Patent Publication Number: US-8538199-B2

Title: Digital image scaling with non integer scaling factors

Description:
BACKGROUND 
     1. Field of the Invention 
     The invention relates to scaling digital images and more specifically to scaling images using non integer factors to reduce artifacts and errors in resultant output images. 
     2. Statement of the Problem 
     Digitization of images has provided many benefits in terms of portability, storage, and reproduction. Often, digitized images can be processed to alter the image, (e.g., change the image size). For example, once an image is digitized, it is converted into image data represented by a two dimensional array of pixels, with each pixel having some color or grayscale value. This two dimensional array of pixels can be reduced in size by removing a certain number of pixels from the array in a manner that still provides an adequate representation of the original image. Similarly, pixels can be added to the array to increase the size of the image. 
     One basic approach to scaling includes the “nearest neighbor” method, which uses sample values that are nearest to a pixel being analyzed. This is generally known as a zero-order or proximal interpolation and generally produces relatively good high frequency response, but degrades image quality due to aliasing. To illustrate, a 240 dots per inch (DPI) image as it would be printed on a 360 DPI printer is now discussed. In this example, the scaling factor is a non integer 1.5 (i.e., 360 dpi/240 dpi=1.5). The scaling ratio is converted to the nearest ratio which is all integer. For this case, the ratio is three to two, meaning that for every two PELs in the input space there are three PELs created in the output space. Using a nearest neighbor pixel replication algorithm, the algorithm outputs one copy of the first pixel, two copies of the second, and so on, in a 1-2-1-2-1-2 . . . pattern. This pattern satisfies the two PELs becoming three in the output space requirement. The same holds true for scanlines in the image in that the first scanline appears once, the second is repeated twice, etc. The problem with this scaling approach is that it can cause undesirable artifacts in the output image, especially if the scaling factor is not an integer. Consider the following image pattern with the same proposed scaling of 1.5, where a 1 in the pattern indicates a black pixel and a 0 indicates a white pixel. 
           111           000           000.       
Suppose, with this scaling, the image is to be replicated 3 times down a page. The output of this 1D scaling would then appear as follows:
 
     
       
         
           
               
               
               
             
               
                   
                   
               
               
                   
