Abstract:
There is disclosed the use of a beehive cell arrangement of shaped quantization blocks for grouping pixels for the digital approximation of analog video information. A frame may consist of beehive-arranged hexagonal quantization cell blocks or brick-wall-arranged rectangular cell quantization blocks, where each pixel belongs only to one shaped quantization block. A beehive cell arrangement of circle-shaped quantization blocks is described for use when the frame is partitioned into overlapping quantization blocks.

Description:
FIELD OF INVENTION 
     The invention relates generally to the processing of video compression, and more particularly to problems related to quantization of video information. 
     BACKGROUND OF THE INVENTION 
     Digital video encoding algorithms, for example MPEG-X series, utilize a process for digital quantization of video information. The quantization process involves approximation of analog video information, for example an analog picture image, by a frame consisting of numerous pixels having the brightness and color attributes. Further MPEG-X series algorithms use such a compression technique that assumes a certain loss of video information. This means that after encoding-decoding procedure the pixels of the digitized video information differ from the original corresponding pixels with color and brightness. On the one hand, such a technique allows a substantial compression of the video information, and the quality of the image may be perceived to be more brimful than real, but on the other hand, several sequential repeats of the encoding-decoding procedure cause a substantial degradation of the video information. The MPEG-X series algorithm technique is based on the grouping of the pixels into “quantization blocks”, such that all the pixels belonging to a particular block are coded separately, i.e. have the same brightness and color quantization rule leading to a certain degradation of video information. Usually the quantization rule is defined by quantization step chosen for each quantization block separately. Such an approximation of the video information allows reducing a bit stream of information by decreasing the video information resolution. These blocks may be grouped into macro-blocks to use a transferring vector for the approximation of the video information of the next frame, thereby further reducing the required bandwidth of the bit stream of information. In the case of movies, a tolerance of video information loss related to pixels aggregated into blocks may differ from one block to another and from a frame to the next one. This degree of freedom permits tracking of the picture elements from one frame to the next thereby further reducing the required bandwidth for the stream of bit information, in principal. 
     Thus known video compression procedures attempt to achieve increased resolution and decreased bandwidth requirements for transmitting video information by using different kinds of quantization rule for each block. Prior art blocks, which are used in MPEG-X algorithms, have form of rectangles arranged as it is shown in  FIG. 1 . In this case each rectangular block has eight neighbors: North, North-West, West, South-West, South, South-East, East and North-East. A degradation of the video information within each block is controlled by the quantization rule, however the degradation of video information on boundaries of the considered block with neighbor blocks is unpredictable in a certain meaning. If blocks and macro-blocks, defined for a frame, are transferred by a transferring vector in order to approximate the video information of the next frame, a statistical error in the imagination of the next frame is defined by the block neighbors, having independent attributes of color and brightness quantization rule, wherein, as it is described, for example, by Torsten Seemann and Peter Tischer and Tetra Lindarto in the paper titled “ Generalised Locally Adaptive DPCM ”—Proc. of IEEE Data Compression Conf., pp473, 1997, the error arises on the block boundaries. 
     U.S. Pat. No. 5,764,805 to Martucci, et al. discloses the use of overlapping polygonal shaped blocks for reducing statistical errors appearing at the quantization block boundaries. 
     SUMMARY OF THE INVENTION 
     Accordingly, it is a principal object of the present invention to overcome the limitations of existing video compression algorithms, and to provide improved algorithms for video compression by the definition of quantization blocks having a shape and arrangement similar to that of beehive cells. 
     The beehive cell shape and arrangement of the quantization block is optimal in accordance with the following optimization criteria. 
     The first mathematical criterion is to achieve the smallest possible ratio of the perimeter of each block to its area, if we consider a class of blocks that completely fill the frame area. Whereby, the statistical boundary error of compressed video decreases with reducing of the quantization blocks total perimeter. 
     The second mathematical criterion consists in reducing the number of adjacent cells. Compared with the number of adjacent cells bordering a cell in the prior art arrangement of rectangular quantization blocks, where each cell has eight adjacent cells, the present invention utilizes beehive-cell shaped and arranged blocks, each having six adjacent neighbors. 
     The third mathematical criterion is Chebyshev&#39;s criterion for optimal approximations of the desired function by the polynomial function of order N. This criterion follows from Chebyshev&#39;s theorem on alternance, i.e. that the approximation polynomial function of given order N (in our case, N is a number of quantization blocks) having the least deviation from the desired function, has equal deviations between the N junctions, where the approximation polynomial function coincides with the desired function. 
     Moreover, the application of the aforementioned second mathematical criterion of statistical error minimization provides a heretofore unknown optimal arrangement of conventional rectangular quantization blocks. This optimal arrangement, i.e. “brick-wall” arrangement, comprises the shifting of even horizontal/vertical lines to odd horizontal/vertical lines of blocks, respectively. Application of the aforementioned Chebyshev&#39;s criterion leads to a symmetrical variant of the “brick-wall” arrangement. 
     The present invention may also be applied where individual cells are overlapping when arranged in a block. The method of the present invention comprising applying the three mathematical optimization criteria may also be applied when it is tolerable to arrange shaped quantization blocks such that the quantization blocks are overlapping. In this case, the preferable arrangement is the beehive cell arrangement and preferable shape of quantization blocks is circle, surrounding the beehive cell hexagons. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       For a better understanding of the invention with regard to the embodiments thereof, reference is made to the accompanying drawings, in which like numerals designate corresponding elements or sections throughout, and in which: 
         FIG. 1  is a schematic illustration of a prior art arrangement of rectangular quantization blocks; 
         FIG. 2  is a schematic illustration of an embodiment of the present invention, showing the optimal grouping of pixels into blocks shaped and arranged similarly to beehive cells; 
         FIG. 3  is a schematic illustration of an embodiment of the present invention, showing the brick-wall arrangement of rectangular quantization blocks; and 
         FIG. 4  is a schematic illustration of an embodiment of the present invention, showing a beehive arrangement of overlapping circle-shaped quantization blocks; 
     
