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ling the JPG_TRANSFORM plugin.

• FastStone Image Viewer using "Lossless Crop to File" and "JPEG Lossless Rotate".
• XnViewMP using "JPEG lossless transformations".
• ACDSee supports lossless rotation (but not lossless cropping) with its "Force lossless JPEG operations" option.

Blocks can be rotated in 90-degree increments, flipped in the horizontal, vertical and diagonal axes and moved about in the image. Not all blocks from the original image need to be used in the modified one.

The top and left edge of a JPEG image must lie on an 8 × 8 pixel block boundary, but the bottom and right edge need not do so. This limits the possible lossless crop operations, and also prevents flips and rotations of an image whose bottom or right edge does not lie on a block boundary for all channels (because the edge would end up on top or left, where – as aforementioned – a block boundary is obligatory).

Rotations where the image is not a multiple of 8 or 16, which value depends upon the chroma subsampling, are not lossless. Rotating such an image causes the blocks to be recomputed which results in loss of quality.

When using lossless cropping, if the bottom or right side of the crop region is not on a block boundary, then the rest of the data from the partially used blocks will still be present in the cropped file and can be recovered. It is also possible to transform between baseline and progressive formats without any loss of quality, since the only difference is the order in which the coefficients are placed in the file.

Furthermore, several JPEG images can be losslessly joined together, as long as they were saved with the same quality and the edges coincide with block boundaries.

JPEG files

The file format known as "JPEG Interchange Format" (JIF) is specified in Annex B of the standard. However, this "pure" file format is rarely used, primarily because of the difficulty of programming encoders and decoders that fully implement all aspects of the standard and because of certain shortcomings of the standard:

• Color space definition
• Component sub-sampling registration
• Pixel aspect ratio definition.

Several additional standards have evolved to address these issues. The first of these, released in 1992, was the JPEG File Interchange Format (or JFIF), followed in recent years by Exchangeable image file format (Exif) and ICC color profiles. Both of these formats use the actual JIF byte layout, consisting of different markers, but in addition, employ one of the JIF standard's extension points, namely the application markers: JFIF uses APP0, while Exif uses APP1. Within these segments of the file that were left for future use in the JIF standard and are not read by it, these standards add specific metadata.

Thus, in some ways, JFIF is a cut-down version of the JIF standard in that it specifies certain constraints (such as not allowing all the different encoding modes), while in other ways, it is an extension of JIF due to the added metadata. The documentation for the original JFIF standard states:

JPEG File Interchange Format is a minimal file format which enables JPEG bitstreams to be exchanged between a wide variety of platforms and applications. This minimal format does not include any of the advanced features found in the TIFF JPEG specification or any application specific file format. Nor should it, for the only purpose of this simplified format is to allow the exchange of JPEG compressed images.

Image files that employ JPEG compression are commonly called "JPEG files", and are stored in variants of the JIF image format. Most image capture devices (such as digital cameras) that output JPEG are actually creating files in the Exif format, the format that the camera industry has standardized on for metadata interchange. On the other hand, since the Exif standard does not allow color profiles, most image editing software stores JPEG in JFIF format, and also includes the APP1 segment from the Exif file to include the metadata in an almost-compliant way; the JFIF standard is interpreted somewhat flexibly.

Strictly speaking, the JFIF and Exif standards are incompatible, because each specifies that its marker segment (APP0 or APP1, respectively) appear first. In practice, most JPEG files contain a JFIF marker segment that precedes the Exif header. This allows older readers to correctly handle the older format JFIF segment, while newer readers also decode the following Exif segment, being less strict about requiring it to appear first.

JPEG filename extensions

The most common filename extensions for files employing JPEG compression are .jpg and .jpeg, though .jpe, .jfif and .jif are also used. It is also possible for JPEG data to be embedded in other file types – TIFF encoded files often embed a JPEG image as a thumbnail of the main image; and MP3 files can contain a JPEG of cover art in the ID3v2 tag.

Color profile

Many JPEG files embed an ICC color profile (color space). Commonly used color profiles include sRGB and Adobe RGB. Because these color spaces use a non-linear transformation, the dynamic range of an 8-bit JPEG file is about 11 stops; see gamma curve.

Syntax and structure

A JPEG image consists of a sequence of segments, each beginning with a marker, each of which begins with a 0xFF byte, followed by a byte indicating what kind of marker it is. Some markers consist of just those two bytes; others are followed by two bytes (high then low), indicating the length of marker-specific payload data that follows. (The length includes the two bytes for the length, but not the two bytes for the marker.) Some markers are followed by entropy-coded data; the length of such a marker does not include the entropy-coded data. Note that consecutive 0xFF bytes are used as fill bytes for padding purposes, although this fill byte padding should only ever take place for markers immediately following entropy-coded scan data (see JPEG specification section B.1.1.2 and E.1.2 for details; specifically "In all cases where markers are appended after the compressed data, optional 0xFF fill bytes may precede the marker").

Within the entropy-coded data, after any 0xFF byte, a 0x00 byte is inserted by the encoder before the next byte, so that there does not appear to be a marker where none is intended, preventing framing errors. Decoders must skip this 0x00 byte. This technique, called byte stuffing (see JPEG specification section F.1.2.3), is only applied to the entropy-coded data, not to marker payload data. Note however that entropy-coded data has a few markers of its own; specifically the Reset markers (0xD0 through 0xD7), which are used to isolate independent chunks of entropy-coded data to allow parallel decoding, and encoders are free to insert these Reset markers at regular intervals (although not all encoders do this).