                 DATA 
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     In this diagram, the left side shows the scaled and replicated pattern. The horizontal lines provide a visual aid to the reader to distinguish the copies of the replicated pattern. The right column shows how many copies of the input line are output by the scaling algorithm. Notice how the first copy of the pattern has a black line that is one pixel wide, but the second copy has a black line that is two pixels wide. These inconsistencies are easily recognized when viewed (e.g., on a printed medium), because a single pixel in the input becomes a varying larger number of pixels in the output, generally referred to as an artifact. If the scaling factor is an integer value, no artifact occurs because each pixel is scaled the same. 
     One method used to overcome these artifacts is a bilinear approach which is regarded as a first-order scaling method. In the bilinear approach, the output pixel value changes linearly according to sampling position. Other more complex methods include the bicubic approach, the use of polynomials, adaptive algorithms, or correlations, but these methods require significant processing capabilities due to their complexities. Additionally, certain images are composed of transparent areas that cause problems in scaling. For example, the image of the font character “O” printed in black on a red background does not overwrite the center of the image or the corners with white data because these pixels are transparent. If the font character was created at a fixed resolution and must be scaled, an efficient scaling is needed that preserves the transparent regions without causing a “halo” effect of white or gray pixels adjacent to the black pixels of the scaled character image. 
     SUMMARY 
     Embodiments herein provide for the scaling of image data and in particular to the scaling of image data in non integer factors. Previously, this type of scaling would generally result in artifacts in the output image. In one embodiment, a scaling algorithm that employs “fractional pixel replication” (FPR) is used to scale images with virtually any scaling factor, including non integer scaling factors. The scaling algorithm uses a weighted average of several input pixel values as opposed to generating each output pixel from a single input pixel. Further, the scaling algorithm includes transparent areas in calculating the weighted average. To simplify the discussion of the FPR scaling algorithm, the embodiments herein are directed to grayscale images as the representation of such images is easily performed with fewer color values (e.g., 0-255 levels of gray). However, the invention is not intended to be limited to simply scaling grayscale images as the FPR scaling algorithm may be used to scale color images as well. 
     An FPR output pixel may take any value in the 0-255 range, where 0=totally white and 255=totally toned (saturated color). Where image regions have opaque pixels that are proximate to transparent regions, the transparent regions may be represented by grayscale values within the grayscale range (e.g., 0-255). To smooth the transition to background colors of the transparent regions, the pixels are made translucent instead of gray by way of a translucency mask. The translucency mask indicates where a blending calculation is to be applied in an image and what weight is to be given to the background at each location. Additionally, the translucency mask allows subsets of a rasterization to be cached and recombined such that results are consistent. 
     One method for scaling an input image includes identifying a pixel resolution of the input image, identifying a pixel resolution of an output device, and determining a scaling resolution based on the pixel resolution of the input image and the pixel resolution of the output device. The pixel resolution of the input image is a first factor of the scaling resolution, the pixel resolution of the output device is a second factor of the scaling resolution, and the first and second factors are different. The scaling resolution may be a resolution that is common to the input resolution in the output resolution (i.e., evenly divided by each); however, such is not a requirement. The input image may include virtually any pixel resolution format, including anamorphic. The method also includes converting the input image to the scaling resolution to change a number of pixels of the input image by the first factor of the scaling resolution and generating a grid to scale the converted image. The grid has a number of sections defined according to the second factor times the pixel resolution of an output device. The method also includes sectioning the converted input image according to the grid. Each section of the grid includes an integer number of pixels of the converted input image. The method also includes averaging color values of the pixels of the converted input image within each section of the grid to compute a single color value for each section of the grid and scale the input image. 
     The method may also include generating a translucency mask and applying the translucency mask to the scaled image to smoothly transition foreground color values from background color values. The method may also include storing at least a portion of the translucency mask for application to in a subsequently received background image to optimize processing of the subsequently received background image with the saved scaled foreground image. The method may also include storing at least a portion of the scaled image to optimize processing of a subsequently received background image. The method may be operable with a variety of devices, such as digital cameras, printers, computer processors, and the like. 
     The color values of the pixels of the input image may be grayscale color values or other color values and formatted in a variety of ways, such as anamorphic. The method may also include generating a translucency mask and applying the translucency mask to the scaled image to smoothly transition color values. When looking at discrete scale ratios, this generally means that certain repeating patterns can allow the calculated transparency values to be cached for improved performance. However, irrational scale ratios where caching is not used are also effective. 
     Other exemplary embodiments may be described below. 
    
    
     
