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JPEG Compression


One of the hottest topics in image compression technology today is JPEG. The acronym JPEG stands for the Joint Photographic Experts Group, a standards committee that had its origins within the International Standard Organization (ISO). In 1982, the ISO formed the Photographic Experts Group (PEG) to research methods of transmitting video, still images, and text over ISDN (Integrated Services Digital Network) lines. PEG's goal was to produce a set of industry standards for the transmission of graphics and image data over digital communications networks.

In 1986, a subgroup of the CCITT began to research methods of compressing color and gray-scale data for facsimile transmission. The compression methods needed for color facsimile systems were very similar to those being researched by PEG. It was therefore agreed that the two groups should combine their resources and work together toward a single standard.

In 1987, the ISO and CCITT combined their two groups into a joint committee that would research and produce a single standard of image data compression for both organizations to use. This new committee was JPEG.

Although the creators of JPEG might have envisioned a multitude of commercial applications for JPEG technology, a consumer public made hungry by the marketing promises of imaging and multimedia technology are benefiting greatly as well. Most previously developed compression methods do a relatively poor job of compressing continuous-tone image data; that is, images containing hundreds or thousands of colors taken from real-world subjects. And very few file formats can support 24-bit raster images.

GIF, for example, can store only images with a maximum pixel depth of eight bits, for a maximum of 256 colors. And its LZW compression algorithm does not work very well on typical scanned image data. The low-level noise commonly found in such data defeats LZW's ability to recognize repeated patterns.

Both TIFF and BMP are capable of storing 24-bit data, but in their pre-JPEG versions are capable of using only encoding schemes (LZW and RLE, respectively) that do not compress this type of image data very well.

JPEG provides a compression method that is capable of compressing continuous-tone image data with a pixel depth of 6 to 24 bits with reasonable speed and efficiency. And although JPEG itself does not define a standard image file format, several have been invented or modified to fill the needs of JPEG data storage.

JPEG in Perspective

Unlike all of the other compression methods described so far in this chapter, JPEG is not a single algorithm. Instead, it may be thought of as a toolkit of image compression methods that may be altered to fit the needs of the user. JPEG may be adjusted to produce very small, compressed images that are of relatively poor quality in appearance but still suitable for many applications. Conversely, JPEG is capable of producing very high-quality compressed images that are still far smaller than the original uncompressed data.

JPEG is also different in that it is primarily a lossy method of compression. Most popular image format compression schemes, such as RLE, LZW, or the CCITT standards, are lossless compression methods. That is, they do not discard any data during the encoding process. An image compressed using a lossless method is guaranteed to be identical to the original image when uncompressed.

Lossy schemes, on the other hand, throw useless data away during encoding. This is, in fact, how lossy schemes manage to obtain superior compression ratios over most lossless schemes. JPEG was designed specifically to discard information that the human eye cannot easily see. Slight changes in color are not perceived well by the human eye, while slight changes in intensity (light and dark) are. Therefore JPEG's lossy encoding tends to be more frugal with the gray-scale part of an image and to be more frivolous with the color.

JPEG was designed to compress color or gray-scale continuous-tone images of real-world subjects: photographs, video stills, or any complex graphics that resemble natural subjects. Animations, ray tracing, line art, black-and-white documents, and typical vector graphics don't compress very well under JPEG and shouldn't be expected to. And, although JPEG is now used to provide motion video compression, the standard makes no special provision for such an application.

The fact that JPEG is lossy and works only on a select type of image data might make you ask, "Why bother to use it?" It depends upon your needs. JPEG is an excellent way to store 24-bit photographic images, such as those used in imaging and multimedia applications. JPEG 24-bit (16 million color) images are superior in appearance to 8-bit (256 color) images on a VGA display and are at their most spectacular when using 24-bit display hardware (which is now quite inexpensive).

The amount of compression achieved depends upon the content of the image data. A typical photographic-quality image may be compressed from 20:1 to 25:1 without experiencing any noticeable degradation in quality. Higher compression ratios will result in image files that differ noticeably from the original image but still have an overall good image quality. And achieving a 20:1 or better compression ratio in many cases not only saves disk space, but also reduces transmission time across data networks and phone lines.

An end user can "tune" the quality of a JPEG encoder using a parameter sometimes called a quality setting or a Q factor. Although different implementations have varying scales of Q factors, a range of 1 to 100 is typical. A factor of 1 produces the smallest, worst quality images; a factor of 100 produces the largest, best quality images. The optimal Q factor depends on the image content and is therefore different for every image. The art of JPEG compression is finding the lowest Q factor that produces an image that is visibly acceptable, and preferably as close to the original as possible.