There are other Start Of Frame markers that introduce other kinds of JPEG encodings.

Since several vendors might use the same APPn marker type, application-specific markers often begin with a standard or vendor name (e.g., "Exif" or "Adobe") or some other identifying string.

At a restart marker, block-to-block predictor variables are reset, and the bitstream is synchronized to a byte boundary. Restart markers provide means for recovery after bitstream error, such as transmission over an unreliable network or file corruption. Since the runs of macroblocks between restart markers may be independently decoded, these runs may be decoded in parallel.

JPEG codec example

Although a JPEG file can be encoded in various ways, most commonly it is done with JFIF encoding. The encoding process consists of several steps:

1. The representation of the colors in the image is converted from RGB to Y′C_BC_R, consisting of one luma component (Y'), representing brightness, and two chroma components, (C_B and C_R), representing color. This step is sometimes skipped.
2. The resolution of the chroma data is reduced, usually by a factor of 2 or 3. This reflects the fact that the eye is less sensitive to fine color details than to fine brightness details.
3. The image is split into blocks of 8×8 pixels, and for each block, each of the Y, C_B, and C_R data undergoes the discrete cosine transform (DCT). A DCT is similar to a Fourier transform in the sense that it produces a kind of spatial frequency spectrum.
4. The amplitudes of the frequency components are quantized. Human vision is much more sensitive to small variations in color or brightness over large areas than to the strength of high-frequency brightness variations. Therefore, the magnitudes of the high-frequency components are stored with a lower accuracy than the low-frequency components. The quality setting of the encoder (for example 50 or 95 on a scale of 0–100 in the Independent JPEG Group's library) affects to what extent the resolution of each frequency component is reduced. If an excessively low quality setting is used, the high-frequency components are discarded altogether.
5. The resulting data for all 8×8 blocks is further compressed with a lossless algorithm, a variant of Huffman encoding.

The decoding process reverses these steps, except the quantization because it is irreversible. In the remainder of this section, the encoding and decoding processes are described in more detail.

Encoding

Many of the options in the JPEG standard are not commonly used, and as mentioned above, most image software uses the simpler JFIF format when creating a JPEG file, which among other things specifies the encoding method. 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 should be converted from RGB into a different color space called Y′C_BC_R (or, informally, YCbCr). It has three components Y', C_B and C_R: the Y' component represents the brightness of a pixel, and the C_B and C_R components represent the chrominance (split into blue and red components). This is basically the same color space as used by digital color television as well as digital video including video DVDs, and is similar to the way color is represented in analog PAL video and MAC (but not by analog NTSC, which uses the YIQ color space). The Y′C_BC_R color space conversion allows greater compression without a significant effect on perceptual image quality (or greater perceptual image quality for the same compression). The compression is more efficient because the brightness information, which is more important to the eventual perceptual quality of the image, is confined to a single channel. This more closely corresponds to the perception of color in the human visual system. The color transformation also improves compression by statistical decorrelation.

A particular conversion to Y′C_BC_R is specified in the JFIF standard, and should be performed for the resulting JPEG file to have maximum compatibility. However, some JPEG implementations in "highest quality" mode do not apply this step and instead keep the color information in the RGB color model, where the image is stored in separate channels for red, green and blue brightness components. This results in less efficient compression, and would not likely be used when file size is especially important.

Downsampling

Due to the densities of color- and brightness-sensitive receptors in the human eye, humans can see considerably more fine detail in the brightness of an image (the Y' component) than in the hue and color saturation of an image (the Cb and Cr components). Using this knowledge, encoders can be designed to compress images more efficiently.

The transformation into the Y′C_BC_R color model enables the next usual step, which is to reduce the spatial resolution of the Cb and Cr components (called "downsampling" or "chroma subsampling"). The ratios at which the downsampling is ordinarily done for JPEG images are 4:4:4 (no downsampling), 4:2:2 (reduction by a factor of 2 in the horizontal direction), or (most commonly) 4:2:0 (reduction by a factor of 2 in both the horizontal and vertical directions). For the rest of the compression process, Y', Cb and Cr are processed separately and in a very similar manner.

Block splitting

After subsampling, each channel must be split into 8×8 blocks. Depending on chroma subsampling, this yields Minimum Coded Unit (MCU) blocks of size 8×8 (4:4:4 – no subsampling), 16×8 (4:2:2), or most commonly 16×16 (4:2:0). In video compression MCUs are called macroblocks.

If the data for a channel does not represent an integer number of blocks then the encoder must fill the remaining area of the incomplete blocks with some form of dummy data. Filling the edges with a fixed color (for example, black) can create ringing artifacts along the visible part of the border; repeating the edge pixels is a common technique that reduces (but does not necessarily completely eliminate) such artifacts, and more sophisticated border filling techniques can also be applied.

Discrete cosine transform

Next, each 8×8 block of each component (Y, Cb, Cr) is converted to a frequency-domain representation, using a normalized, two-dimensional type-II discrete cosine transform (DCT), see Citation 1 in discrete cosine transform. The DCT is sometimes referred to as "type-II DCT" in the context of a family of transforms as in discrete cosine transform, and the corresponding inverse (IDCT) is denoted as "type-III DCT".

