the scale factor  230 , and the force mode  240 . The scale factor  230  is a positive real number representing the degree to which the input row should be scaled horizontally. When the scale factor  230  is less than one, the input row  200  is decimated. When the scale factor  230  is greater than or equal to one, the input row  200  is interpolated. It is possible to scale the image both horizontally and vertically using this technique, but the scaler  250  only accomplishes horizontal scaling. The force mode  240  input allows the user to override the pixel type determiner  210  by indicating whether the image is artificial or natural. The force mode  240  could either be a single value that overrides the pixel type determiner  210  for a whole row, or it could be provided on a pixel by pixel basis. In this example, the force mode  240  is provided on an image by image basis and can have three values: ignore, force natural, and force artificial. For the remainder of this example, it will be assumed that the force mode  240  is set to ignore. 
     Because only a horizontal scale factor is being considered, each input row will produce only a single output row. More generally, the scaler  250  might need to access the entire image to properly interpolate, or decimate, it in both the horizontal and vertical directions. Similarly, more generally, the output from the scaler  250  might be an output image rather than the output row  260 . 
     The scaler  250  produces the output row  260 . In producing the output row  260 , the scaler  250  uses the pixel types  220  for each pixel to select a scaling function from the memory  270  to apply to that pixel of the input row  200 . Because the pixel type determiner  210  has determined the pixel types  220 , the selected interpolation function is appropriate for the image type, either artificial or natural images, of each pixel in the input row  200 . 
     The memory  270  might contain any number of interpolation functions. Each interpolation function stored in the memory should be tagged to indicate if it is more suitable for artificial or natural images. The interpolation functions stored in the memory might be parameterized interpolation functions such as the linear interpolation of Equation 1 using the parameterization of the linear coefficients by λ as shown by Equation 4. The scaler  250  can then select any interpolation function from memory that is tagged as being appropriate for the current pixel&#39;s type. In this example, there are two functions for scaling artificial images, the scale artificial function  274  and the scale artificial function  276 . Thus if the pixel type of the current pixel is an artificial image pixel, either scale artificial function  274  or scale artificial function  276  can be used. 
     In this example, the scaler  250  examines the pixel types  220  to determine the pixel type for each pixel of the input row  200 . For example, the input row  200  might have a pixel p(a) with a pixel type e(a)=1, or artificial image pixel, while another pixel in the input row  200 , p(b), might have a pixel type e(b)=0, or natural image. When the scaler  250  is interpolating the pixel p(m) by the scale factor  230 , it uses the value of e(m) to select a scaling function. In this example, e(b) is 0, or natural image, so the scale natural function  272  can be used to interpolate pixel p(b). Similarly, e(a) is 1, or artificial image, so the scale artificial function  274  or the scale artificial function  276  can be used to interpolate pixel p(a). 
     It is possible for each interpolation function to have additional information stored with it to further refine the selection process. For example, scale artificial function  274  might indicate that it is only for scale factors less than a certain amount. In this example, the scale natural function  272  is the bilinear interpolation; the scale artificial function  274  is the EW1 interpolation; and the scale artificial function  276  is the EW2 interpolation. The EW1 interpolation works best for certain scale factors while the EW2 algorithm works best for others. Therefore, the scaler  250  can select the scale artificial function  274 , a smoother interpolation function EW2, when the scale factor is less than a threshold scaling factor. A typical threshold scaling factor would be in the range of 2.0 to 4.0. The scale artificial function  276 , a sharper interpolation function EW1, for scale factors larger than the threshold. 
     D. Pixel Type Determiner Detail 
     FIG. 3 is a logic diagram of a pixel type determiner. This could be used as the pixel type determiner  210  in FIG.  2 . 
     FIG. 3 includes unique logic blocks  320 A-C and verify uniqueness logic block  360 . The unique logic blocks  320 A-C analyze whether a pixel is distinct, or unique, from its neighbors. The verify uniqueness logic block  360  refines the initial determination of uniqueness based on information gathered as to whether the surrounding pixels are also unique. 
     The unique logic block  320 A accepts as inputs a first pixel  302 , a second pixel  304 , a target pixel  306 , a third pixel  308 , and a fourth pixel  310 . The output of the unique logic block  320 A is a 1 if the target pixel  306  is the same as any of its neighboring pixels, the first pixel  302 , the second pixel  304 , the third pixel  308 , and the fourth pixel  310 , and a 0 when the target pixel  306  is unique. The output of the unique logic block  320 A is the preliminary pixel type determination  344 , or d(m). 
     The input pixels to the unique logic block  320 A are a portion of a row of pixels such as the input row  110  (see FIG.  1 ). The inputs surround the target pixel  306  in the input row  110 . The correspondence between the inputs and the positions of the pixels in the row is best seen in Table 2. 
     