The JPEG library supplied by the Independent JPEG Group uses a quality setting scale of 1 to 100. To find the optimal compression for an image using the JPEG library, follow these steps:

  1. Encode the image using a quality setting of 75 (-Q 75).

  2. If you observe unacceptable defects in the image, increase the value, and re-encode the image.

  3. If the image quality is acceptable, decrease the setting until the image quality is barely acceptable. This will be the optimal quality setting for this image.

  4. Repeat this process for every image you have (or just encode them all using a quality setting of 75).

JPEG isn't always an ideal compression solution. There are several reasons:

  • As we have said, JPEG doesn't fit every compression need. Images containing large areas of a single color do not compress very well. In fact, JPEG will introduce "artifacts" into such images that are visible against a flat background, making them considerably worse in appearance than if you used a conventional lossless compression method. Images of a "busier" composition contain even worse artifacts, but they are considerably less noticeable against the image's more complex background.

  • JPEG can be rather slow when it is implemented only in software. If fast decompression is required, a hardware-based JPEG solution is your best bet, unless you are willing to wait for a faster software-only solution to come along or buy a faster computer.

  • JPEG is not trivial to implement. It is not likely you will be able to sit down and write your own JPEG encoder/decoder in a few evenings. We recommend that you obtain a third-party JPEG library, rather than writing your own.

  • JPEG is not supported by very many file formats. The formats that do support JPEG are all fairly new and can be expected to be revised at frequent intervals.

Baseline JPEG

The JPEG specification defines a minimal subset of the standard called baseline JPEG, which all JPEG-aware applications are required to support. This baseline uses an encoding scheme based on the Discrete Cosine Transform (DCT) to achieve compression. DCT is a generic name for a class of operations identified and published some years ago. DCT-based algorithms have since made their way into various compression methods.

DCT-based encoding algorithms are always lossy by nature. DCT algorithms are capable of achieving a high degree of compression with only minimal loss of data. This scheme is effective only for compressing continuous-tone images in which the differences between adjacent pixels are usually small. In practice, JPEG works well only on images with depths of at least four or five bits per color channel. The baseline standard actually specifies eight bits per input sample. Data of lesser bit depth can be handled by scaling it up to eight bits per sample, but the results will be bad for low-bit-depth source data, because of the large jumps between adjacent pixel values. For similar reasons, colormapped source data does not work very well, especially if the image has been dithered.

The JPEG compression scheme is divided into the following stages:

  1. Transform the image into an optimal color space.

  2. Downsample chrominance components by averaging groups of pixels together.

  3. Apply a Discrete Cosine Transform (DCT) to blocks of pixels, thus removing redundant image data.

  4. Quantize each block of DCT coefficients using weighting functions optimized for the human eye.

  5. Encode the resulting coefficients (image data) using a Huffman variable word-length algorithm to remove redundancies in the coefficients.

Figure 9-11 summarizes these steps, and the following subsections look at each of them in turn. Note that JPEG decoding performs the reverse of these steps.

Figure 9-11: JPEG compression and decompression

[Graphic: Figure 9-11]

Transform the image

The JPEG algorithm is capable of encoding images that use any type of color space. JPEG itself encodes each component in a color model separately, and it is completely independent of any color-space model, such as RGB, HSI, or CMY. The best compression ratios result if a luminance/chrominance color space, such as YUV or YCbCr, is used. (See Chapter 2 for a description of these color spaces.)

Most of the visual information to which human eyes are most sensitive is found in the high-frequency, gray-scale, luminance component (Y) of the YCbCr color space. The other two chrominance components (Cb and Cr) contain high-frequency color information to which the human eye is less sensitive. Most of this information can therefore be discarded.

In comparison, the RGB, HSI, and CMY color models spread their useful visual image information evenly across each of their three color components, making the selective discarding of information very difficult. All three color components would need to be encoded at the highest quality, resulting in a poorer compression ratio. Gray-scale images do not have a color space as such and therefore do not require transforming.