As an example, one such 8×8 8-bit subimage might be:

${\displaystyle \left.}$

Before computing the DCT of the 8×8 block, its values are shifted from a positive range to one centered on zero. For an 8-bit image, each entry in the original block falls in the range ${\displaystyle }$. The midpoint of the range (in this case, the value 128) is subtracted from each entry to produce a data range that is centered on zero, so that the modified range is ${\displaystyle }$. This step reduces the dynamic range requirements in the DCT processing stage that follows.

This step results in the following values:

${\displaystyle g={\begin{array}{c}x\\\longrightarrow \\\left\end{array}}{\Bigg \downarrow }y.}$

The next step is to take the two-dimensional DCT, which is given by:

${\displaystyle \ G_{u,v}={\frac {1}{4}}\alpha (u)\alpha (v)\sum _{x=0}^{7}\sum _{y=0}^{7}g_{x,y}\cos \left\cos \left}$

where

• ${\displaystyle \ u}$ is the horizontal spatial frequency, for the integers ${\displaystyle \ 0\leq u<8}$.
• ${\displaystyle \ v}$ is the vertical spatial frequency, for the integers ${\displaystyle \ 0\leq v<8}$.
• ${\displaystyle \alpha (u)={\begin{cases}{\frac {1}{\sqrt {2}}},&{\mbox{if }}u=0\\1,&{\mbox{otherwise}}\end{cases}}}$ is a normalizing scale factor to make the transformation orthonormal
• ${\displaystyle \ g_{x,y}}$ is the pixel value at coordinates ${\displaystyle \ (x,y)}$
• ${\displaystyle \ G_{u,v}}$ is the DCT coefficient at coordinates ${\displaystyle \ (u,v).}$

If we perform this transformation on our matrix above, we get the following (rounded to the nearest two digits beyond the decimal point):

${\displaystyle G={\begin{array}{c}u\\\longrightarrow \\\left\end{array}}{\Bigg \downarrow }v.}$

Note the top-left corner entry with the rather large magnitude. This is the DC coefficient (also called the constant component), which defines the basic hue for the entire block. The remaining 63 coefficients are the AC coefficients (also called the alternating components). The advantage of the DCT is its tendency to aggregate most of the signal in one corner of the result, as may be seen above. The quantization step to follow accentuates this effect while simultaneously reducing the overall size of the DCT coefficients, resulting in a signal that is easy to compress efficiently in the entropy stage.

The DCT temporarily increases the bit-depth of the data, since the DCT coefficients of an 8-bit/component image take up to 11 or more bits (depending on fidelity of the DCT calculation) to store. This may force the codec to temporarily use 16-bit numbers to hold these coefficients, doubling the size of the image representation at this point; these values are typically reduced back to 8-bit values by the quantization step. The temporary increase in size at this stage is not a performance concern for most JPEG implementations, since typically only a very small part of the image is stored in full DCT form at any given time during the image encoding or decoding process.

Quantization

The human eye is 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 allows one to greatly reduce 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 rounding operation is the only lossy operation in the whole process (other than chroma subsampling) if the DCT computation is performed with sufficiently high precision. 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, which take many fewer bits to represent.

The elements in the quantization matrix control the compression ratio, with larger values producing greater compression. A typical quantization matrix (for a quality of 50% as specified in the original JPEG Standard), is as follows:

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

The quantized DCT coefficients are computed with

${\displaystyle B_{j,k}=\mathrm {round} \left({\frac {G_{j,k}}{Q_{j,k}}}\right){\mbox{ for }}j=0,1,2,\ldots ,7;k=0,1,2,\ldots ,7}$

where ${\displaystyle G}$ is the unquantized DCT coefficients; ${\displaystyle Q}$ is the quantization matrix above; and ${\displaystyle B}$ is the quantized DCT coefficients.

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

${\displaystyle B=\left.}$

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

${\displaystyle \mathrm {round} \left({\frac {-415.37}{16}}\right)=\mathrm {round} \left(-25.96\right)=-26.}$

Notice that most of the higher-frequency elements of the sub-block (i.e., those with an x or y spatial frequency greater than 4) are quantized into zero values.

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, decoders to support the use of arithmetic coding, which is mathematically superior to Huffman coding. However, this feature has rarely been used, as it was historically covered by patents requiring royalty-bearing licenses, and because it is slower to encode and decode compared to Huffman coding. Arithmetic coding typically makes files about 5–7% smaller.

The previous quantized DC coefficient is used to predict the current quantized DC coefficient. The difference between the two is encoded rather than the actual value. The encoding of the 63 quantized AC coefficients does not use such prediction differencing.

The zigzag sequence for the above quantized coefficients are shown below. (The format shown is just for ease of understanding/viewing.)

