Abstract:
Rules for the signaling and interpretation of chroma position are described. One rule, called the short rule, defines fifteen discrete chroma centering positions and corresponding four-bit syntax element. Another rule, called the extended rule, defines 81 discrete chroma centering positions and corresponding seven-bit syntax elements. A described method includes receiving digital media data at a digital media encoder, determining chroma position information for the received digital media data, and representing the chroma position information with one or more syntax elements in an encoded bitstream. The one or more syntax elements are operable to communicate the chroma position information to a digital media decoder. The chroma position information facilitates an image rotation or flip.

Description:
RELATED APPLICATION INFORMATION 
       [0001]    This application claims the benefit of U.S. Provisional Patent Application No. 60/891,030, filed Feb. 21, 2007, the disclosure of which is hereby incorporated by reference. 
     
    
     SUMMARY 
       [0002]    In summary, the detailed description is directed to aspects of encoding and decoding digital media data, and in particular, encoding and decoding digital media data in digital media encoders and decoders. 
         [0003]    For example, rules for the signaling and interpretation of chroma position are described. One rule, called the short rule, defines fifteen discrete chroma centering positions and a corresponding four-bit syntax element. Another rule, called the extended rule, defines  81  discrete chroma centering positions and corresponding seven-bit syntax elements. Variations on these rules and other aspects also are described. 
         [0004]    In one aspect, a method comprises receiving digital media data at a digital media encoder; determining chroma position information for the received digital media data; representing the chroma position information with one or more syntax elements in an encoded bitstream, wherein the syntax element is operable to communicate the chroma position information to a digital media decoder, and wherein the chroma position information facilitates an image rotation or flip; and outputting the encoded bitstream. In another aspect, the chroma position information is decoded. 
         [0005]    This summary is provided to introduce a selection of concepts in a simplified form that are further described below in the detailed description. This summary is not intended to identify key features or essential features of the claimed subject matter, nor is it intended to be used to limit the scope of the claimed subject matter. 
         [0006]    The foregoing and other objects, features, and advantages will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0007]      FIG. 1  is a block diagram of a suitable computing environment for implementing techniques and tools for signaling and use of chroma position information in one or more described implementations. 
           [0008]      FIG. 2  is a diagram showing a first example chroma sample position rule. 
           [0009]      FIG. 3  is a diagram showing a second example chroma sample position rule. 
           [0010]      FIG. 4  is a diagram showing chroma downsampling of interlace data. 
           [0011]      FIG. 5  is a block diagram of a block transform-based codec. 
           [0012]      FIG. 6  is a flow diagram of a representative encoder. 
           [0013]      FIG. 7  is a flow diagram of a representative decoder. 
       
    
    