Downsample chrominance components

The simplest way of exploiting the eye's lesser sensitivity to chrominance information is simply to use fewer pixels for the chrominance channels. For example, in an image nominally 1000x1000 pixels, we might use a full 1000x1000 luminance pixels but only 500x500 pixels for each chrominance component. In this representation, each chrominance pixel covers the same area as a 2x2 block of luminance pixels. We store a total of six pixel values for each 2x2 block (four luminance values, one each for the two chrominance channels), rather than the twelve values needed if each component is represented at full resolution. Remarkably, this 50 percent reduction in data volume has almost no effect on the perceived quality of most images. Equivalent savings are not possible with conventional color models such as RGB, because in RGB each color channel carries some luminance information and so any loss of resolution is quite visible.

When the uncompressed data is supplied in a conventional format (equal resolution for all channels), a JPEG compressor must reduce the resolution of the chrominance channels by downsampling, or averaging together groups of pixels. The JPEG standard allows several different choices for the sampling ratios, or relative sizes, of the downsampled channels. The luminance channel is always left at full resolution (1:1 sampling). Typically both chrominance channels are downsampled 2:1 horizontally and either 1:1 or 2:1 vertically, meaning that a chrominance pixel covers the same area as either a 2x1 or a 2x2 block of luminance pixels. JPEG refers to these downsampling processes as 2h1v and 2h2v sampling, respectively.

Another notation commonly used is 4:2:2 sampling for 2h1v and 4:2:0 sampling for 2h2v; this notation derives from television customs (color transformation and downsampling have been in use since the beginning of color TV transmission). 2h1v sampling is fairly common because it corresponds to National Television Standards Committee (NTSC) standard TV practice, but it offers less compression than 2h2v sampling, with hardly any gain in perceived quality.

Apply a Discrete Cosine Transform

The image data is divided up into 8x8 blocks of pixels. (From this point on, each color component is processed independently, so a "pixel" means a single value, even in a color image.) A DCT is applied to each 8x8 block. DCT converts the spatial image representation into a frequency map: the low-order or "DC" term represents the average value in the block, while successive higher-order ("AC") terms represent the strength of more and more rapid changes across the width or height of the block. The highest AC term represents the strength of a cosine wave alternating from maximum to minimum at adjacent pixels.

The DCT calculation is fairly complex; in fact, this is the most costly step in JPEG compression. The point of doing it is that we have now separated out the high- and low-frequency information present in the image. We can discard high-frequency data easily without losing low-frequency information. The DCT step itself is lossless except for roundoff errors.

Quantize each block

To discard an appropriate amount of information, the compressor divides each DCT output value by a "quantization coefficient" and rounds the result to an integer. The larger the quantization coefficient, the more data is lost, because the actual DCT value is represented less and less accurately. Each of the 64 positions of the DCT output block has its own quantization coefficient, with the higher-order terms being quantized more heavily than the low-order terms (that is, the higher-order terms have larger quantization coefficients). Furthermore, separate quantization tables are employed for luminance and chrominance data, with the chrominance data being quantized more heavily than the luminance data. This allows JPEG to exploit further the eye's differing sensitivity to luminance and chrominance.

It is this step that is controlled by the "quality" setting of most JPEG compressors. The compressor starts from a built-in table that is appropriate for a medium-quality setting and increases or decreases the value of each table entry in inverse proportion to the requested quality. The complete quantization tables actually used are recorded in the compressed file so that the decompressor will know how to (approximately) reconstruct the DCT coefficients.

Selection of an appropriate quantization table is something of a black art. Most existing compressors start from a sample table developed by the ISO JPEG committee. It is likely that future research will yield better tables that provide more compression for the same perceived image quality. Implementation of improved tables should not cause any compatibility problems, because decompressors merely read the tables from the compressed file; they don't care how the table was picked.

Encode the resulting coefficients

The resulting coefficients contain a significant amount of redundant data. Huffman compression will losslessly remove the redundancies, resulting in smaller JPEG data. An optional extension to the JPEG specification allows arithmetic encoding to be used instead of Huffman for an even greater compression ratio. (See the section called "JPEG Extensions (Part 1)" below.) At this point, the JPEG data stream is ready to be transmitted across a communications channel or encapsulated inside an image file format.

JPEG Extensions (Part 1)

What we have examined thus far is only the baseline specification for JPEG. A number of extensions have been defined in Part 1 of the JPEG specification that provide progressive image buildup, improved compression ratios using arithmetic encoding, and a lossless compression scheme. These features are beyond the needs of most JPEG implementations and have therefore been defined as "not required to be supported" extensions to the JPEG standard.

