JPEG

n computing, JPEG (pronounced /ˈdʒeɪpɛɡ/, jay-peg) is a commonly used method of lossy compression for photographic images. The degree of compression can be adjusted, allowing a selectable tradeoff between storage size and image quality. JPEG typically achieves 10:1 compression with little perceptible loss in image quality.

JPEG compression is used in a number of image file formats. JPEG/Exif is the most common image format used by digital cameras and other photographic image capture devices; along with JPEG/JFIF, it is the most common format for storing and transmitting photographic images on the World Wide Web.^{[citation needed]}These format variations are often not distinguished, and are simply called JPEG.

The term “JPEG” is an acronym for the Joint Photographic Experts Group which created the standard. TheMIME media type for JPEG is image/jpeg (defined in RFC 1341).

JFIF

The JPEG File Interchange Format (JFIF) is an iff standard. It is a format for exchanging JPEG encoded files compliant with the JPEG Interchange Format(JIF) standard. It solves some of JIF’s limitations in regard to simple JPEG encoded file interchange. As with all JIF compliant files, image data in JFIF files is compressed using the techniques in the JPEG standard, hence JFIF is sometimes referred to as “JPEG/JFIF”. JFIF defines a number of details that are left unspecified by the JPEG Part 1 standard.

Component sample registration

JPEG allows multiple components (such as Y, Cb, and Cr) to have different resolutions, but it doesn’t define how those differing sample arrays should bealigned. The JFIF standard requires samples to be sited ”interstitially” — meaning the decoder can treat each component array as representing an array of equal-sized rectangular pixels sampled in their centers, with each array having the same exterior boundaries as the image. This is convenient for computer users, but is not the alignment used in MPEG-2 and most video applications.

[edit]Resolution and aspect ratio

The JPEG standard does not include any method of coding the resolution or aspect ratio of an image. JFIF provides resolution or aspect ratio information using an application segment extension to JPEG. It uses Application Segment #0, with a segment header of ‘JFIF\x00′, and specifies that this must be the first segment in the file, hence making it simple to recognise a JFIF file. Exif images recorded by digital cameras generally do not include this segment, but typically comply in all other respects with the JFIF standard.

[edit]Color space

JPEG does not define which color encoding is to be used for images. JFIF defines the color model to be used: either Y for greyscale, or YCbCr as defined byCCIR 601. Since this is not an absolute color space — unless an ICC profile, colorspace metadata, or an sRGB tag is provided and interpreted – a decoded JFIF image will be in a device-dependent RGB colorspace. Hence, JFIF does not by itself provide a mechanism for accurately transporting color-managed images across the Internet.

Discrete cosine transform

A discrete cosine transform (DCT) expresses a sequence of finitely many data points in terms of a sum of cosine functions oscillating at differentfrequencies. DCTs are important to numerous applications in science and engineering, from lossy compression of audio and images (where small high-frequency components can be discarded), to spectral methods for the numerical solution of partial differential equations. The use of cosine rather than sinefunctions is critical in these applications: for compression, it turns out that cosine functions are much more efficient (as explained below, fewer are needed to approximate a typical signal), whereas for differential equations the cosines express a particular choice of boundary conditions.

In particular, a DCT is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. DCTs are equivalent to DFTs ofroughly twice the length, operating on real data with even symmetry (since the Fourier transform of a real and even function is real and even), where in some variants the input and/or output data are shifted by half a sample. There are eight standard DCT variants, of which four are common.

The most common variant of discrete cosine transform is the type-II DCT, which is often called simply “the DCT”; its inverse, the type-III DCT, is correspondingly often called simply “the inverse DCT” or “the IDCT”.

The DCT is used in JPEG image compression, MJPEG, MPEG, DV, and Theora video compression. There, the two-dimensional DCT-II of  blocks are computed and the results are quantized and entropy coded. In this case, N is typically 8 and the DCT-II formula is applied to each row and column of the block. The result is an 8 × 8 transform coefficient array in which the (0,0) element (top-left) is the DC (zero-frequency) component and entries with increasing vertical and horizontal index values represent higher vertical and horizontal spatial frequencies.

JPEG compression

The compression method is usually lossy, meaning that some original image information is lost and cannot be restored (possibly affecting image quality.) There are variations on the standard baseline JPEG that are lossless; however, these are not widely supported.

There is also an interlaced “Progressive JPEG” format, in which data is compressed in multiple passes of progressively higher detail. This is ideal for large images that will be displayed while downloading over a slow connection, allowing a reasonable preview after receiving only a portion of the data. However, progressive JPEGs are not as widely supported, and even some software which does support them (such as some versions of Internet Explorer) only displays the image once it has been completely downloaded.

There are also many medical imaging and traffic systems that create and process 12-bit JPEG images, normally grayscale images. The 12-bit JPEG format has been part of the JPEG specification for some time, but again, this format is not as widely supported.

Lossless JPEG

Lossless JPEG was developed as a late addition to JPEG in 1993, using a completely different technique from the lossy JPEG standard. It uses a predictive scheme based on the three nearest (causal) neighbors (upper, left, and upper-left), and entropy coding is used on the prediction error. It is not supported by the standard Independent JPEG Group libraries, although Ken Murchison of Oceana Matrix Ltd. wrote a patch that extends the IJG library to support Lossless JPEG. Lossless JPEG has some popularity in medical imaging, and is used in DNG and some digital cameras to compress raw images, but otherwise was never widely adopted.

Lossless mode of operation

Lossless JPEG ^[1] is actually a mode of operation of JPEG. This mode exists because the Discrete Cosine Transform (DCT) based form cannot guarantee that encoder input would exactly match decoder output since the Inverse DCT is not rigorously defined. Unlike the lossy mode which is based on the DCT, the lossless coding process employs a simple predictive coding model called differential pulse code modulation (DPCM). This is a model in which predictions of the sample values are estimated from the neighboring samples that are already coded in the image. Most predictors take the average of the samples immediately above and to the left of the target sample. DPCM encodes the differences between the predicted samples instead of encoding each sample independently. The differences from one sample to the next are usually close to zero. A typical DPCM encoder is displayed in Fig.1. The block in the figure acts as a storage of the current sample which will later be a previous sample.

The main steps of lossless operation mode are depicted in Fig.2. In the process, the predictor combines up to three neighboring samples at A, B, and C shown in Fig.3 in order to produce a prediction of the sample value at the position labeled by X. The three neighboring samples must be already predicted samples. Any one of the predictors shown in the table below can be used to estimate the sample located at X ^[2]. Any one of the eight predictors listed in the table can be used. Note that selections 1, 2, and 3 are one-dimensional predictors and selections 4, 5, 6, and 7 are two-dimensional predictors. The first selection value in the table, zero, is only used for differential coding in the hierarchical mode of operation. Once all the samples are predicted, the differences between the samples can be obtained and entropy-coded in a lossless fashion usingHuffman coding or arithmetic coding.

Selection-value	Prediction
0	No prediction
1	A
2	B
3	C
4	A + B – C
5	A + (B – C)/2
6	B + (A – C)/2
7	(A + B)/2

Typically, compressions using