     DETAILED DESCRIPTION 
       [0014]    The present application relates to techniques and tools for efficient compression and decompression of digital media data. In various described embodiments, a still image encoder and/or decoder incorporate techniques for compressing and/or decompressing image data. 
         [0015]    Various alternatives to the implementations described herein are possible. For example, techniques described with reference to flowchart diagrams can be altered by changing the ordering of stages shown in the flowcharts, by repeating or omitting certain stages, etc. As another example, although some implementations are described with reference to specific digital media formats, other formats also can be used. 
         [0016]    The various techniques and tools can be used in combination or independently. Different embodiments implement one or more of the described techniques and tools. Some techniques and tools described herein can be used in a still image encoder or decoder, or in some other system not specifically limited to still image encoding or decoding. 
       I. Computing Environment 
       [0017]      FIG. 1  illustrates a generalized example of a suitable computing environment  100  in which several of the described embodiments may be implemented. The computing environment  100  is not intended to suggest any limitation as to scope of use or functionality, as the techniques and tools may be implemented in diverse general-purpose or special-purpose computing environments. 
         [0018]    With reference to  FIG. 1 , the computing environment  100  includes at least one processing unit  110  and memory  120 . In  FIG. 1 , this most basic configuration  130  is included within a dashed line. The processing unit  110  executes computer-executable instructions and may be a real or a virtual processor. In a multi-processing system, multiple processing units execute computer-executable instructions to increase processing power. The memory  120  may be volatile memory (e.g., registers, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or some combination of the two. The memory  120  stores software  180  implementing a digital media encoder or decoder with one or more of the described techniques and tools. 
         [0019]    A computing environment may have additional features. For example, the computing environment  100  includes storage  140 , one or more input devices  150 , one or more output devices  160 , and one or more communication connections  170 . An interconnection mechanism (not shown) such as a bus, controller, or network interconnects the components of the computing environment  100 . Typically, operating system software (not shown) provides an operating environment for other software executing in the computing environment  100 , and coordinates activities of the components of the computing environment  100 . 
         [0020]    The storage  140  may be removable or non-removable, and includes magnetic disks, magnetic tapes or cassettes, CD-ROMs, DVDs (including high-definition DVDs), or any other medium which can be used to store information and which can be accessed within the computing environment  100 . The storage  140  stores instructions for the software  180  implementing the digital media encoder or decoder. 
         [0021]    The input device(s)  150  may be a touch input device such as a keyboard, mouse, pen, or trackball, a voice input device, a scanning device, still image capture device (e.g., digital camera), or another device that provides input to the computing environment  100 . For audio or video encoding, the input device(s)  150  may be a sound card, video card, TV tuner card, or similar device that accepts audio or video input in analog or digital form, or a CD-ROM or CD-RW that reads audio or video samples into the computing environment  100 . The output device(s)  160  may be a display, printer, speaker, CD- or DVD-writer, or another device that provides output from the computing environment  100 . 
         [0022]    The communication connection(s)  170  enable communication over a communication medium to another computing entity. The communication medium conveys information such as computer-executable instructions, digital media input or output, or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media include wired or wireless techniques implemented with an electrical, optical, RF, infrared, acoustic, or other carrier. 
         [0023]    The techniques and tools can be described in the general context of computer-readable media. Computer-readable media are any available media that can be accessed within a computing environment. By way of example, and not limitation, with the computing environment  100 , computer-readable media include memory  120 , storage  140 , communication media, and combinations of any of the above. 
         [0024]    The techniques and tools can be described in the general context of computer-executable instructions, such as those included in program modules, being executed in a computing environment on a target real or virtual processor. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc., that perform particular tasks or implement particular abstract data types. The functionality of the program modules may be combined or split between program modules as desired in various embodiments. Computer-executable instructions for program modules may be executed within a local or distributed computing environment. 
         [0025]    For the sake of presentation, the detailed description uses terms like “select” and “receive” to describe computer operations in a computing environment. These terms are high-level abstractions for operations performed by a computer, and should not be confused with acts performed by a human being. The actual computer operations corresponding to these terms vary depending on implementation. 
       II. Signaling and Use of Chroma Sample Position Information 
       [0026]    Described embodiments provide advanced still image codec bitstream features, including the ability to perform cardinal rotations and mirror flips on an image without a full decode and re-encode. This feature can be supported by multiple design techniques, including:
       1. Lapped Biorthogonal Transform (LBT)—
           a. The symmetry of basis functions of the LBT allows a mirror flip of spatial data within the transform block by merely negating the sign of odd-symmetric transform coefficients. This is true for both spatial orientations, X and Y.   b. The isotropic nature of basis functions of the LBT allows the spatial data within the transform block to be transposed by merely transposing the transform coefficients. Cardinal rotations can be implemented as combinations of transpose and mirror flips.   
           2. Block, macroblock and tile spatial hierarchies
           a. In order to realize a mirror flip within a macroblock of data, the modified transform blocks are scanned in the laterally inversed sequence (in X and/or Y depending on the requirement). Likewise, within a tile the modified macroblocks are scanned in the laterally inversed order, and within an image the modified tiles are scanned in the laterally inversed order.   b. In order to realize a transpose, the modified blocks, macroblocks and tiles are transposed. Cardinal rotations can be implemented as combinations of transpose and mirror flips.   
           3. Signaling of an inscribed area within an extended crop area—this allows for non-macroblock aligned images to be mirror flipped or rotated freely and the non-zero offset of the image from the macroblock grid to be allowed in any direction, not merely the right and bottom.   4. Signaling of position of chroma sample—This allows chroma sub-sampled color formats such as YUV4:2:0 and YUV4:2:2 to be rotated by permitting the independent specification of the location of the chroma sample. It also allows the relative alignments of luma/chroma sample positions to be signaled to the decoder, so an upsampling filter with the appropriate phase can be chosen.
 