    
    
     DETAILED DESCRIPTION OF PREFERRED EMBODIMENTS 
     1. Prior Art Rectangular Blocks. 
     Prior art quantization blocks, which are used in MPEG-X algorithms, have form of rectangles, arranged by the way, as it is shown in  FIG. 1 . In this case each rectangular block  10  has eight neighbors: North 11, North-West 12, West 13, South-West 14, South 15, South-East 16, East 17 and North-East 18. If the quantization blocks and macro-blocks, i.e. group of the quantization blocks, defined for some frame, are transferred by a transferring vector in order to approximate the video information of the next frame, a statistical error of the next picture imagination is defined by the block neighbors, having independent color and brightness quantization rule, wherein the error arises on the block boundaries. 
     2. Beehive Cell Arrangement of Shaped Blocks. 
     The beehive cell  20  type of quantization, i.e. grouping the pixels into blocks  20  having the shape and arrangement of beehive cells, shown in  FIG. 2 , one preferred embodiment of the present invention, has several benefits in comparison to prior art grouping the pixels into rectangular quantization blocks  10 ,  11 ,  12 , etc., arranged as it is shown in  FIG. 1 . These benefits include: 
     Improved Quality of Static Compressed Picture Imaging 
     Static compressed picture imaging is improved by about 7.5%. The static desired picture, approximated by the compressed quantization blocks, has an approximation error that directly depends on the ratio of the block&#39;s perimeter to area. Comparison of perimeters of the cells having equal areas, prior art rectangular cell  10  and beehive cell  20  represented in this invention, gives the following characteristic ratio P 4 /P 6 , that is equal to: 
     
       
         
           
             
               
                 P 
                 4 
               
               
                 P 
                 6 
               
             
             = 
             
               
                 
                   2 
                   ⁢ 
                   
                     
                       3 
                       ⁢ 
                       
                         3 
                       
                     
                   
                 
                 
                   3 
                   ⁢ 
                   
                     2 
                   
                 
               
               ≈ 
               1.0746 
             
           
         
       
         
         
           
             where
           P 4  is the perimeter of rectangle, having area S 4 =(P 4 /4)^2   P 6  is the perimeter of the bee cell, having area S 6 =S 4 .
 