       
         
               
             
           
               
                 TABLE 2 
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
     The pixels to the right of p(m), the target pixel  306 , have yet to be processed to determine their pixel types and the pixels to the left of p(m) have already had their pixel types determined. Thus, the pixel type determination is proceeding from the left edge of the image in a single row across to the right edge of the image. 
     The first pixel  302 , the second pixel  304 , the third pixel  308 , and the fourth pixel  310  are coupled to the comparators  322 - 328  respectively. The target pixel is coupled to the comparators  322 - 328 . The comparators  322 - 328  output a 1 when the two pixels are identical and a 0 otherwise. The outputs of the comparators  322 - 328  are coupled to an OR gate  330 . The output of the OR gate  330  is the preliminary target determination  344  and is a 1 if at least one of the comparators  322 - 328  outputs a 1 and a 0 otherwise. 
     The unique logic blocks  320 B-C can be comprised in the same fashion as the unique logic block  320 A. Alternatively, delay circuits can be used to store the results of d(m−1) and d(m) until d(m+1) is computed. The unique logic block  320 B produces the first determination  342 , or d(m−1). The unique logic block  320 C produces the second determination  346 , or d(m+1). The correspondence between the preliminary pixel type determinations and the positions of pixels in the row is shown by Table 3. 
     
       
         
               
             
           
               
                 TABLE 3 
               
               
                   
               
             
             
               
                 
                   
                             
                     
                         
                         
                     
                   
                 
               
               
                   
               
             
          
         
       
     