Signaling of positions of chroma samples is covered in detail below. Described signaling techniques allow images to be rotated within the compressed domain with no loss of information and no significant change in compressed size. This is a desirable bitstream feature and has complexity benefits.
       
 
         [0035]    A. Chroma Centering 
         [0036]    An image consists of multiple planes of data. In the primary space, an image is typically made up of 3 color planes corresponding respectively to the Red, Green and Blue (R, G and B) channels. In the internal color space used in most popular codecs, an image is made up of 3 converted color planes often referred to as Y, U and V. The Y component is called the luminance or luma plane, which roughly corresponds to a grayscale rendering of the image. The U and V components are referred to as chroma, chrominance or color difference planes. The nomenclature Y, U, V is used here in a generic sense with the understanding that described techniques and tools are applicable to a variety of “YUV type” color formats such as YCbCr, YCoCg, etc. A color format called YUV 4:4:4 has one U and one V sample for each Y sample. 
         [0037]    The human eye is very sensitive to the intensity variation and resolution of the luminance channel. It is relatively less sensitive to chroma. This allows for a simple means of reducing pixel count in the data by sub-sampling or dropping the resolution of the chroma (U and V) components. 
         [0038]    Two chroma sub-sampling techniques are popular:
       1. YUV 4:2:2—here, the spatial resolution of U and V in the X direction is reduced by a factor of 2 (usually with some anti-aliasing filter).   2. YUV 4:2:0—here, the spatial resolution of U and V in both X and Y directions is reduced by a factor of 2.       
 
         [0041]    For the YUV 4:2:2 case, each chroma sample corresponds to two luma samples. Likewise, for the YUV 4:2:0 case, each chroma sample corresponds to four luma samples. 
         [0042]    The chroma subsampling is usually performed after filtering the samples with an anti-aliasing filter. 
         [0043]    The phase of this filter determines the relative position of the chroma and luma samples. 
         [0044]    When converting back from either of these formats to YUV 4:4:4 for the purpose of display or printing, the knowledge of the relative sample positions must be available so that the proper upsampling filter can be used. 
         [0045]    One approach to this problem is to either mandate or signal the exact upsampling filter that should be used. However, this approach imposes additional requirements on the system and may not compatible with the rest of the industry. 
         [0046]    A simpler and more flexible solution of indicating how to reconstruct full resolution data from a sub-sampled version is by signaling “position” information regarding alignment of luma and chroma samples. This approach allows the decoder to use any upsampling filter whose phase is matched to the position information. 
         [0047]    While this approach does not specify a unique reconstruction rule (i.e. unique upsampling filter), it has a sufficiently good performance and has widespread acceptance. 
         [0048]    The “position” of a sub-sampled data point is the location or phase of this value within a full-resolution grid. The position information is used to pick between upsampling filters that are compliant with the phase constraint. The position information is two dimensional in general—a shift is specified in both the horizontal and vertical directions.  FIGS. 2 and 3  show examples of two common chroma position rules used for YUV 4:2:0. In  FIG. 2 , phase=(0, 0), and in  FIG. 3 , phase=(0.5, 0.5) in luma pixel units. 
         [0049]    B. Chroma Centering with Image Rotation/Flips 
         [0050]    The two examples shown in  FIGS. 2 and 3  are the most common cases for YUV 4:2:0 sub-sampling of chroma. These two centering rules are usually sufficient for video data but usually insufficient for image data. A difference between video and images is that video is seldom rotated or mirror flipped, whereas images are very often rotated and/or mirror flipped. 
         [0051]    To see why the two centering rules are usually insufficient for image data, consider the following cases. 
         [0052]    Case 1: Consider a mirror flip along the horizontal direction for the centering example 1. Now the chroma sample is co-located not with the top left luma sample but with the top right luma sample. The corresponding phase of chroma is (1, 0) in luma pixel units, which is not defined by the rules shown in  FIGS. 2 and 3 . 
         [0053]    Case 2: Likewise, a mirror flip along the vertical direction of an image with chroma position shown in example 1 results in a chroma position with (0, 1) phase in luma pixel units which is not defined by the rules shown in  FIGS. 2 and 3 . 
         [0054]    The above cases show the usefulness of defining additional chroma centering rules as side information to a bitstream to aid the process of correct reconstruction when the image is subject to the basic operations of cardinal rotations and mirror flips. 
         [0055]    C. Chroma Centering with Interlace Data 
         [0056]    Another complication is introduced by interlaced video. A frame of interlaced video contains two fields—the top field and the bottom field. A field of video may be stored at its full resolution with no chroma downsampling. More commonly, it is carried in a chroma downsampled form such as YUV 4:2:2 where the chroma is downsampled in the X direction by a factor of 2, and matches the luma resolution in the Y direction. In the recent video codecs, however, a field of interlaced video is defined in the YUV 4:2:0 space so its chroma is downsampled by a factor of 2 in both X and Y directions. 
         [0057]    This operation often results in a chroma centering with a phase shift of 0.25 or 0.75 (in luma pixel units) in the vertical direction depending on whether it is top or bottom field data, respectively. Such a centering can be used to ensure the following:
       1. Alternating lines of chroma in the frame are produced by alternating fields.       
 