−26
−3	0
−3	−2	−6
2	−4	1	−3
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

If the i-th block is represented by ${\displaystyle B_{i}}$ and positions within each block are represented by ${\displaystyle (p,q)}$ where ${\displaystyle p=0,1,...,7}$ and ${\displaystyle q=0,1,...,7}$, then any coefficient in the DCT image can be represented as ${\displaystyle B_{i}(p,q)}$. Thus, in the above scheme, the order of encoding pixels (for the i-th block) is ${\displaystyle B_{i}(0,0)}$, ${\displaystyle B_{i}(0,1)}$, ${\displaystyle B_{i}(1,0)}$, ${\displaystyle B_{i}(2,0)}$, ${\displaystyle B_{i}(1,1)}$, ${\displaystyle B_{i}(0,2)}$, ${\displaystyle B_{i}(0,3)}$, ${\displaystyle B_{i}(1,2)}$ and so on.

This encoding mode is called baseline sequential encoding. Baseline JPEG also supports progressive encoding. While sequential encoding encodes coefficients of a single block at a time (in a zigzag manner), progressive encoding encodes similar-positioned batch of coefficients of all blocks in one go (called a scan), followed by the next batch of coefficients of all blocks, and so on. For example, if the image is divided into N 8×8 blocks ${\displaystyle B_{0},B_{1},B_{2},...,B_{n-1}}$, then a 3-scan progressive encoding encodes DC component, ${\displaystyle B_{i}(0,0)}$ for all blocks, i.e., for all ${\displaystyle i=0,1,2,...,N-1}$, in first scan. This is followed by the second scan which encoding a few more components (assuming four more components, they are ${\displaystyle B_{i}(0,1)}$ to ${\displaystyle B_{i}(1,1)}$, still in a zigzag manner) coefficients of all blocks (so the sequence is: ${\displaystyle B_{0}(0,1),B_{0}(1,0),B_{0}(2,0),B_{0}(1,1),B_{1}(0,1),B_{1}(1,0),...,B_{N}(2,0),B_{N}(1,1)}$), followed by all the remained coefficients of all blocks in the last scan.

Once all similar-positioned coefficients have been encoded, the next position to be encoded is the one occurring next in the zigzag traversal as indicated in the figure above. It has been found that baseline progressive JPEG encoding usually gives better compression as compared to baseline sequential JPEG due to the ability to use different Huffman tables (see below) tailored for different frequencies on each "scan" or "pass" (which includes similar-positioned coefficients), though the difference is not too large.

In the rest of the article, it is assumed that the coefficient pattern generated is due to sequential mode.

In order to encode the above generated coefficient pattern, JPEG uses Huffman encoding. 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.

The process of encoding the zig-zag quantized data begins with a run-length encoding explained below, where:

• x is the non-zero, quantized AC coefficient.
• RUNLENGTH is the number of zeroes that came before this non-zero AC coefficient.
• SIZE is the number of bits required to represent x.
• AMPLITUDE is the bit-representation of x.

The run-length encoding works by examining each non-zero AC coefficient x and determining how many zeroes came before the previous AC coefficient. With this information, two symbols are created:

Symbol 1	Symbol 2
(RUNLENGTH, SIZE)	(AMPLITUDE)

Both RUNLENGTH and SIZE rest on the same byte, meaning that each only contains four bits of information. The higher bits deal with the number of zeroes, while the lower bits denote the number of bits necessary to encode the value of x.

This has the immediate implication of Symbol 1 being only able store information regarding the first 15 zeroes preceding the non-zero AC coefficient. However, JPEG defines two special Huffman code words. One is for ending the sequence prematurely when the remaining coefficients are zero (called "End-of-Block" or "EOB"), and another when the run of zeroes goes beyond 15 before reaching a non-zero AC coefficient. In such a case where 16 zeroes are encountered before a given non-zero AC coefficient, Symbol 1 is encoded "specially" as: (15, 0)(0).

The overall process continues until "EOB" – denoted by (0, 0) – is reached.

With this in mind, the sequence from earlier becomes:

(0, 2)(-3);(1, 2)(-3);(0, 1)(-2);(0, 2)(-6);(0, 1)(2);(0, 1)(-4);(0, 1)(1);(0, 2)(-3);(0, 1)(1);(0, 1)(1);

(0, 2)(5);(0, 1)(1);(0, 1)(2);(0, 1)(-1);(0, 1)(1);(0, 1)(-1);(0, 1)(2);(5, 1)(-1);(0, 1)(-1);(0, 0);

(The first value in the matrix, −26, is the DC coefficient; it is not encoded the same way. See above.)

From here, frequency calculations are made based on occurrences of the coefficients. In our example block, most of the quantized coefficients are small numbers that are not preceded immediately by a zero coefficient. These more-frequent cases will be represented by shorter code words.

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 cannot be distinguished by eye from the original. A compression ratio of 100:1 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.

External image
Illustration of edge busyness

Those who use the World Wide Web may be familiar with the irregularities known as compression artifacts that appear in JPEG images, which may take the form of noise around contrasting edges (especially curves and corners), or "blocky" images. These are due to the quantization step of the JPEG algorithm. They are especially noticeable around sharp corners between contrasting colors (text is a good example, as it contains many such corners). The analogous artifacts in MPEG video are referred to as mosquito noise, as the resulting "edge busyness" and spurious dots, which change over time, resemble mosquitoes swarming around the object.