       DESCRIPTION OF THE DRAWINGS 
       Some embodiments of the present invention are now described, by way of example only and with reference to the accompanying drawings. The same reference number represents the same element or the same type of element on all drawings. 
         FIG. 1  illustrates an image scaling system in an exemplary embodiment. 
         FIG. 2  is a flow chart illustrating a method of scaling an image in an exemplary embodiment. 
         FIGS. 3-6  illustrate scaling of an image from one resolution to another using non integer scaling factors in an exemplary embodiment. 
         FIG. 7  is a flowchart illustrating an application of a translucency mask in an exemplary embodiment. 
         FIG. 8  is a pixel diagram illustrating the application of the translucency mask in an exemplary embodiment. 
         FIG. 9  illustrates a computer system operable to execute computer readable medium embodying programmed instructions to perform desired functions in an exemplary embodiment. 
         FIG. 10  is a block diagram illustrating a printing system implementing non integer scaling factors in an exemplary embodiment. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     The figures and the following description illustrate specific exemplary embodiments of the invention. It will thus be appreciated that those skilled in the art will be able to devise various arrangements that, although not explicitly described or shown herein, embody the principles of the invention and are included within the scope of the invention. Furthermore, any examples described herein are intended to aid in understanding the principles of the invention and are to be construed as being without limitation to such specifically recited examples and conditions. As a result, the invention is not limited to the specific embodiments or examples described below, but by the claims and their equivalents. 
       FIG. 1  illustrates an image scaling system  140  in an exemplary embodiment. The image scaling system  140  may be any system, device, software, circuitry and/or other suitable component that is operable to scale an image  120  of X*Y resolution to X′*Y′ resolution using non integer scaling factors. Once the image  120  is scaled to the X′*Y′ resolution, the image scaling system  140  transfers the scaled image  130  to an output device  170  for presentation of the scaled image  130 . Examples of the output device  170  include computer monitors, digital cameras, printers, and the like. The image scaling system  140  may be configured as part of the output device  170  or external thereto. 
       FIG. 2  is a flow chart  200  illustrating a method of scaling an image in one exemplary embodiment. In this embodiment, the image scaling system  140  receives the image  120  having a particular number of pixels (e.g., dpi) and scales the image  120  according to a number of pixels of the desired output device  170 . The ratio of the number of pixels of the input image  120  to the number of pixels of the output device  170  generally results in a non-integer scaling factor to which the image scaling system  140  accordingly scales the image. In doing so, the image scaling system  140  first identifies the pixel resolution of the input image  120  and a pixel resolution of the output device  170 , in the process element  201 . From there, the image scaling system  140  determines a ratio of the two pixel resolutions (e.g., the number of pixels of the input image  120  and the number of pixels of the output device  170 ), in the process element  202 , to determine the scaling ratio. For the purposes of illustration, the discussion is focused on converting a 240 dpi image to a 360 dpi output, although virtually any scaling ratio may be performed. Moreover, the scaling may be performed in either direction (i.e., from a higher resolution to a lower resolution or vice versa). In this example, when a 240 dpi image is received by the image scaling system  140  and the desired output device  170  presents the image in a 360 dpi format, the ratio of 360 dpi to 240 dpi results in a non integer scaling factor of 1.5. The image scaling system  140  determines a resolution which is a multiple of both the 240 dpi image and the 360 dpi of the output device  170 . In this case, 720 dpi is divided evenly by 240 dpi three times and by 360 dpi twice. 
     Based on this common scaling resolution, the image scaling system  140  converts the input image to the scaling resolution, in the process element  203 , thereby increasing the number of pixels in the input image. For example, each pixel in the input image is increased to nine pixels due to a scaling factor of three in the horizontal and vertical directions, as illustrated in  FIG. 3  (e.g., one pixel  401  of the 240 dpi format is represented by 3×3 pixels  402  in the 720 dpi format, each having the same color value). 
     The image scaling system  140  also generates a grid  500  as shown in  FIG. 4  based on the common resolution, in the process element  204 . The grid  500  is configured by increasing the resolution of the 360 dpi format to the 720 dpi format, wherein each pixel of the grid  500  is represented by a placeholder color value J (e.g., at the locations (1,1), (1,2), (1,3) . . . (3,3)). For example, for a single grid pixel J(1,1) in the 360 dpi format, a total of four grid pixels would exist in the 720 dpi format due to a scaling factor of two in the horizontal and vertical directions, (e.g., one pixel J(1,1) of the 360 dpi format is represented by the four grid pixels J(1,1), J(1,2), J(2,1), and J(2,2) in the 720 dpi format). Because of the common scaling resolution, the grid lines  501  of the grid  500  lie on the lines that define the pixels  402 , as shown in  FIG. 5 . For example, each of the grid pixels J(1,1), J(1,2), J(2,1), and J(2,2) of the 720 dpi format representing the J(1,1) grid pixel of the 360 dpi format lie on the same lines that define the pixels  402 . 
     The grid  500  may then be used to compute pixel values for the scaled image based on the input image pixels  402 . For example, the input image  400  illustrates four pixels in a 240 dpi format having various color values of I at pixel locations (1,1), (1,2), (2,1), and (2,2). When scaled to the 720 dpi format, each pixel location is represented by nine pixels  402  having the same color value. Based on the grid  500 , the image scaling system  140  may section the converted input image  400  such that each section of the grid  500  includes an integer number of pixels  402  of the converted input image  400 , in the process element  205  (i.e., in this instance, 4 pixels of the converted image). Afterwards, the image scaling system  140  may compute color values in the grid  500  by averaging the color values of the pixels  402  falling within each section of the grid  500 , in the process element  206 . In this regard, the J color values (1,1), (1,2), (1,3) . . . (3,3) may be computed as a function of the I color values at the pixel locations (1,1), (1,2), (2,1), and (2,2) according to how they overlap those pixel locations. Such is shown to the immediate right of the final scaled 360 dpi image  600  of  FIG. 6 . 
     The model for this image scaling algorithm can be mathematically written as follows: 
                       ∫       A   1     →   0               ⁢         r   2     ⁡     (       x     0   ⁢               ,     y   0     ,   x   ,   y     )       ⁢           ⁢     ⅆ         A   1     ⁡     (     x   ,   y     )       @       ∫     A     2   →   0                 ⁢         r   2     ⁡     (       x     0   ⁢               ,     y   0     ,   x   ,   y     )       ⁢           ⁢       ⅆ       A   2     ⁡     (     x   ,   y     )         .                 ⁢     
             Equation   ⁢           ⁢   1               
where x 0  and y 0  are coordinate locations for the input image and the desired scaled image, respectively, x and y are spatial local variables, A 1  is a local area in the input image, A 2  is a local area in the desired scaled image, r 1  is a reflectance function for the input image, and r 2  is a reflectance function for desired scaled image. Equation 1 can be approximated as the following discrete function for digital processing as follows:
 
                       ∑     A   1               ⁢           ⁢         r   1     ⁡     (       x     0   ⁢               ,     y   0     ,   x   ,   y     )       ⁢   Δ   ⁢           ⁢       A   1     ⁡     (     x   ,   y     )           ≈       ∑     A   2               ⁢           ⁢         r   2     ⁡     (       x     0   ⁢               ,     y   0     ,   x   ,   y     )       ⁢   Δ   ⁢           ⁢         A   2     ⁡     (     x   ,   y     )       .                 Equation   ⁢           ⁢   2.               
Factoring of the common terms and assuming a reflectance constant over a subdivided area (i.e., the common resolution), yields the following equation:
 
     
       
         
           
             
               
                 
                   
                     
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     In image regions where there are transitions from opaque to transparent color values, the output of the scaling algorithm may yield an intermediate grayscale value in the range 1-254. In these regions, the background of the printed image should show through to improve the transition from the foreground color value to the background color value. In this regard, the image scaling system  140  may generate and apply a translucency mask to an image to remove the halo effect and blend the color transitions.  FIGS. 7 and 8  illustrate creation of a translucency mask  800  in an exemplary embodiment. To generate the translucency mask  800 , the image scaling system  140  may locate regions  802 ,  805 , and  806  where opaque to transparent and transparent to opaque transitions  807  occur in an image  801  before scaling, in the process element  701 . Once located, the image scaling system  140  may determine that the output regions  802 ,  805 , and  806  occupied by the color transition are translucent regions, in the process element  702 . If the regions  808  and  809  do not include a transition, the corresponding regions in translucency mask  800  may be set to zero. In this regard, the image scaling system  140  may configure the translucency mask  800  to contain mostly 0 values corresponding to regions where the scaled image is either completely opaque  808  or completely transparent  809 , in the process element  704 , and then return to the process element  702 . 
     The translucency weight, represented by various pixel values in the transparency mask  800 , is calculated by the portions of the translucent regions  802 ,  805 , and  806  which are occupied by the opaque pixels in the input image. In one embodiment, the translucency weight is 128 representing roughly the middle of the 0 to 255 grayscale. In places where the translucency mask  800  is nonzero, the following generalized equation may be performed to obtain the translucency mask  800  pixel value:
 
Pixel Value=(area occupied by transparent area in a region)/(total area occupied by the region)*255.  Equation 4.
 
     For example, in region  802 , the pixel value would be 128. The pixel value 2 from regions  805  would be a lower (more opaque) value, and the pixel value 3 from regions  806  would be a higher (more transparent) 
     If, on the other hand, the region  802 ,  805 , and  806  includes a transition, the image scaling system  140  may use the translucency mask  800  to smooth color transitions. For example, the image scaling system  140  may apply a translucency mask value proportionally to opaque areas, in the process element  703 . This is performed using the pixel value in the corresponding translucency mask  800 :
 
Output Value=(color value of background pixels  809 )*(Pixel Value/255)+(255−Pixel Value)/255*(color value of opaque pixels  808 ).  Equation 5.
 