         [0059]    Chroma centering is uniform across successive lines of the frame. 
         [0060]    The chroma downsampling of interlace data is shown in  FIG. 4 . The X axis downsampling may have any phase and is not relevant to this discussion. Therefore, the figure only shows the Y axis centering and displacements. 
         [0061]    D. Chroma Positions 
         [0062]    With the above in mind, we define two rules for chroma position. The first rule, referred to as the short rule defines  15  chroma centering phases. This rule is signaled using a 4 bit word within an image bitstream. Table 1 enumerates the values and corresponding phases of the syntax element CHROMA_CENTERING_SHORT in one implementation. In the example shown in Table 1, CHROMA_CENTERING_SHORT can take on values between 0 and 15, but the value 14 is reserved and not used. CHROMA_CENTERING_SHORT can be signaled, for example, in an image header or an image plane header. 
         [0000]    
       
         
               
             
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Enumeration of values of CHROMA_CENTERING_SHORT 
               
               
                 and corresponding phases. 
               
             
          
           
               
                   
                 X Phase = 
                 X Phase = 
                 X Phase = 
               
               
                 CHROMA_CENTERING_SHORT 
                 0 
                 0.5 
                 1 
               
               
                   
               
               
                 Y Phase = 0 
                 0 
                 10 
                 1 
               
               
                 Y Phase = 0.25 
                 6 
                 12 
                 7 
               
               
                 Y Phase = 0.5 
                 4 
                 15 
                 5 
               
               
                 Y Phase = 0.75 
                 8 
                 13 
                 9 
               
               
                 Y Phase = 1 
                 2 
                 11 
                 3 
               
               
                   
               
             
          
         
       
     
         [0063]    A second and more comprehensive chroma centering rule, referred to as extended rule, is also described. This rule has the advantage of allowing an image to be translated, without loss of data, by any integer number of pixels. This is in addition to rotates and mirror flips. 
         [0064]    In one implementation, the extended rule is signaled with a seven-bit word (CHROMA_CENTERING_LONG) within the image bitstream, and the enumeration of phases corresponding to the syntax element CHROMA_CENTERING_LONG is as follows. CHROMA_CENTERING_LONG=CHROMA_CENTERING_X+CHROMA_CENTERING_Y*9, where CHROMA_CENTERING_X and CHROMA_CENTERING_Y are syntax elements defining the phase in the X and Y directions, as shown below in Table 2. CHROMA_CENTERING_X and CHROMA_CENTERING_Y take values between 0 and 8. Therefore, CHROMA_CENTERING_LONG can take on values between 0 and 80. Values outside this range are reserved. CHROMA_CENTERING_LONG, CHROMA_CENTERING_X and/or CHROMA_CENTERING_Y can be signaled, for example, in an image header or an image plane header. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Enumeration of values of CHROMA_CENTERING_X and 
               
               
                 CHROMA_CENTERING_Y and corresponding phase 
               
             
          
           
               
                   
                 CHROMA_CENTERING_X or Y 
                 Phase X or Y 
               
               
                   
                   
               
             
          
           
               
                   
                 8 
                 −0.5 
               
               
                   
                 7 
                 −0.25 
               
               
                   
                 0 
                 0 
               
               
                   
                 1 
                 0.25 
               
               
                   
                 2 
                 0.5 
               
               
                   
                 3 
                 0.75 
               
               
                   