     Once the outputs of unique logic blocks  320 A-C are computed, the verify uniqueness logic block  360  can determine the type of the target pixel  306 . 
     The verify uniqueness logic block  360  accepts as inputs the target determination  344  for the target pixel  306 , the first determination  342 , and the second determination  346 . The verify uniqueness logic block  360  identifies the pixel type of the target pixel  306 . Equation 7 is a mathematical formula for computing the target pixel type  382  from the inputs.                  e   H          (   m   )       =     {           d        (     m   -   1     )                 if                   d        (     m   -   1     )         ⊕     d        (     m   +   1     )         =   0               d        (   m   )           otherwise                   (   7   )                                
     This can be computed by coupling the target determination  344  and the first determination  342  to an OR gate  362  and to an AND gate  364 . The second determination  346  and the output of the OR gate  362  are coupled to an AND gate  366 . The outputs of the AND gates  364 - 366  are coupled to an OR gate  368 . The output of the OR gate  368  is the target pixel type  382 . The target pixel type  382  is 1 when the target pixel  306  is an artificial image pixel and a 0 for a natural image pixel. 
     In another embodiment, d(m+1), or the first determination  342 , is used as the target pixel type  382 , e H (m), when the exclusive-or of the second determination  346  and the first determination  342  is 0. 
     E. Detailed Example 
     FIG. 4 illustrates a source image similar to that shown in FIG.  1 . FIGS. 5A-E show different stages of processing a row of data from the source image in FIG. 4 using the logic circuits of FIG.  3 . 
     FIG. 4 contains a source image  400 , a detail row  402 , an artificial image target pixel  410 , a natural image target pixel  412 , and a third target pixel  414 . 
     The source image  400  is a digital image and is comprised of pixels arranged in a matrix of columns and rows. The detail row  402  is a row of pixels in the source image  400 . The artificial image target pixel  410  is a pixel in the detail row  402  that is at the left edge of the letter ‘G’ in the detail row  402 . The natural image target pixel  412  is in the grayscale photograph of the woman in the detail row  402 . The third target pixel  414  is the single black pixel of the single-pixel wide line in the source image  400  where the single-pixel wide line crosses the detail row  402 . In this example, each pixel has a grayscale intensity value from 0, black, to 7, white. 
     FIG. 5A shows a detailed view of the inputs to the pixel type determiner  210  as implemented by FIG.  3 . The inputs, p(m−2) to p(m+2), to the unique logic block  320 A are shown for three different target pixels surrounded by parenthesis, ‘( )’. Additional pixel values needed to fully compute the pixel type are surrounded by braces, ‘{ }’. The target pixel type  382 , e H (m), depends on the three pixels to the left and the three pixels to the right of the target pixel. The detailed view  502  shows the pixel value inputs for artificial image target pixel  410 . The detailed view  504  shows the pixel value inputs for the natural image target pixel  412 . The detailed view  506  shows the pixel value inputs for the third target pixel  414 . 
     As the detail row  402  is processed, the inputs shown in FIG. 5A are provided to FIG.  5 B. FIG. 5B includes the unique logic block  320 A. The entire row is processed by the unique logic block  320 A (see FIG. 3) to compute the preliminary pixel type determinations for the detail row  402  as shown in FIG.  5 C. 
     FIG. 5C shows a detailed view of the preliminary pixel types, d(m), for the pixels of the detail row  402 . The detailed view  508  shows the preliminary determination for the artificial image target pixel  410  and the preliminary determinations for the nearest neighbors. The detailed view  510  shows the preliminary determination for the natural image target pixel  412  and the preliminary determinations for the nearest neighbors. The detailed view  512  shows the preliminary determination for the third target pixel  414  and the preliminary determinations for the nearest neighbors. 
     The preliminary determinations from FIG. 5C are provided to FIG.  5 D. FIG. 5D includes the verify uniqueness logic block  360  (See FIG.  3 ). The result, the target pixel type  382  is shown in FIG.  5 E. 
     In FIG. 5E, the target pixel type  382  is shown for three different target pixels. The detail view  514  shows the pixel type for artificial image target pixel  410 . The detail view  516  shows the pixel type for natural image target pixel  412 . The detail view  518  shows the pixel type for the third target pixel  414 . 
     1. Artificial Image Target Pixel 
     The artificial image target pixel  410  is the last white pixel before the edge of the letter ‘G’ in the detail row  402 . In detail view  502  of FIG. 5A, the surrounding pixel values are shown. The black pixels that make up the ‘G’ are 0&#39;s while the white background pixels are 7&#39;s. 
     At the unique logic block  320 A of FIG. 5B, the comparisons on the target pixel with the four surrounding pixels will result in a 1, or artificial image, as a preliminary determination. 
     In more detail, artificial image target pixel  410  is the target pixel  306 . The two pixels with pixel values of 7 to the left of the text target pixel  410  are the third pixel  308  and the fourth pixel  310 . The two pixels with pixel values of 0 to the right of the text target pixel  410  are the first pixel  302  and the second pixel  304 . 
     In FIG. 5B, the inputs are processed in the preliminary pixel type determination block  320 A. The comparators  322 - 328  compare each of the surrounding pixels with the target pixel  306 . Here, the text target pixel  410  is the target pixel  306  and is compared with the first pixel  302 , resulting in a 0, not equal. The target pixel  306  is compared with the second pixel  304 , resulting in a 0, not equal. The target pixel  306  is compared with the third pixel  308 , resulting in a 1, equal. The target pixel  306  is compared with the fourth pixel  310 , resulting in a 1, equal. These results are OR&#39;ed together resulting in a 1 as the target determination  344  for the artificial image target pixel  410 . This is shown in FIG. 5C which includes the preliminary pixel type determination  344  for the artificial image target pixel  410  in detailed view  508 . 
     Because the preliminary pixel types for the two surrounding pixels are necessary to compute the target pixel type  382  of the text target pixel  410 , they have been computed in the same fashion as shown above by the unique logic block  320 A. 
     The preliminary pixel type determinations shown in detail view  508  are then used to compute the final pixel type for the artificial image target pixel  410 . The preliminary pixel types are provided to FIG. 5D where the verify uniqueness logic block  360  computes the final pixel type. 