Progressive image buildup

Progressive image buildup is an extension for use in applications that need to receive JPEG data streams and display them on the fly. A baseline JPEG image can be displayed only after all of the image data has been received and decoded. But some applications require that the image be displayed after only some of the data is received. Using a conventional compression method, this means displaying the first few scan lines of the image as it is decoded. In this case, even if the scan lines were interlaced, you would need at least 50 percent of the image data to get a good clue as to the content of the image. The progressive buildup extension of JPEG offers a better solution.

Progressive buildup allows an image to be sent in layers rather than scan lines. But instead of transmitting each bitplane or color channel in sequence (which wouldn't be very useful), a succession of images built up from approximations of the original image are sent. The first scan provides a low-accuracy representation of the entire image--in effect, a very low-quality JPEG compressed image. Subsequent scans gradually refine the image by increasing the effective quality factor. If the data is displayed on the fly, you would first see a crude, but recognizable, rendering of the whole image. This would appear very quickly because only a small amount of data would need to be transmitted to produce it. Each subsequent scan would improve the displayed image's quality one block at a time.

A limitation of progressive JPEG is that each scan takes essentially a full JPEG decompression cycle to display. Therefore, with typical data transmission rates, a very fast JPEG decoder (probably specialized hardware) would be needed to make effective use of progressive transmission.

A related JPEG extension provides for hierarchical storage of the same image at multiple resolutions. For example, an image might be stored at 250x250, 500x500, 1000x1000, and 2000x2000 pixels, so that the same image file could support display on low-resolution screens, medium-resolution laser printers, and high-resolution imagesetters. The higher-resolution images are stored as differences from the lower-resolution ones, so they need less space than they would need if they were stored independently. This is not the same as a progressive series, because each image is available in its own right at the full desired quality.

Arithmetic encoding

The baseline JPEG standard defines Huffman compression as the final step in the encoding process. A JPEG extension replaces the Huffman engine with a binary arithmetic entropy encoder. The use of an arithmetic coder reduces the resulting size of the JPEG data by a further 10 percent to 15 percent over the results that would be achieved by the Huffman coder. With no change in resulting image quality, this gain could be of importance in implementations where enormous quantities of JPEG images are archived.

Arithmetic encoding has several drawbacks:

  • Not all JPEG decoders support arithmetic decoding. Baseline JPEG decoders are required to support only the Huffman algorithm.

  • The arithmetic algorithm is slower in both encoding and decoding than Huffman.

  • The arithmetic coder used by JPEG (called a Q-coder) is owned by IBM and AT&T. (Mitsubishi also holds patents on arithmetic coding.) You must obtain a license from the appropriate vendors if their Q-coders are to be used as the back end of your JPEG implementation.

Lossless JPEG compression

A question that commonly arises is "At what Q factor does JPEG become lossless?" The answer is "never." Baseline JPEG is a lossy method of compression regardless of adjustments you may make in the parameters. In fact, DCT-based encoders are always lossy, because roundoff errors are inevitable in the color conversion and DCT steps. You can suppress deliberate information loss in the downsampling and quantization steps, but you still won't get an exact recreation of the original bits. Further, this minimum-loss setting is a very inefficient way to use lossy JPEG.

The JPEG standard does offer a separate lossless mode. This mode has nothing in common with the regular DCT-based algorithms, and it is currently implemented only in a few commercial applications. JPEG lossless is a form of Predictive Lossless Coding using a 2D Differential Pulse Code Modulation (DPCM) scheme. The basic premise is that the value of a pixel is combined with the values of up to three neighboring pixels to form a predictor value. The predictor value is then subtracted from the original pixel value. When the entire bitmap has been processed, the resulting predictors are compressed using either the Huffman or the binary arithmetic entropy encoding methods described in the JPEG standard.

Lossless JPEG works on images with 2 to 16 bits per pixel, but performs best on images with 6 or more bits per pixel. For such images, the typical compression ratio achieved is 2:1. For image data with fewer bits per pixels, other compression schemes do perform better.

JPEG Extensions (Part 3)

The following JPEG extensions are described in Part 3 of the JPEG specification.

Variable quantization

Variable quantization is an enhancement available to the quantization procedure of DCT-based processes. This enhancement may be used with any of the DCT-based processes defined by JPEG with the exception of the baseline process.

The process of quantization used in JPEG quantizes each of the 64 DCT coefficients using a corresponding value from a quantization table. Quantization values may be redefined prior to the start of a scan but must not be changed once they are within a scan of the compressed data stream.

Variable quantization allows the scaling of quantization values within the compressed data stream. At the start of each 8x8 block is a quantizer scale factor used to scale the quantization table values within an image component and to match these values with the AC coefficients stored in the compressed data. Quantization values may then be located and changed as needed.

Variable quantization allows the characteristics of an image to be changed to control the quality of the output based on a given model. The variable quantizer can constantly adjust during decoding to provide optimal output.

The amount of output data can also be decreased or increased by raising or lowering the quantizer scale factor. The maximum size of the resulting JPEG file or data stream may be imposed by constant adaptive adjustments made by the variable quantizer.

The variable quantization extension also allows JPEG to store image data originally encoded using a variable quantization scheme, such as MPEG. For MPEG data to be accurately transcoded into another format, the other format must support variable quantization to maintain a high compression ratio. This extension allows JPEG to support a data stream originally derived from a variably quantized source, such as an MPEG I-frame.

Selective refinement

Selective refinement is used to select a region of an image for further enhancement. This enhancement improves the resolution and detail of a region of an image. JPEG supports three types of selective refinement: hierarchical, progressive, and component. Each of these refinement processes differs in its application, effectiveness, complexity, and amount of memory required.

  • Hierarchical selective refinement is used only in the hierarchical mode of operation. It allows for a region of a frame to be refined by the next differential frame of a hierarchical sequence.

  • Progressive selective refinement is used only in the progressive mode and adds refinement. It allows a greater bit resolution of zero and non-zero DCT coefficients in a coded region of a frame.

  • Component selective refinement may be used in any mode of operation. It allows a region of a frame to contain fewer colors than are defined in the frame header.

Image tiling

Tiling is used to divide a single image into two or more smaller subimages. Tiling allows easier buffering of the image data in memory, quicker random access of the image data on disk, and the storage of images larger than 64Kx64K samples in size. JPEG supports three types of tiling: simple, pyramidal, and composite.

  • Simple tiling divides an image into two or more fixed-size tiles. All simple tiles are coded from left to right and from top to bottom and are contiguous and non-overlapping. All tiles must have the same number of samples and component identifiers and must be encoded using the same processes. Tiles on the bottom and right of the image may be smaller than the designated size of the image dimensions and will therefore not be a multiple of the tile size.

  • Pyramidal tiling also divides the image into tiles, but each tile is also tiled using several different levels of resolution. The model of this process is the JPEG Tiled Image Pyramid (JTIP), which is a model of how to create a multi-resolution pyramidal JPEG image.

    A JTIP image stores successive layers of the same image at different resolutions. The first image stored at the top of the pyramid is one-sixteenth of the defined screen size and is called a vignette. This image is used for quick displays of image contents, especially for file browsers. The next image occupies one-fourth of the screen and is called an imagette. This image is typically used when two or more images must be displayed at the same time on the screen. The next is a low-resolution, full-screen image, followed by successively higher-resolution images and ending with the original image.

    Pyramidal tiling typically uses the process of "internal tiling," where each tile is encoded as part of the same JPEG data stream. Tiles may optionally use the process of "external tiling," where each tile is a separately encoded JPEG data stream. External tiling may allow quicker access of image data, easier application of image encryption, and enhanced compatibility with certain JPEG decoders.

  • Composite tiling allows multiple-resolution versions of images to be stored and displayed as a mosaic. Composite tiling allows overlapping tiles that may be different sizes and have different scaling factors and compression parameters. Each tile is encoded separately and may be combined with other tiles without resampling.

SPIFF (Still Picture Interchange File Format)

SPIFF is an officially sanctioned JPEG file format that is intended to replace the defacto JFIF (JPEG File Interchange Format) format in use today. SPIFF includes all of the features of JFIF and adds quite a bit more functionality. SPIFF is designed so that properly written JFIF readers will read SPIFF-JPEG files as well.

For more information, see the article about SPIFF.

Other extensions

Other JPEG extensions include the addition of a version marker segment that stores the minimum level of functionality required to decode the JPEG data stream. Multiple version markers may be included to mark areas of the data stream that have differing minimum functionality requirements. The version marker also contains information indicating the processes and extension used to encode the JPEG data stream.

For Further Information About JPEG

The JPEG standard is available in English, French, or Spanish, and as a paper copy or a PostScript or Word for Windows document from the International Standards Organization (ISO) or International Telecommunication Union (ITU). Copies of the standard may be ordered from:

American National Standards Institute, Inc.
Attention: Customer Service
11 West 42nd St.
New York, NY 10036 USA
Voice: 212-642-4900

The standard is published as both an ITU Recommendation and as an ISO/IEC International Standard, and is divided into three parts: Part 1 is the actual specification, Part 2 covers compliance-testing methods, and Part 3 covers extensions to the JPEG specification. Parts 1 and 2 are at International Standard status. See these documents:

"Digital Compression and Coding of Continuous-Tone Still Images, Requirements and Guidelines," Document number ITU-T T.81 or ISO/IEC 10918-1.

"Digital Compression and Coding of Continuous-Tone Still Images, Compliance testing," Document number ITU-T T.83 or ISO/IEC 10918-2.

Part 3 is still at Committee Draft status. See this document:

"Digital Compression and Coding of Continuous-Tone Still Images, Extensions," Document number ITU-T T.84 or ISO/IEC 10918-3.

New information on JPEG and related algorithms is constantly appearing. The majority of the commercial work for JPEG is being carried out at these companies:

Eastman Kodak Corporation
232 State Street
Rochester, NY 14650
Voice: 800-242-2424
WWW: http://www.kodak.com
C-Cube Microsystems
1778 McCarthy Boulevard
Milpitas, CA 95035
Voice: 408-944-6300

See the article about the JFIF file format supported by C-Cube and the SPIFF file format defined by Part 3 of the JPEG specification.

The JPEG FAQ (Frequently Asked Questions) is a useful source of general information about JPEG. This FAQ is included on the CD-ROM ; however, because the FAQ is updated frequently, the CD-ROM version should be used only for general information. The FAQ is posted every two weeks to USENET newsgroups comp.graphics.misc, news.answers, and comp.answers. You can get the latest version of this FAQ from the news.answers archive at:

ftp://rtfm.mit.edu/pub/usenet/news.answers/jpeg-faq.

You can also get this FAQ by sending email to:

mail-server@rtfm.mit.edu

with the message "send usenet/news.answers/jpeg-faq" in the body.

A consortium of programmers, the Independent JPEG Group (IJG), has produced a public domain version of a JPEG encoder and decoder in C source code form. We have included this code on the CD-ROM. You can obtain the IJG library from various FTP sites, information services, and computer bulletin boards.

The best short technical introduction to the JPEG compression algorithm is:

Wallace, Gregory K., "The JPEG Still Picture Compression Standard," Communications of the ACM, vol. 34, no. 4, April 1991, pp. 30-44.

A more complete explanation of JPEG can be found in the following texts:

Pennebaker, William B. and Joan L. Mitchell, JPEG: Still Image Data Compression Standard, Van Nostrand Reinhold, New York, 1993.

This book contains the complete text of the ISO JPEG standards (DIS 10918-1 and 10918-2). This is by far the most complete exposition of JPEG in existence and is highly recommended.

Nelson, Mark, The Data Compression Book, M&T Books, Redwood City, CA. 1991.

This book provides good explanations and example C code for a multitude of compression methods, including JPEG. It is an excellent source if you are comfortable reading C code but don't know much about data compression in general. The book's JPEG sample code is incomplete and not very robust, but the book is a good tutorial.

Here is a short bibliography of additional JPEG reading:

Barda, J.F., "Codage et Compression des Grandes Images," Proceedings of AFNOR Multimedia and Standardization Conference, vol. 1, March 1993, pp. 300-315.

Hudson, G., H. Yasuda, and I. Sebestyen, "The International Standardization of Still Picture Compression Technique," Proceedings of the IEEE Global Telecommunications Conference, November 1988, pp. 1016-1021.

Leger, A., J. Mitchell, and Y. Yamazaki, "Still Picture Compression Algorithms Evaluated for International Standardization," Proceedings of the IEEE Global Telecommunications Conference, November 1988, pp. 1028-1032.

Leger, A., T. Omachi, and T.K. Wallace, "JPEG Still Picture Compression Algorithm," Optical Engineering, vol. 30, no. 7, July 1991, pp. 947-954.

Mitchell, J.L., and W.B. Pennebaker, "Evolving JPEG Color Data Compression Standard," in Standards for Electronic Imaging Systems, Neir, M. and M.E. Courtot, eds., vol. CR37, SPIE Press, 1991, pp. 68-97.

Netravali, A.N., and B.G. Haskell, Digital Pictures: Representation and Compression, Plenum Press, New York, 1988.

Rabbani, M., and Jones, P., Digital Image Compression Techniques, Tutorial Texts in Optical Engineering, vol. TT7, SPIE Press, 1991.


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