                 4 
                 1.0 
               
               
                   
                 5 
                 1.25 
               
               
                   
                 6 
                 1.5 
               
               
                   
                   
               
             
          
         
       
     
         [0065]    It is possible to use other mappings in place of Tables 1 and 2. It is also possible to use other encodings of the CHROMA_CENTERING elements such as variable length codes. 
       III. Block Transform-Based Coding 
       [0066]    Transform coding is a compression technique used in many digital media (e.g., audio, image and video) compression systems. Uncompressed digital image and video is typically represented or captured as samples of picture elements or colors at locations in an image or video frame arranged in a two-dimensional (2D) grid. This is referred to as a spatial-domain representation of the image or video. For example, a typical format for images consists of a stream of 24-bit color picture element samples arranged as a grid. Each sample is a number representing color components at a pixel location in the grid within a color space, such as RGB, or YIQ, among others. Various image and video systems may use various different color, spatial and time resolutions of sampling. Similarly, digital audio is typically represented as time-sampled audio signal stream. For example, a typical audio format consists of a stream of 16-bit amplitude samples of an audio signal taken at regular time intervals. 
         [0067]    Uncompressed digital audio, image and video signals can consume considerable storage and transmission capacity. Transform coding reduces the size of digital audio, images and video by transforming the spatial-domain representation of the signal into a frequency-domain (or other like transform domain) representation, and then reducing resolution of certain generally less perceptible frequency components of the transform-domain representation. This generally produces much less perceptible degradation of the digital signal compared to reducing color or spatial resolution of images or video in the spatial domain, or of audio in the time domain. 
         [0068]    More specifically, a typical block transform-based encoder/decoder system  500  (also called a “codec”) shown in  FIG. 5  divides the uncompressed digital image&#39;s pixels into fixed-size two dimensional blocks (X 1 , . . . X n ), each block possibly overlapping with other blocks. At an encoder  510 , a linear transform  520 - 521  that does spatial-frequency analysis is applied to each block, which converts the spaced samples within the block to a set of frequency (or transform) coefficients generally representing the strength of the digital signal in corresponding frequency bands over the block interval. For compression, the transform coefficients may be selectively quantized  530  (i.e., reduced in resolution, such as by dropping least significant bits of the coefficient values or otherwise mapping values in a higher resolution number set to a lower resolution), and also entropy or variable-length coded  530  into a compressed data stream. At decoding, the transform coefficients will inversely transform  570 - 571  to nearly reconstruct the original color/spatial sampled image/video signal (reconstructed blocks {circumflex over (X)}{circumflex over (X 1 )}, {circumflex over (X)}{circumflex over (X n )}). 
         [0069]    The block transform  520 - 521  can be defined as a mathematical operation on a vector x of size N. Most often, the operation is a linear multiplication, producing the transform domain output y=Mx, M being the transform matrix. When the input data is arbitrarily long, it is segmented into N sized vectors and a block transform is applied to each segment. For the purpose of data compression, reversible block transforms are chosen. In other words, the matrix M is invertible. In multiple dimensions (e.g., for image and video), block transforms are typically implemented as separable operations. The matrix multiplication is applied separably along each dimension of the data (i.e., both rows and columns). 
         [0070]    For compression, the transform coefficients (components of vector y) may be selectively quantized (i.e., reduced in resolution, such as by dropping least significant bits of the coefficient values or otherwise mapping values in a higher resolution number set to a lower resolution), and also entropy or variable-length coded into a compressed data stream. 
         [0071]    At decoding in the decoder  550 , the inverse of these operations (dequantization/entropy decoding  560  and inverse block transform  570 - 571 ) are applied on the decoder  550  side, as shown in  FIG. 5 . While reconstructing the data, the inverse matrix M −1  (inverse transform  570 - 571 ) is applied as a multiplier to the transform domain data. When applied to the transform domain data, the inverse transform nearly reconstructs the original time-domain or spatial-domain digital media. 
         [0072]    In many block transform-based coding applications, the transform is desirably reversible to support both lossy and lossless compression depending on the quantization factor. With no quantization (generally represented as a quantization factor of 1) for example, a codec utilizing a reversible transform can exactly reproduce the input data at decoding. However, the requirement of reversibility in these applications constrains the choice of transforms upon which the codec can be designed. 
         [0073]    Many image and video compression systems, such as MPEG and Windows Media, among others, utilize transforms based on the Discrete Cosine Transform (DCT). The DCT is known to have favorable energy compaction properties that result in near-optimal data compression. In these compression systems, the inverse DCT (IDCT) is employed in the reconstruction loops in both the encoder and the decoder of the compression system for reconstructing individual image blocks. 
       IV. Exemplary Encoder/Decoder Implementation 