     The image scaling system  140  then determines whether all regions have been examined, in the process element  705 . If so, the image scaling system  140  prepares the image for output/printing, in the process element  706 . Otherwise, the image scaling system  140  continues processing the image data by returning to the process element  702 . Blurring by the Human Vision System (HVS) may assist in the accurate representation of the image when displayed. Typically, a transparency mask is used with a translucency mask to determine whether pixels set to 0 in the translucency mask  800  are transparent  809  or opaque  808 . This determines the non-translucent color values of the final image  801 . 
     Additionally, the translucency mask  800  may be stored for application to another image. For example, the translucency mask values that were used to adjust a series of previous images may be saved and applied to another background of pixels. Such may be performed according to the following.
 
 Xn =(1 −M 1)* X 1 +M 1 *X 0,  Equation 6.
 
where M is a translucency range from 0 (opaque) to 1 (totally translucent), X is an opacity range from 0 (all white) to 255 (all black), Xn is a new value derived from the translucency mask M 1  of a new image&#39;s translucency, and X 1  is the color value of the new image&#39;s color using X 0  as an existing bitmap color value. To save the translucency in the mask M 1 , the following equation is used
 
 Mn=M 1 *M 0,  Equation 7.
 
where Mn is a new value derived from a new translucency mask M 1  and M 0  is the existing translucency mask value. M 0  is generally initialized to 1 for a stored image whereas X 0  is initialized to 0. To add a stored image with its associated translucency mask to an existing bitmap for printing, the following formula is used:
 
 Xnc=Xc+Mc*X 0  Equation 8.
 
where Xnc is a new bitmap value, Xc is a value in the added stored bitmap, and Mc is the translucency mask value of the added stored bitmap for a particular pixel. Since M is generally in units of 1-255 for grayscale, the range for M values yields the following equations:
 
 Xn =(255 −M 1)* X 1/255 +M 1 *X 0/255
 
 Mn=M 1 *M 0/255
 
 Xnc=Xc+Mc*X 0/255.  Equations 9-11.
 
     An extension of this scaling to the anamorphic case also can be accomplished using the scaling factors for two different uniform scalings. For example, the factors can be computed for each scaling ratio, vertical and horizontal. The factors for the first rows of each instance may be used to compute the anamorphic factors for each of the different scan lines in the image (e.g., in the vertical direction). Instead of interpreting the factors applied to individual pixels, the factors are applied to all of the pixels in an image. 
     Alternatively or additionally, the scaling algorithm may operate once in the horizontal direction to determine the mapping of input pixels to the output pixels for each row. The horizontal scaling may be performed in the same manner for each row (i.e., the horizontal indices of the pixels of the input image generally do not change from row to row). The scaling algorithm may also perform a vertical scaling once to determine a mapping of input scanlines to output scanlines. The vertical calculations may also be performed for a single column in the image. The final result of these computations is a list of contributing input scanline indices for each output scanline and a list of contributing input pixel indices for each output pixel along with weights for each. 
     Based on the scaling factor and the computed weights, the scaling algorithm may be optimized to decrease the number of multiplications in the output image. For example, if a common scale factor results most often in 4 input pixel locations contributing to an output pixel value (e.g., assuming a 240 dpi to 360 dpi scaling), the image scaling system  140  may configure a “lookup table” for the 16 possible combinations of 4 input pixel values such that a value for the output pixel is selected as opposed to being computed. Further optimizations may include a using a lookup table that includes values for the most common combinations of the 4 input pixels (e.g., all white values, all black values, etc.) 
     Additionally, a transparency mask may be used after the image is scaled and the translucency mask is applied. For example, the transparency mask may convey information about image regions that are either completely opaque or completely transparent. In this regard, the image scaling system  140  may merge the scaled image directly into the final bitmap. Some portions of the image may be transparent (e.g., a bi-level IOCA input is assumed to have a transparent background). The image scaling system  140  may account for such by applying the transparency mask to the final bitmap. Transparency masks are known to those skilled in the art. 
     Embodiments of the invention can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment containing both hardware and software elements. In one embodiment, the invention is implemented in software, which includes but is not limited to firmware, resident software, microcode, etc.  FIG. 9  is a block diagram depicting a computer system  900  operable to provide features and aspects hereof by executing programmed instructions and accessing data stored on a computer readable storage medium  912 . 
     Furthermore, embodiments of the invention can take the form of a computer program accessible via a computer-readable medium  912  providing program code for use by a computer or any other instruction execution system. For the purposes of this description, a computer readable medium  912  can be anything that can contain, store, communicate, or transport the program for use by the computer other instruction execution system. 
     The computer readable medium  912  can be an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor device. Examples of the computer readable medium  912  include a solid state memory, a magnetic tape, a removable computer diskette, a random access memory (RAM), a read-only memory (ROM), a rigid magnetic disk, and an optical disk. Current examples of optical disks include compact disk-read only memory (CD-ROM), compact disk-read/write (CD-R/W), and DVD. 
     The computer system  900 , being suitable for storing and/or executing the program code, includes at least one processor  902  coupled to memory elements  904  through a system bus  950 . The memory elements  904  can include local memory employed during actual execution of the program code, bulk storage, and cache memories that provide temporary storage of at least some program code and/or data in order to reduce the number of times the code and/or data are retrieved from bulk storage during execution. 
     Input/output or I/O devices  906  (including but not limited to keyboards, displays, pointing devices, etc) can be coupled to the system either directly or through intervening I/O controllers. Network adapter interfaces  908  may also be coupled to the system to enable the computer system  900  to become coupled to other data processing systems or storage devices through intervening private or public networks. Modems, cable modems, IBM Channel attachments, SCSI, Fibre Channel, and Ethernet cards are just a few of the currently available types of network or host interface adapters. Presentation device interface  910  may be coupled to the system to interface to one or more presentation devices, such as printing systems and displays for presentation of presentation data generated by processor  902 . 
       FIG. 10  is a block diagram illustrating a printing system  1030  using non integer scaling factors in an exemplary embodiment. A host system  1010  is in communication with the printing system  1030  to print a sheet image  1020  onto a print medium  1080  via a printer  1060 . The resulting print medium  1080  may be printed in color and/or in any of a number of gray shades. The host system  1010  may comprise any computing device, such as a personal computer or a server. The sheet image  1020  may be any file or data that describes how an image on a sheet of print medium should be printed. For example, the sheet image  1020  may include PostScript data, Printer Command Language (“PCL”) data, the Intelligent Printer Data Stream (“IPDS”) data, and/or any other printer language data. The printing system  1030  may be a high-speed printer operable to print relatively high volumes (e.g., greater than 100 pages per minute). The print medium  1080  may be continuous form paper, cut sheet paper, and/or any other medium suitable for printing. The printing system  1030 , in one generalized form, includes the printer  1060  that presents a bitmap  1050  onto the print medium  1080  (e.g., via toner, ink, etc.) based on the sheet image  1020 . 
     The image scaling system  140  may be any system, device, software, circuitry and/or other suitable component configured within the printing system  1030  that is operable to transform the sheet image  1020  and generate a scaled bitmap  1050  for printing onto the print medium  1080  in accordance with the non integer scaling described above. The image scaling system  140  may be configured as part of a print controller of the printing system  1030  and/or any other portion of the printing system  1030 . In another embodiment, the image scaling system  140  may be configured with the host system  1010 . 
     Although specific embodiments were described herein, the scope of the invention is not limited to those specific embodiments. For example, the scaling algorithms are often described herein with respect to printing systems. However, the scaling algorithms may be employed in virtually any device which is used to display images. Examples of such include computer monitors, televisions, digital cameras, and the like. To illustrate, an image may be captured using a digital camera. A user may desire to display the image on a computer monitor that requires non integer scaling of the image, accomplished via scaling algorithms presented herein. Additionally, although shown and described with respect to non integer scaling factors, the invention is not intended to be so limited. The scaling algorithms presented herein may be used to scale images via virtually any scaling factor. For example, the previous embodiments show and describe a scaling ratio of 1.5 that provides a relatively easy scaling resolution that is evenly divisible by both the input and output pixel resolutions. However, the systems and methods presented herein may also be used for scaling ratios that do not provide such common scaling resolutions. Moreover, the systems and methods presented herein may be used to scale image data from a lower resolution to a higher resolution and vice versa. Accordingly, the scope of the invention is only defined by the following claims and any equivalents thereof.