     In FIG. 5D, the target determination  344  used by the verify uniqueness logic block  560  is the value computed in FIG.  5 B and shown in FIG.  5 C. The first determination  342  and the second determination  346  are shown in FIG. 5C as well. Here, the first determination  342  of 1 is AND&#39;ed with the target determination  344  of 1 by the AND gate  364  to compute 1. The OR of those two values is also 1 and that is the result of the OR gate  362 . The result of the OR gate  362  is AND&#39;ed with the second determination  346  of 1 by the AND gate  366  to compute 1. The result of the AND gate  364  and the result of the AND gate  366  are OR&#39;ed together to produce the target pixel type  382  of 1 by the OR gate  368 . 
     In FIG. 5E, the pixel type of the artificial image target pixel  410  is shown. In detail view  514 , the type of the artificial image target pixel  410  is shown to be 1, or an artificial image pixel. 
     2. Natural Image Target Pixel 
     The processing of the natural image target pixel  412  proceeds much like the previous case. The input pixels of the natural image portion of the detail row surrounding the natural image target pixel  412  have a variety of different values. The detail view  504  shows the different pixel values surrounding the natural image target pixel  412 . 
     The resulting uniqueness determinations are shown in the detail view  510 . The natural image target pixel  412  has a preliminary determination of 0, or natural image pixel. That determination is refined to reveal the pixel type of that the natural image target pixel  412  is 0, or natural image, in detail view  516 . 
     3. Third Target Pixel 
     The processing of the third target pixel  414  proceeds much like the previous cases. Because third target pixel  414  is a singular point of discontinuity from the surrounding pixels, the target determination from unique logic block  320 A is that the third target pixel  414  is a natural image pixel, 0. However, the detail view  512  reveals, the surrounding pixels were typed as artificial image pixels at the preliminary determination stage. 
     If the third target pixel  414  is treated as a natural image pixel, it would produce an interpolated image that allowed the hard edges of the line to blur because it was mistakenly identified as a natural image pixel. The verify uniqueness logic block  360  serves the important purpose of ensuring that a determination that a pixel is unique, d(m)=0, is supported by the determinations of the adjacent pixels. 
     Here, even though the preliminary determination for the third target pixel  414  was 0, the exclusive-or of the surrounding preliminary determinations was 0so instead of using the current preliminary determination, the preliminary determination of the last pixel that was processed which here was a 1, or an artificial image pixel, is used. Thus, the third target pixel is correctly identified as an artificial image pixel and the line is preserved. 
     F. Process Description 
     FIG. 6 is a process flow diagram illustrating a method of selecting interpolation functions based on image type on a pixel by pixel basis. 
     At the start block  600 , a source image is provided along with a scale factor. The source image could be the input  100  (see FIG. 1 or any other digital image. The scale factor is given as a real number that represents the amount of horizontal scaling to be applied. 
     Control is then passed to process block  610  where the image analysis begins in a row by row fashion. Each row can be analyzed pixel by pixel using a pixel type determiner. This can be done by using the logic circuits of FIG.  3 . 
     Control is then passed to process block  620  where the uniqueness of each pixel is determined using the unique logic block  320 A (see FIG.  3 ). Process block  620  outputs a row of bits with the uniqueness determinations. The bit, d(m), is 0 if the pixel, p(m), is unique, e.g. surrounded by two pixels to the left and two pixels to the right that have different pixel values. The bit, d(m), is 1 for the pixel, p(m), otherwise. This process is repeated for all of the rows of the image. Alternatively, Equation 8 can be used to determine uniqueness.                d        (   m   )       =     {         1         if                 min        {              p        (   m   )       -     p        (     m   +   k     )              :     k   ∈     {       -   2     ,     -   1     ,   1   ,   2     }         }               0       otherwise                   (   8   )                                
     Control is then passed to process block  630  where the uniqueness of each pixel is verified using the verify uniqueness logic block  360  (see FIG.  3 ). This process refines the initial judgment that a pixel was unique by looking at the uniqueness determinations for the surrounding pixels in the row. The result is a row bits of pixel type determinations, e H (m), for each pixel, p(m), in the row. The bit, e H (m), is 1 if the pixel, p(m), is an artificial pixel and 0 if the pixel, p(m), is a natural pixel. Alternatively, Equation 7 can be used to compute the values of e H  (m). This process is repeated for all of the rows of the image. 
     Control is then passed to process block  640  where an interpolation function is chosen for each pixel based on the pixel type. There are a number of interpolation functions that can be used to scale images. The interpolation functions can be stored along with a tag indicating whether the function is best for scaling artificial images or natural images. The memory  270  (see FIG. 2) includes three interpolation functions that are tagged to indicate the type of image they work best on. For each pixel, an interpolation function is chosen with a tag that matches the e H  (m) determination. Thus for a pixel p(a) with e H (a)=1, or artificial image pixel, either the scale artificial function  274  or the scale artificial function  276  will be chosen (see FIG.  2 ). Similarly, for a pixel p(b) with e H (b)=0, or natural image pixel, the scale natural function  272  will be chosen (see FIG.  2 ). In some embodiments, the scale factor can be used to select among the different interpolation functions that have matching tags. For example, the scale artificial function  274  could be used for scale factors less than a certain threshold scaling factor, and the scale artificial function  276  could be used for scale factors greater than the threshold scaling factor. 
