JPEG

Encyclopedia : J : JP : JPE : JPEG

In computing, JPEG (pronounced JAY-peg) is a commonly used standard method of lossy compression for photographic images. The file format which employs this compression is commonly also called JPEG; the most common file extensions for this format are .jpeg, .jfif, .jpg, .JPG, or .JPE although .jpg is the most common on all platforms.

JPEG itself specifies only how an image is transformed into a stream of bytes, but not how those bytes are encapsulated in any particular storage medium. A further standard, created by the Independent JPEG Group, called JFIF (JPEG File Interchange Format) specifies how to produce a file suitable for computer storage and transmission (such as over the Internet) from a JPEG stream. In common usage, when one speaks of a "JPEG file" one generally means a JFIF file, or sometimes an Exif JPEG file. There are, however, other JPEG-based file formats, such as JNG, and the TIFF format can carry JPEG data as well.

JPEG/JFIF is the format most used for storing and transmitting photographs on the World Wide Web. For this application, it is preferred to formats such as GIF, which has a limit of 256 distinct colors that is insufficient for colour photographs, and PNG, which produces much larger image files for this type of image. It is not as well suited for line drawings and other textual or iconic graphics because its compression method performs badly on these types of images, for which the PNG and GIF formats are more commonly used.

A photo of a flower compressed with successively lossier compression ratios from left to right.

The MIME media type for JPEG is image/jpeg (defined in RFC 1341).

The name JPEG stands for Joint Photographic Experts Group, the name of the joint ISO/CCITT committee which created the standard. The group was organized in 1986, issuing a standard in 1992 which was approved in 1994 as ISO 10918-1.

Contents

1 Encoding

1.1 Color space transformation
1.2 Downsampling
1.3 Discrete cosine transform
1.4 Quantization
1.5 Entropy coding
1.6 Compression ratio and artifacts
1.7 Decoding

2 Color profile
3 Usage

3.1 Photographs
3.2 Medical Imaging: JPEG's 12 bit mode

4 Other Joint Photographic Experts Group image encoding formats
5 Potential patent issues
6 See also
7 External links

Encoding

Many of the options in the JPEG standard are not commonly used. Here is a brief description of one of the more common methods of encoding when applied to an input that has 24 bits per pixel (eight each of red, green, and blue). This particular option is a lossy data compression method.

Color space transformation

First, the image is converted from RGB into a different color space called YCbCr. This is similar to the color space used by NTSC and PAL color television transmission, but is most similar to the way the MAC television transmission system works.

The Y component represents the brightness of a pixel
The Cb and Cr components together represent the chrominance

This encoding system is useful because the human eye can see more detail in the Y component than in Cb and Cr. Using this knowledge, encoders can be designed to compress images more efficiently.

Downsampling

The above transformation enables the next step, which is to reduce the Cb and Cr components (called "downsampling" or "chroma subsampling"). The ratios at which the downsampling can be done on JPEG are (no downsampling), (reduce by factor of 2 in horizontal direction), and most commonly (reduce by factor of 2 in horizontal and vertical directions). For the rest of the compression process, Y, Cb and Cr are processed separately and in a very similar manner.

Discrete cosine transform

The DCT transforms 64 pixel to a linear combination of these 64 squares

The 8x8 subimage shown in 8-bit greyscale

The compressed 8x8-squares are visible in the scaled up picture, as well as the visual artifact of the lossy compression

Next, each component (Y, Cb, Cr) of the image is "tiled" into sections of eight by eight pixels each, then each tile is converted to frequency space using a two-dimensional forward discrete cosine transform (DCT, type II). If one such 8×8 8-bit subimage is:

[\begin 52 & 55 & 61 & 66 & 70 & 61 & 64 & 73 \\ 63 & 59 & 55 & 90 & 109 & 85 & 69 & 72 \\ 62 & 59 & 68 & 113 & 144 & 104 & 66 & 73 \\ 63 & 58 & 71 & 122 & 154 & 106 & 70 & 69 \\ 67 & 61 & 68 & 104 & 126 & 88 & 68 & 70 \\ 79 & 65 & 60 & 70 & 77 & 68 & 58 & 75 \\ 85 & 71 & 64 & 59 & 55 & 61 & 65 & 83 \\ 87 & 79 & 69 & 68 & 65 & 76 & 78 & 94\end]