Reduction of Quality Loss in Motion Vector Processes for Transferring Quantization Block Video Information from One Frame to a Successive Frame
   
         
           
         
       
    
     A reduction of quality loss on the order of about 33% is achieved by the present invention. This effect is explained by the specific beehive-cells arrangement of hexagonal quantization blocks. When a block, defined for some frame, is transferred by a transferring vector in order to approximate the video information of the next frame, the value of statistical error in the next compressed picture image directly depends on the number of compressed neighbor blocks contiguous to the compressed block. In contrast to the prior art use of blocks  10 ,  11 ,  12 , etc., having rectangular-shaped cells arranged in a way that results in each block having eight contiguous neighbors: North, North-West, West, South-West, South, South-East, East and North-East, the use of hexagonal blocks  20  shaped and arranged in the form of the beehive cells according to the present invention, leads to each block having six contiguous neighbors and therefore having a lower value of statistical error in successive images. 
     Optimal Quantization According to Chebyshev&#39;s Criterion of the Desired Function Approximation by Polynomial Function 
     Chebyshev&#39;s theorem on alternance says that the approximation polynomial function of given order N, having the minimal deviation from the desired function, has equal deviations between the N junctions, where the approximation polynomial function coincides with the desired function. In the present invention, the desired function is the initial full (i.e. uncompressed) video information; the approximation polynomial function is the frame built from quantization blocks having compressed video information; and the given order N is the number of the quantization blocks. So the present invention&#39;s use of blocks  20  shaped and arranged in a beehive cell-formation leads to six equivalent neighbors, thereby providing equivalent statistical errors, i.e. equal deviations of the approximation polynomial function due to symmetrical statistical influence of the neighbors, in contrast to the prior art use of blocks  10 ,  11 ,  12 , etc., which causes different statistical errors, i.e. different deviations of the approximation polynomial function. 
     The effect of applying the three mathematical criteria together results in movie compression that is significantly better than when using the known grouping of pixels into rectangular quantization blocks. 
     With reference to  FIG. 4 , optimizing by arranging and shaping overlapping quantization blocks using the mathematical criteria of the present invention leads to a beehive cells arrangement of circle-shaped overlapping quantization blocks  40 . Circle-shaped blocks surround the beehive cell hexagons. A slight variation of this embodiment includes where the circle shape is approximated by a polygon covering the beehive cell (not shown). 
     3. Brick-Wall Arrangement of Rectangular Blocks. 
     Referring now to  FIG. 3 , it is shown that the use of the “brick-wall” arrangement of rectangular quantization blocks, as an alternative embodiment of present invention, leads to six neighbors  31 ,  32 ,  33 ,  34 ,  35  and  36  of the arbitrary chosen quantization block  30 , in contrast to the prior art arrangement shown in  FIG. 1 . This fact also provides significantly reduced quality loss in the process of a vector transferring the video information of quantization blocks from the previous frame to the next. This effect is explained by the fact that if blocks, defined for some frame, are transferred by a transferring vector in order to approximate the video information of the next frame, a statistical error of the next picture image directly depends on number of the nearest neighbor blocks. Taking into consideration Chebyshev&#39;s theorem on alternance, the symmetrical variant of the brick-wall arrangement, as it is shown in  FIG. 3 , is optimal. Moreover, with respect to the theorem, the prior art arrangement of rectangular quantization blocks, as it shown in FIG.  1 ., is extremely non-optimal. 
     It should be appreciated that the above-described embodiments are merely exemplary in nature. It is anticipated that one of ordinary skill in the art will be able to make many alterations and modifications to the exemplary embodiments without departing from the spirit of the invention, the true scope of which should only be determined by reference to the claims which follow in conjunction with the broadest interpretation of the teachings of the specification.