     Control then passes to process block  650  where the image is interpolated using the selected interpolation functions. The interpolation of the image proceeds by using the interpolation function identified by process block  640  for each pixel of the image. This ensures that the interpolation function being used for a particular pixel is suitable for the pixel type, artificial or natural, and that the undesirable interpolation artifacts of blurring and aliasing will be minimized. For artificial image pixels, blurring will be minimized because the interpolation functions chosen by process block  640  are suitable for artificial images, e.g. edge preserving. Similarly, for natural image pixels, aliasing will be minimized because the selected interpolation functions are suitable for natural images. 
     The process ends at end block  660  with the scaled output image. 
     G. Handling Color Pixels 
     FIG. 7 is a logic diagram of a color pixel comparator. The color pixel comparator could be used as the comparators  322 - 328  of the unique logic block  320 A of FIG.  3 . 
     FIG. 7 comprises the comparator  322 B, a pixel  702  and a pixel  704 , a comparator  712 , a comparator  714 , a comparator  716 , and an AND gate  720 . The comparator  322 B comprises the comparators  712 - 716  and the AND gate  720 . 
     The color components of the pixel  702  and the color components of the pixel  704  are compared against each other by the comparators  712 - 716 . The comparators  712 - 716  output a 1 when the two input color components are the same and 0 otherwise. The results of the comparators  712 - 716  are coupled to the AND gate  720 . The AND gate  720  outputs a 1 if all of the color components are identical and a 0 otherwise. 
     Pixels in computer images are typically comprised of three color components, a red component, a green component and a blue component. The pixel  702  and the pixel  704  each have a red, a green, and a blue color component. Alternatively, these color components can be expressed in other systems such as hue, saturation, and lightness. 
     Here, it is notable that pixel  702  and pixel  704  are different because the color components are not all identical, the green component of pixel  702  is 0 while the green component of pixel  704  is 1. Thus, the output from the comparator  714  will be 0, and the AND gate  720  will output a 0. 
     The comparator  322 B can be use in place of the comparators  322 - 328  in the unique logic block  320 A of FIG. 3 to enable color pixels to have their pixel types determined. 
     H. Optimized Pixel Type Determiner 
     FIG. 8 is a logic diagram of a pixel type determiner. The logic setup is similar to that of the pixel type determiner of FIG. 3; however, the pixel type determiner of FIG. 8 has been optimized to reduce the amount of circuitry required for delay elements and comparators. 
     The pixels flow into the pixel type determiner at the upper left of FIG. 8 one at a time. As an input pixel  830  flows into the logic circuit, the input pixel  830  flows into a delay  800  and a comparator  806 . The input pixel  830  is p(m+2). The delays  800 - 804  are setup so that the pixel p(m−1) is fed as the input to the scaler  250  at the same time that the pixel type determination e(m−1) reaches the scaler  250 . The delay  800  produces the first output pixel  832 , p(m+1). The first output pixel  832  flows into the delay  802 . The delay  802  produces the second output pixel  834 , p(m). The second output pixel  834  flows into the delay  804 . The delay  804  produces the third output pixel  836 , p(m−1), and provides the third output pixel to the scaler  250 . 
     Because the optimized pixel determiner operates like a pipeline, the functionality of the four comparators used in the pixel determiner of FIG. 3 can be replaced by two comparators coupled to delay elements. The inputs to the comparator  806  are coupled to the input pixel  830  and the second output pixel  834 . The output of the comparator  806  flows into the one bit delay  810  and an OR gate  816 . The output of the one bit delay  810  is coupled to a one bit delay  814 . The output of the one bit delay  814  is coupled to the OR gate  816 . The inputs to a comparator  808  are coupled to the first output pixel  832  and the second output pixel  834 . The output of the comparator  808  flows into a one bit delay  812  and the OR gate  816 . The output of the one bit delay  812  flows into the OR gate  816 . The comparators  806 - 808  output a 1 if the two inputs are identical and a zero otherwise. 
     The OR gate  816  computes the functionally equivalent result as the OR gate  330  (see FIG.  3 ). The organization of the comparators  806 - 808  with the one bit delays  810 - 814  reduced the number of comparators and facilitated a pipeline organization to the pixel type determiner. The output of the OR gate  816  is a first preliminary type determination  840 , d(m). 
     The first preliminary type termination  840  is the input to a one bit delay  818 . The output of the one bit delay  818  is a second preliminary type determination  842 , d(m−1). The second preliminary type determination is the input to a one bit delay  820 . The output of the one bit delay  820  is a third preliminary type determination  844 , d(m−2). 
     The preliminary type determinations  840 - 844  can be provided to the verify uniqueness logic block  360  (see FIG. 3) to compute a pixel type determination  850 , e(m−1), for the third output pixel  836 , p(m−1). The pixel type determination  850  is provided to the scaler  250 . 
     I. Working in Two-Dimensions 
     The discussion so far has primarily focused on a one dimensional approach to pixel type determination. However, the invention is easily extended to two dimensions in several different ways. 
     In one embodiment, after performing the pixel type determination process on rows to compute e H (m,n), the process is repeated on the columns to compute e V (m,n). The two results are then OR&#39;ed together to compute the final pixel type determination: e(m,n)=e H  (m,n) OR e V (m,n). Then, e(m,n) is used to select an interpolation function. When e(m,n)=1, or artificial, an interpolation function suitable for that type of pixel is then chosen, otherwise an interpolation function suitable for natural pixels is chosen. 
     In another embodiment, different interpolation functions can be used in the horizontal and vertical directions. Here, e H (m,n) is used to select the horizontal interpolation function for pixel p(m,n) and e V (m,n) is used to select the vertical interpolation function for the pixel. 
     In yet another embodiment, no vertical pass is made at all and e(m,n)=e H (m,n). That is to say, the horizontal pixel type determination is used to select the interpolation function for the pixel without the addition of a vertical pass. This still produces high quality results without the added computation and hardware necessary for the two pass embodiments discussed above. 
     J. Selecting an Interpolation Function when Adjacent Pixel Types are Mismatched 
     Because at least two pixels are needed to interpolate any pixel in between the two source pixels for interpolation in one dimension, it will be a problem if the adjacent pixel types are different at the two source pixel positions. Consider the following horizontal interpolation as shown by Table 4. 
     
       
         
               
               
               
               
             
           
               
                   
                 TABLE 4 
               
               
                   
                   
               
             
             
               
                   
                 . . . Artificial Pixel 
                 Interpolated Pixel 
                 Natural Pixel . . . 
               
               
                   
                   
               
             
          
         
       
     
     Since the interpolated pixel is related to the adjacent source pixels with different types, there is a mismatch of types to address in selecting an interpolation function. When interpolation is done in two dimensions, four pixels will be used to interpolate a pixel between the source pixels as shown by Table 5. 
     
       
         
               
               
               
             
           
               
                 TABLE 5 
               
               
                   
               
             
             
               
                 . 
                   
                  . 
               
               
                  . 
                 Artificial Pixel 
                  . 
               
               
                  . 
                   
                 . 
               
               
                 Artificial Pixel 
                 Interpolated Pixel 
                 Natural Pixel 
               
               
                  . 
                   
                 . 
               
               
                  . 
                 Artificial Pixel 
                  . 
               
               
                 . 
                   
                  . 
               
               
                   
               
             
          
         
       
     
     Therefore, a decision scheme is desirable to select the appropriate interpolation function when the adjacent pixel types are mismatched. 
     One approach is use an artificial image interpolation function if any one of the source pixels is detected to be an artificial image pixel. Another approach is to use a natural image interpolation function if any one of the pixels is detected to be a natural image pixel. A third approach is to adopt the interpolation function based on the predominant source pixel type. If more of the source pixels are of the artificial image pixel type, then the artificial image interpolation function is used. Otherwise, the natural image interpolation function is used. If the source pixels are evenly split between the two types, one of the other two approaches can be used. 
     K. Conclusion 
     Some embodiments of the invention are included in computer usable media such as CD-ROMs, or other computer usable media. The computer usable media can comprise the software for pixel type determiners, interpolation and scaling functions, and scaler programs. 
     Some embodiments of the invention are included in an electromagnetic wave form. The electromagnetic wave form comprises information such as software for pixel type determiners, interpolation and scaling functions, and scaler programs. 
     Thus, a method and apparatus for selecting interpolation functions based on image type on a pixel by pixel basis has been described. The method permits highly localized decisions to be made about image type. The method offers unique benefits for selecting the most appropriate type of interpolation function for each part of an image on a pixel by pixel basis.