       [0074]      FIGS. 6 and 7  are a generalized diagram of the processes employed in a representative 2-dimensional (2D) data encoder  600  and decoder  700 . The diagrams present a generalized or simplified illustration of a compression/decompression system that can be used to implement described techniques and tools. In alternative compression/decompression systems, additional or fewer processes than those illustrated in this representative encoder and decoder can be used for the 2D data compression. For example, some encoders/decoders may also include color conversion, color formats, scalable coding, lossless coding, macroblock modes, etc. The compression system (encoder and decoder) can provide lossless and/or lossy compression of the 2D data, depending on the quantization which may be based on a quantization parameter varying from lossless to lossy. 
         [0075]    The 2D data encoder  600  produces a compressed bitstream  620  that is a more compact representation (for typical input) of 2D data  610  presented as input to the encoder. For example, the 2D data input can be an image, a frame of a video sequence, or other data having two dimensions. The 2D data encoder divides a frame of the input data into blocks (illustrated generally in  FIG. 6  as partitioning  630 ), which in the illustrated implementation are non-overlapping 4×4 pixel blocks that form a regular pattern across the plane of the frame. These blocks are grouped in clusters, called macroblocks, which are 16×16 pixels in size in this representative encoder. In turn, the macroblocks are grouped into regular structures called tiles. The tiles also form a regular pattern over the image, such that tiles in a horizontal row are of uniform height and aligned, and tiles in a vertical column are of uniform width and aligned. In the representative encoder, the tiles can be any arbitrary size that is a multiple of 16 in the horizontal and/or vertical direction. Alternative encoder implementations can divide the image into block, macroblock, tiles, or other units of other size and structure. 
         [0076]    A “forward overlap” operator  640  is applied to each edge between blocks, after which each 4×4 block is transformed using a block transform  650 . This block transform  650  can be the reversible, scale-free 2D transform described by Srinivasan, U.S. patent application Ser. No. 11/015,707, entitled, “Reversible Transform For Lossy And Lossless 2-D Data Compression,” filed Dec. 17, 2004. The overlap operator  640  can be the reversible overlap operator described by Tu et al., U.S. patent application Ser. No. 11/015,148, entitled, “Reversible Overlap Operator for Efficient Lossless Data Compression,” filed Dec. 17, 2004; and by Tu et al., U.S. patent application Ser. No. 11/035,991, entitled, “Reversible 2-Dimensional Pre-/Post-Filtering For Lapped Biorthogonal Transform,” filed Jan. 14, 2005. Alternatively, the discrete cosine transform or other block transforms and overlap operators can be used. Subsequent to the transform, the DC coefficient  660  of each 4×4 transform block is subject to a similar processing chain (tiling, forward overlap, followed by 4×4 block transform). The resulting DC transform coefficients and the AC transform coefficients  662  are quantized  670 , entropy coded  680  and packetized  690 . 
         [0077]    The decoder performs the reverse process. On the decoder side, the transform coefficient bits are extracted  710  from their respective packets, from which the coefficients are themselves decoded  720  and dequantized  730 . The DC coefficients  740  are regenerated by applying an inverse transform, and the plane of DC coefficients is “inverse overlapped” using a suitable smoothing operator applied across the DC block edges. Subsequently, the entire data is regenerated by applying the 4×4 inverse transform  750  to the DC coefficients, and the AC coefficients  742  decoded from the bitstream. Finally, the block edges in the resulting image planes are inverse overlap filtered  760 . This produces a reconstructed 2D data output  790 . 
         [0078]    In an exemplary implementation, the encoder  600  ( FIG. 6 ) compresses an input image into the compressed bitstream  620  (e.g., a file), and the decoder  700  ( FIG. 7 ) reconstructs the original input or an approximation thereof, based on whether lossless or lossy coding is employed. The process of encoding involves the application of a forward lapped transform (LT) discussed below, which is implemented with reversible 2-dimensional pre-/post-filtering also described more fully below. The decoding process involves the application of the inverse lapped transform (ILT) using the reversible 2-dimensional pre-/post-filtering. 
         [0079]    The illustrated LT and the ILT are inverses of each other, in an exact sense, and therefore can be collectively referred to as a reversible lapped transform. As a reversible transform, the LT/ILT pair can be used for lossless image compression. 
         [0080]    The input data  610  compressed by the illustrated encoder  600 /decoder  700  can be images of various color formats (e.g., RGB/YUV4:4:4, YUV4:2:2 or YUV4:2:0 color image formats). Typically, the input image always has a luminance (Y) component. If it is a RGB/YUV4:4:4, YUV4:2:2 or YUV4:2:0 image, the image also has chrominance components, such as a U component and a V component. The separate color planes or components of the image can have different spatial resolutions. In case of an input image in the YUV 4:2:0 color format for example, the U and V components have half of the width and height of the Y component. 
         [0081]    As discussed above, the encoder  600  tiles the input image or picture into macroblocks. In an exemplary implementation, the encoder  600  tiles the input image into 16×16 pixel areas (called “macroblocks”) in the Y channel (which may be 16×16, 16×8 or 8×8 areas in the U and V channels depending on the color format). Each macroblock color plane is tiled into 4×4 pixel regions or blocks. Therefore, a macroblock is composed for the various color formats in the following manner for this exemplary encoder implementation:
       For a grayscale image, each macroblock contains 16 4×4 luminance (Y) blocks.   For a YUV4:2:0 format color image, each macroblock contains 16 4×4 Y blocks, and 4 each 4×4 chrominance (U and V) blocks.   For a YUV4:2:2 format color image, each macroblock contains 16 4×4 Y blocks, and 8 each 4×4 chrominance (U and V) blocks.   For a RGB or YUV4:4:4 color image, each macroblock contains 16 blocks each of Y, U and V channels.       
 