which is then shifted by 128 results in

[\begin -76 & -73 & -67 & -62 & -58 & -67 & -64 & -55 \\ -65 & -69 & -73 & -38 & -19 & -43 & -59 & -56 \\ -66 & -69 & -60 & -15 & 16 & -24 & -62 & -55 \\ -65 & -70 & -57 & -6 & 26 & -22 & -58 & -59 \\ -61 & -67 & -60 & -24 & -2 & -40 & -60 & -58 \\ -49 & -63 & -68 & -58 & -51 & -60 & -70 & -53 \\ -43 & -57 & -64 & -69 & -73 & -67 & -63 & -45 \\ -41 & -49 & -59 & -60 & -63 & -52 & -50 & -34\end]

and then taking the DCT and rounding to the nearest integer results in

[\begin -415 & -30 & -61 & 27 & 56 & -20 & -2 & 0 \\ 4 & -22 & -61 & 10 & 13 & -7 & -9 & 5 \\ -47 & 7 & 77 & -25 & -29 & 10 & 5 & -6 \\ -49 & 12 & 34 & -15 & -10 & 6 & 2 & 2 \\ 12 & -7 & -13 & -4 & -2 & 2 & -3 & 3 \\ -8 & 3 & 2 & -6 & -2 & 1 & 4 & 2 \\ -1 & 0 & 0 & -2 & -1 & -3 & 4 & -1 \\ 0 & 0 & -1 & -4 & -1 & 0 & 1 & 2\end]

Note the rather large value of the top-left corner. This is the DC coefficient.

Quantization

The human eye is fairly good at seeing small differences in brightness over a relatively large area, but not so good at distinguishing the exact strength of a high frequency brightness variation. This fact allows one to get away with greatly reducing the amount of information in the high frequency components. This is done by simply dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer. This is the main lossy operation in the whole process. As a result of this, it is typically the case that many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers.

A common quantization matrix is:

[\begin 16 & 11 & 10 & 16 & 24 & 40 & 51 & 61 \\ 12 & 12 & 14 & 19 & 26 & 58 & 60 & 55 \\ 14 & 13 & 16 & 24 & 40 & 57 & 69 & 56 \\ 14 & 17 & 22 & 29 & 51 & 87 & 80 & 62 \\ 18 & 22 & 37 & 56 & 68 & 109 & 103 & 77 \\ 24 & 35 & 55 & 64 & 81 & 104 & 113 & 92 \\ 49 & 64 & 78 & 87 & 103 & 121 & 120 & 101 \\ 72 & 92 & 95 & 98 & 112 & 100 & 103 & 99\end]

Using this quantization matrix with the DCT coefficient matrix from above results in:

[\begin -26 & -3 & -6 & 2 & 2 & -1 & 0 & 0 \\ 0 & -2 & -4 & 1 & 1 & 0 & 0 & 0 \\ -3 & 1 & 5 & -1 & -1 & 0 & 0 & 0 \\ -4 & 1 & 2 & -1 & 0 & 0 & 0 & 0 \\ 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end]

For example, using −415 (the DC coefficient) and rounding to the nearest integer

[\mathrm\left( \frac\right)=\mathrm\left( -25.9375\right)=-26]

Entropy coding

Entropy coding is a special form of lossless data compression. It involves arranging the image components in a "zigzag" order employing run-length encoding (RLE) algorithm that groups similar frequencies together, inserting length coding zeros, and then using Huffman coding on what is left. The JPEG standard also allows, but does not require, the use of arithmetic coding which is mathematically superior to Huffman coding. However, this feature is rarely used as it is covered by patents and because it is much slower to encode and decode compared to Huffman coding. Arithmetic coding typically makes files about 5% smaller.

The zig-zag sequence for the above quantized coefficients would be:

−26, −3, 0, −3, −2, −6, 2, −4, 1, −4, 1, 1, 5, 1, 2, −1, 1, −1, 2, 0, 0, 0, 0, 0, −1, −1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

JPEG has a special Huffman code word for ending the sequence prematurely when the remaining coefficients are zero. Using this special code word, EOB, the sequence becomes:

−26, −3, 0, −3, −2, −6, 2, −4, 1, −4, 1, 1, 5, 1, 2, −1, 1, −1, 2, 0, 0, 0, 0, 0, −1, −1, EOB

JPEG's other code words represent combinations of (a) the number of significant bits of a coefficient, including sign, and (b) the number of consecutive zero coefficients that follow it. (Once you know how many bits to expect, it takes 1 bit to represent the choices , 2 bits to represent the choices , and so forth.) In our example block, most of the quantized coefficients are small numbers that are not followed immediately by a zero coefficient. These more-frequent cases will be represented by shorter code words.

The JPEG standard provides general-purpose huffman tables; encoders may also choose to generate huffman tables optimized for the actual frequency distributions in images being encoded.

Compression ratio and artifacts

The resulting compression ratio can be varied according to need by being more or less aggressive in the divisors used in the quantization phase. Ten to one compression usually results in an image that can't be distinguished by eye from the original. 100 to one compression is usually possible, but will look distinctly artifacted compared to the original. The appropriate level of compression depends on the use to which the image will be put.

Those who use the World Wide Web may be familiar with the irregularities known as compression artifacts that appear in JPEG digital images. These are due to the quantization step of the JPEG algorithm. They are especially noticeable around eyes in pictures of faces. They can be reduced by choosing a lower level of compression; they may be eliminated by saving an image using a lossless file format, though for photographic images this will usually result in a larger file size. Compression artifacts make low-quality JPEGs unacceptable for storing heightmaps. The images created with ray-tracing programs have noticeable blocky shapes on the terrain.

Some programs allow the user to vary the amount by which individual blocks are compressed. Stronger compression is applied to areas of the image that show less artifacts. This way it is possible to make a JPEG file smaller/prettier by hand.

Decoding

Decoding to display the image consists of doing all the above in reverse.

Taking the DCT coefficient matrix (after adding the difference of the DC coefficient back in)

and multiplying it by the quantization matrix from above results in

[\begin -416 & -33 & -60 & 32 & 48 & -40 & 0 & 0 \\ 0 & -24 & -56 & 19 & 26 & 0 & 0 & 0 \\ -42 & 13 & 80 & -24 & -40 & 0 & 0 & 0 \\ -56 & 17 & 44 & -29 & 0 & 0 & 0 & 0 \\ 18 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end]

which closely resembles the original DCT coefficient matrix for the top-left portion. Taking the inverse DCT (type-III DCT) results in an image with values (still shifted down by 128)

Color profile

Usage

Photographs

NOTE: The above images are not IEEE / CCIR / EBU test images, and the encoder settings are not specified or available.

The mid-quality photo uses only one sixth the storage space but has little noticeable loss of detail or visible artifacts. However, once a certain threshold of compression is passed, compressed images show increasingly visible defects. See the article on rate distortion theory for a mathematical explanation of this threshold effect.

Medical Imaging: JPEG's 12 bit mode

Other Joint Photographic Experts Group image encoding formats

JPEG 2000 includes a lossless image compression mode, the third such JPEG standard, following Lossless JPEG (1993) and JPEG-LS (1998). These original standards, however, are not in as widespread use as lossy JPEG (1992) or lossless PNG (1996), again due to legacy and patent concerns.

Potential patent issues

The JPEG committee investigated the patent claims in 2002 and are of the opinion that they were invalidated by prior art. [link] Others have also concluded that Forgent does not have a patent that covers JPEG. [link] Nevertheless, between 2002 and 2004 Forgent was able to obtain about $90 million by licensing their patent to some 30 companies. In April 2004 Forgent sued 31 other companies to enforce further license payments. In July of the same year, a consortium of 21 large computer companies filed a countersuit, with the goal of invalidating the patent. Surprisingly, in contrast to the other major computer companies such as Sony and Philips, Microsoft has launched a major lawsuit against Forgent. In February 2006, the United States Patent and Trademark Office agreed to re-examine Forgent's JPEG patent at the request of the Public Patent Foundation ([Published news article]). On May 26, 2006 the USPTO found the patent invalid based on prior art. The USPTO also found that Forgent knew about the prior art, and didn't tell the Patent Office, making any appeal to reinstate the patent highly unlikely to succeed. ([Groklaw article])

Forgent also possesses a similar patent granted by the European Patent Office in 1994, though it is unclear how enforceable it is.[link]

The JPEG committee has as one of its explicit goals that their standards (in particular their baseline methods) be implementable without payment of license fees, and they have secured appropriate license rights for their upcoming JPEG 2000 standard from over 20 large organizations.