These artifacts can be reduced by choosing a lower level of compression; they may be completely avoided by saving an image using a lossless file format, though this will result in a larger file size. The images created with ray-tracing programs have noticeable blocky shapes on the terrain. Certain low-intensity compression artifacts might be acceptable when simply viewing the images, but can be emphasized if the image is subsequently processed, usually resulting in unacceptable quality. Consider the example below, demonstrating the effect of lossy compression on an edge detection processing step.

Image	Lossless compression	Lossy compression
Original
Processed by Canny edge detector

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 fewer artifacts. This way it is possible to manually reduce JPEG file size with less loss of quality.

Since the quantization stage always results in a loss of information, JPEG standard is always a lossy compression codec. (Information is lost both in quantizing and rounding of the floating-point numbers.) Even if the quantization matrix is a matrix of ones, information will still be lost in the rounding step.

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)

${\displaystyle \left}$

and taking the entry-for-entry product with the quantization matrix from above results in

${\displaystyle \left}$

which closely resembles the original DCT coefficient matrix for the top-left portion.

The next step is to take the two-dimensional inverse DCT (a 2D type-III DCT), which is given by:

${\displaystyle f_{x,y}={\frac {1}{4}}\sum _{u=0}^{7}\sum _{v=0}^{7}\alpha (u)\alpha (v)F_{u,v}\cos \left\cos \left}$

where

• ${\displaystyle \ x}$ is the pixel row, for the integers ${\displaystyle \ 0\leq x<8}$.
• ${\displaystyle \ y}$ is the pixel column, for the integers ${\displaystyle \ 0\leq y<8}$.
• ${\displaystyle \ \alpha (u)}$ is defined as above, for the integers ${\displaystyle \ 0\leq u<8}$.
• ${\displaystyle \ F_{u,v}}$ is the reconstructed approximate coefficient at coordinates ${\displaystyle \ (u,v).}$
• ${\displaystyle \ f_{x,y}}$ is the reconstructed pixel value at coordinates ${\displaystyle \ (x,y)}$

Rounding the output to integer values (since the original had integer values) results in an image with values (still shifted down by 128)

${\displaystyle \left}$

and adding 128 to each entry

${\displaystyle \left.}$

This is the decompressed subimage. In general, the decompression process may produce values outside the original input range of ${\displaystyle }$. If this occurs, the decoder needs to clip the output values so as to keep them within that range to prevent overflow when storing the decompressed image with the original bit depth.

The decompressed subimage can be compared to the original subimage (also see images to the right) by taking the difference (original − uncompressed) results in the following error values:

${\displaystyle \left}$

with an average absolute error of about 5 values per pixels (i.e., ${\displaystyle {\frac {1}{64}}\sum _{x=0}^{7}\sum _{y=0}^{7}|e(x,y)|=4.8750}$).

The error is most noticeable in the bottom-left corner where the bottom-left pixel becomes darker than the pixel to its immediate right.

Required precision

The encoding description in the JPEG standard does not fix the precision needed for the output compressed image. However, the JPEG standard (and the similar MPEG standards) includes some precision requirements for the decoding, including all parts of the decoding process (variable length decoding, inverse DCT, dequantization, renormalization of outputs); the output from the reference algorithm must not exceed:

• a maximum of one bit of difference for each pixel component
• low mean square error over each 8×8-pixel block
• very low mean error over each 8×8-pixel block
• very low mean square error over the whole image
• extremely low mean error over the whole image

These assertions are tested on a large set of randomized input images, to handle the worst cases. The former IEEE 1180–1990 standard contained some similar precision requirements. The precision has a consequence on the implementation of decoders, and it is critical because some encoding processes (notably used for encoding sequences of images like MPEG) need to be able to construct, on the encoder side, a reference decoded image. In order to support 8-bit precision per pixel component output, dequantization and inverse DCT transforms are typically implemented with at least 14-bit precision in optimized decoders.

Effects of JPEG compression

JPEG compression artifacts blend well into photographs with detailed non-uniform textures, allowing higher compression ratios. Notice how a higher compression ratio first affects the high-frequency textures in the upper-left corner of the image, and how the contrasting lines become more fuzzy. The very high compression ratio severely affects the quality of the image, although the overall colors and image form are still recognizable. However, the precision of colors suffer less (for a human eye) than the precision of contours (based on luminance). This justifies the fact that images should be first transformed in a color model separating the luminance from the chromatic information, before subsampling the chromatic planes (which may also use lower quality quantization) in order to preserve the precision of the luminance plane with more information bits.

Sample photographs

For information, the uncompressed 24-bit RGB bitmap image below (73,242 pixels) would require 219,726 bytes (excluding all other information headers). The filesizes indicated below include the internal JPEG information headers and some metadata. For highest quality images (Q=100), about 8.25 bits per color pixel is required. On grayscale images, a minimum of 6.5 bits per pixel is enough (a comparable Q=100 quality color information requires about 25% more encoded bits). The highest quality image below (Q=100) is encoded at nine bits per color pixel, the medium quality image (Q=25) uses one bit per color pixel. For most applications, the quality factor should not go below 0.75 bit per pixel (Q=12.5), as demonstrated by the low quality image. The image at lowest quality uses only 0.13 bit per pixel, and displays very poor color. This is useful when the image will be displayed in a significantly scaled-down size. A method for creating better quantization matrices for a given image quality using PSNR instead of the Q factor is described in Minguillón & Pujol (2001).

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

Image	Quality	Size (bytes)	Compression ratio	Comment
	Highest quality (Q = 100)	81,447	2.7:1	Extremely minor artifacts
	High quality (Q = 50)	14,679	15:1	Initial signs of subimage artifacts
	Medium quality (Q = 25)	9,407	23:1	Stronger artifacts; loss of high frequency information
	Low quality (Q = 10)	4,787	46:1	Severe high frequency loss leads to obvious artifacts on subimage boundaries ("macroblocking")
	Lowest quality (Q = 1)	1,523	144:1	Extreme loss of color and detail; the leaves are nearly unrecognizable.

The medium quality photo uses only 4.3% of the storage space required for the uncompressed image, 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. A particular limitation of JPEG in this regard is its non-overlapped 8×8 block transform structure. More modern designs such as JPEG 2000 and JPEG XR exhibit a more graceful degradation of quality as the bit usage decreases – by using transforms with a larger spatial extent for the lower frequency coefficients and by using overlapping transform basis functions.

Lossless further compression

From 2004 to 2008, new research emerged on ways to further compress the data contained in JPEG images without modifying the represented image. This has applications in scenarios where the original image is only available in JPEG format, and its size needs to be reduced for archiving or transmission. Standard general-purpose compression tools cannot significantly compress JPEG files.

Typically, such schemes take advantage of improvements to the naive scheme for coding DCT coefficients, which fails to take into account:

• Correlations between magnitudes of adjacent coefficients in the same block;
• Correlations between magnitudes of the same coefficient in adjacent blocks;
• Correlations between magnitudes of the same coefficient/block in different channels;
• The DC coefficients when taken together resemble a downscale version of the original image multiplied by a scaling factor. Well-known schemes for lossless coding of continuous-tone images can be applied, achieving somewhat better compression than the Huffman coded DPCM used in JPEG.

Some standard but rarely used options already exist in JPEG to improve the efficiency of coding DCT coefficients: the arithmetic coding option, and the progressive coding option (which produces lower bitrates because values for each coefficient are coded independently, and each coefficient has a significantly different distribution). Modern methods have improved on these techniques by reordering coefficients to group coefficients of larger magnitude together; using adjacent coefficients and blocks to predict new coefficient values; dividing blocks or coefficients up among a small number of independently coded models based on their statistics and adjacent values; and most recently, by decoding blocks, predicting subsequent blocks in the spatial domain, and then encoding these to generate predictions for DCT coefficients.

Typically, such methods can compress existing JPEG files between 15 and 25 percent, and for JPEGs compressed at low-quality settings, can produce improvements of up to 65%.

A freely available tool called packJPG is based on the 2007 paper "Improved Redundancy Reduction for JPEG Files."

Derived formats for stereoscopic 3D

JPEG Stereoscopic

JPS is a stereoscopic JPEG image used for creating 3D effects from 2D images. It contains two static images, one for the left eye and one for the right eye; encoded as two side-by-side images in a single JPG file. JPEG Stereoscopic (JPS, extension .jps) is a JPEG-based format for stereoscopic images. It has a range of configurations stored in the JPEG APP3 marker field, but usually contains one image of double width, representing two images of identical size in cross-eyed (i.e. left frame on the right half of the image and vice versa) side-by-side arrangement. This file format can be viewed as a JPEG without any special software, or can be processed for rendering in other modes.

JPEG Multi-Picture Format

JPEG Multi-Picture Format (MPO, extension .mpo) is a JPEG-based format for storing multiple images in a single file. It contains two or more JPEG files concatenated together. It also defines a JPEG APP2 marker segment for image description. Various devices use it to store 3D images, such as Fujifilm FinePix Real 3D W1, HTC Evo 3D, JVC GY-HMZ1U AVCHD/MVC extension camcorder, Nintendo 3DS, Panasonic Lumix DMC-TZ20, DMC-TZ30, DMC-TZ60, DMC-TS4 (FT4), and Sony DSC-HX7V. Other devices use it to store "preview images" that can be displayed on a TV.

In the last few years, due to the growing use of stereoscopic images, much effort has been spent by the scientific community to develop algorithms for stereoscopic image compression.

Implementations

A very important implementation of a JPEG codec is the free programming library libjpeg of the Independent JPEG Group. It was first published in 1991 and was key for the success of the standard. This library or a direct derivative of it is used in countless applications. Recent versions introduce proprietary extensions which broke ABI compatibility with previous versions.

In March 2017, Google released the open source project Guetzli, which trades off a much longer encoding time for smaller file size (similar to what Zopfli does for PNG and other lossless data formats).

ISO/IEC Joint Photography Experts Group maintains a reference software implementation which can encode both base JPEG (ISO/IEC 10918-1 and 18477-1) and JPEG XT extensions (ISO/IEC 18477 Parts 2 and 6-9), as well as JPEG-LS (ISO/IEC 14495).

JPEG XT

JPEG XT (ISO/IEC 18477) was published in June 2015; it extends base JPEG format with support for higher integer bit depths (up to 16 bit), high dynamic range imaging and floating-point coding, lossless coding, and alpha channel coding. Extensions are backward compatible with the base JPEG/JFIF file format and 8-bit lossy compressed image. JPEG XT uses an extensible file format based on JFIF. Extension layers are used to modify the JPEG 8-bit base layer and restore the high-resolution image. Existing software is forward compatible and can read the JPEG XT binary stream, though it would only decode the base 8-bit layer.

JPEG XL

Since August 2017, JTC1/SC29/WG1 issued a series of draft calls for proposals on JPEG XL – the next generation image compression standard with substantially better compression efficiency (60% improvement) comparing to JPEG. The standard is expected to exceed the still image compression performance shown by HEVC HM, Daala and WebP, and unlike previous efforts attempting to replace JPEG, to provide lossless more efficient recompression transport and storage option for traditional JPEG images. The core requirements include support for very high-resolution images (at least 40 MP), 8–10 bits per component, RGB/YCbCr/ICtCp color encoding, animated images, alpha channel coding, Rec. 709 color space (sRGB) and gamma function (2.4-power), Rec. 2100 wide color gamut color space (Rec. 2020) and high dynamic range transfer functions (PQ and HLG), and high-quality compression of synthetic images, such as bitmap fonts and gradients. The standard should also offer higher bit depths (12–16 bit integer and floating point), additional color spaces and transfer functions (such as Log C from Arri), embedded preview images, lossless alpha channel encoding, image region coding, and low-complexity encoding. Any patented technologies would be licensed on a royalty-free basis. The proposals were submitted by September 2018, leading to a committee draft in July 2019, with current target publication date in October 2019.

See also

• Better Portable Graphics, a format based on intra-frame encoding of the HEVC
• C-Cube, an early implementer of JPEG in chip form
• Comparison of graphics file formats
• Comparison of layout engines (graphics)
• Deblocking filter (video), the similar deblocking methods could be applied to JPEG
• Design rule for Camera File system (DCF)
• File extensions
• Graphics editing program
• High Efficiency Image File Format, image container format for HEVC and other image coding formats
• Lenna (test image), the traditional standard image used to test image processing algorithms
• Lossless Image Codec FELICS
• Motion JPEG
• WebP

References

1. "Why You Should Always Rotate Original JPEG Photos Losslessly". Petapixel.com. 14 August 2012. Retrieved 16 October 2017.
2. "JFIF File Format as PDF" (PDF).
3. Tom Lane (1999-03-29). "JPEG image compression FAQ". Retrieved 2007-09-11. (q. 14: "Why all the argument about file formats?")
4. "ISO/IEC 10918-1 : 1993(E) p.36".
5. Thomas G. Lane. "Advanced Features: Compression parameter selection". Using the IJG JPEG Library.
6. Ryan, Dan (2012-06-20). E - Learning Modules: Dlr Associates Series. AuthorHouse. ISBN 9781468575200.
7. "DC / AC Frequency Questions - Doom9's Forum". forum.doom9.org. Retrieved 16 October 2017.
8. ^ Phuc-Tue Le Dinh and Jacques Patry. Video compression artifacts and MPEG noise reduction Archived 2006-03-14 at the Wayback Machine. Video Imaging DesignLine. February 24, 2006. Retrieved May 28, 2009.
9. "3.9 mosquito noise: Form of edge busyness distortion sometimes associated with movement, characterized by moving artifacts and/or blotchy noise patterns superimposed over the objects (resembling a mosquito flying around a person's head and shoulders)." ITU-T Rec. P.930 (08/96) Principles of a reference impairment system for video Archived 2010-02-16 at the Wayback Machine
10. Julià Minguillón, Jaume Pujol (April 2001). "JPEG standard uniform quantization error modeling with applications to sequential and progressive operation modes" (PDF). Electronic Imaging. 10 (2): 475–485. Bibcode:2001JEI....10..475M. doi:10.1117/1.1344592. hdl:10609/6263.
11. ^ I. Bauermann and E. Steinbacj. Further Lossless Compression of JPEG Images. Proc. of Picture Coding Symposium (PCS 2004), San Francisco, US, December 15–17, 2004.
12. ^ N. Ponomarenko, K. Egiazarian, V. Lukin and J. Astola. Additional Lossless Compression of JPEG Images, Proc. of the 4th Intl. Symposium on Image and Signal Processing and Analysis (ISPA 2005), Zagreb, Croatia, pp. 117–120, September 15–17, 2005.
13. ^ M. Stirner and G. Seelmann. Improved Redundancy Reduction for JPEG Files. Proc. of Picture Coding Symposium (PCS 2007), Lisbon, Portugal, November 7–9, 2007
14. ^ Ichiro Matsuda, Yukio Nomoto, Kei Wakabayashi and Susumu Itoh. Lossless Re-encoding of JPEG images using block-adaptive intra prediction. Proceedings of the 16th European Signal Processing Conference (EUSIPCO 2008).
15. "Latest Binary Releases of packJPG: V2.3a". January 3, 2008. Archived from the original on January 23, 2009.
16. "General Purpose Stereoscopic Data Descriptor" (PDF). VRex, Inc., Elmsford, New York, US. 1997. Archived from the original (PDF) on 2011-10-30. {{cite web}}: Unknown parameter |authors= ignored (help)
17. Tim Kemp, JPS files
18. "Multi-Picture Format" (PDF). 2009. Archived from the original (PDF) on 2016-04-05. Retrieved 2015-12-30.
19. "MPO2Stereo: Convert Fujifilm MPO files to JPEG stereo pairs", Mtbs3d.com, retrieved 12 January 2010
20. Alessandro Ortis; Sebastiano Battiato (2015), Sitnik, Robert; Puech, William (eds.), "A new fast matching method for adaptive compression of stereoscopic images", Three-Dimensional Image Processing, Three-Dimensional Image Processing, Measurement (3DIPM), and Applications 2015, 9393, SPIE - Three-Dimensional Image Processing, Measurement (3DIPM), and Applications 2015: 93930K, Bibcode:2015SPIE.9393E..0KO, doi:10.1117/12.2086372, S2CID 18879942, retrieved 30 April 2015
21. Alessandro Ortis; Francesco Rundo; Giuseppe Di Giore; Sebastiano Battiato, Adaptive Compression of Stereoscopic Images, International Conference on Image Analysis and Processing (ICIAP) 2013, retrieved 30 April 2015
22. "Overview of JPEG". jpeg.org. Retrieved 2017-10-16.
23. "Announcing Guetzli: A New Open Source JPEG Encoder". Research.googleblog.com. Retrieved 16 October 2017.
24. "JPEG - JPEG XT". jpeg.org.
25. "JPEG - JPEG XT". jpeg.org.
26. "JPEG - Next-Generation Image Compression (JPEG XL) Final Draft Call for Proposals". Jpeg.org. Retrieved 29 May 2018.
27. Alakuijala, Jyrki; van Asseldonk, Ruud; Boukortt, Sami; Bruse, Martin; Comșa, Iulia-Maria; Firsching, Moritz; Fischbacher, Thomas; Kliuchnikov, Evgenii; Gomez, Sebastian; Obryk, Robert; Potempa, Krzysztof; Rhatushnyak, Alexander; Sneyers, Jon; Szabadka, Zoltan; Vandervenne, Lode; Versari, Luca; Wassenberg, Jan (2019-09-06). "JPEG XL next-generation image compression architecture and coding tools". In Tescher, Andrew G; Ebrahimi, Touradj (eds.). Applications of Digital Image Processing XLII. p. 20. doi:10.1117/12.2529237. ISBN 9781510629677. S2CID 202785129.
28. "Archived copy". Archived from the original on 22 August 2019. Retrieved 22 August 2019.{{cite web}}: CS1 maint: archived copy as title (link)
29. ^ Rhatushnyak, Alexander; Wassenberg, Jan; Sneyers, Jon; Alakuijala, Jyrki; Vandevenne, Lode; Versari, Luca; Obryk, Robert; Szabadka, Zoltan; Kliuchnikov, Evgenii; Comsa, Iulia-Maria; Potempa, Krzysztof; Bruse, Martin; Firsching, Moritz; Khasanova, Renata; Ruud van Asseldonk; Boukortt, Sami; Gomez, Sebastian; Fischbacher, Thomas (2019). "Committee Draft of JPEG XL Image Coding System". arXiv:1908.03565 .
30. "N79010 Final Call for Proposals for a Next-Generation Image Coding Standard (JPEG XL)" (PDF). ISO/IEC JTC 1/SC 29/WG 1 (ITU-T SG16). Retrieved 29 May 2018.

External links

• JPEG Standard (JPEG ISO/IEC 10918-1 ITU-T Recommendation T.81) at W3.org
• Official Joint Photographic Experts Group (JPEG) site
• JFIF File Format at W3.org
• JPEG viewer in 250 lines of easy to understand Python code
• Example images over the full range of quantization levels from 1 to 100 at visengi.com
• Public domain JPEG compressor in a single C++ source file, along with a matching decompressor at code.google.com
• JPEG decoder open source code, copyright (C) 1995–1997, Thomas G. Lane

v t e Graphics file formats
Raster	ANI ANIM APNG ART AVIF BMP BPG BSAVE CAL CIN CPC CPT DDS DPX ECW EXR FITS FLIC FLIF FPX GIF HDRi HEVC ICER ICNS ICO/CUR ICS ILBM JBIG JBIG2 JNG JPEG JPEG-LS JPEG 2000 JPEG XL JPEG XR JPEG XS JPEG XT JPEG-HDR KRA MNG MIFF NRRD ORA PAM PBM/PGM/PPM/PNM PCX PGF PICtor PNG PSD/PSB PSP QOI QTVR RAS RGBE Logluv TIFF SGI TGA TIFF TIFF/EP TIFF/IT UFO/UFP WBMP WebP XBM XCF XPM XWD
Raw	CIFF DNG
Vector	AI CDR CGM DXF EMF EMF+ Gerber HVIF IGES PGML SVG VML WMF Xar
Compound	CDF DjVu EPS MODCA PDF PICT PS SWF XAML
Metadata	Exchangeable image file format (Exif) International Press Telecommunications Council § Photo metadata Extensible Metadata Platform (XMP) GIF § Metadata Steganography
Comparison • Category

• JPEG
• Computer-related introductions in 1992
• Discovery and invention controversies
• American inventions
• Indian inventions
• Japanese inventions
• Taiwanese inventions
• ITU-T recommendations
• ITU-T Recommendations Series
• IEC standards
• ISO standards
• Lossy compression algorithms
• Image compression
• Open formats
• Raster graphics file formats