         [0086]    Accordingly, after transform, a macroblock in this representative encoder  600 /decoder  700  has three frequency sub bands: a DC sub band (DC macroblock), a low pass sub band (low pass macroblock), and a high pass sub band (high pass macroblock). In the representative system, the low pass and/or high pass sub bands are optional in the bitstream—these sub bands may be entirely dropped. 
         [0087]    Further, the compressed data can be packed into the bitstream in one of two orderings: spatial order and frequency order. For the spatial order, different sub bands of the same macroblock within a tile are ordered together, and the resulting bitstream of each tile is written into one packet. For the frequency order, the same sub band from different macroblocks within a tile are grouped together, and thus the bitstream of a tile is written into three packets: a DC tile packet, a low pass tile packet, and a high pass tile packet. In addition, there may be other data layers. 
         [0088]    Thus, for the representative system, an image is organized in the following “dimensions”:
       Spatial dimension: Frame→Tile →Macroblock;   Frequency dimension: DC|Low pass|High pass; and   Channel dimension: Luminance|Chrominance|Chrominance — 1 . . . (e.g. as Y|U|V).       
 
         [0092]    The arrows above denote a hierarchy, whereas the vertical bars denote a partitioning. 
         [0093]    Although the representative system organizes the compressed digital media data in spatial, frequency and channel dimensions, the flexible quantization approach described here can be applied in alternative encoder/decoder systems that organize their data along fewer, additional or other dimensions. For example, the flexible quantization approach can be applied to coding using a larger number of frequency bands, other format of color channels (e.g., YIQ, RGB, etc.), additional image channels (e.g., for stereo vision or other multiple camera arrays). 
         [0094]    Having described and illustrated the principles of our invention with reference to various embodiments, it will be recognized that the various embodiments can be modified in arrangement and detail without departing from such principles. It should be understood that the programs, processes, or methods described herein are not related or limited to any particular type of computing environment, unless indicated otherwise. Various types of general purpose or specialized computing environments may be used with or perform operations in accordance with the teachings described herein. Elements of embodiments shown in software may be implemented in hardware and vice versa. 
         [0095]    In view of the many possible embodiments to which the principles of the disclosed invention may be applied, it should be recognized that the illustrated embodiments are only preferred examples of the invention and should not be taken as limiting the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims.