JPEG

JPEG is a commonly used method of lossy compression for digital images, produced especially for those images through digital photography. The degree of compression can be set so that a selectable tradeoff between storage enbeeldkwaliteit. JPEG typically reaches. 10: 1 compression with little perceptible loss in image quality

JPEG compression is used in a number of image formats. JPEG / Exif is the most common image format used by digital camera’sen capture other photographic imaging devices; along with JPEG / JFIF is the most used for storing and transmitting photographs on the World Wide Web. [3] This format variations are often not distinguished and simply called JPEG.

The term “JPEG” is an acronym for Joint Photographic Experts Group who created the standard. The MIME media type for JPEG is image / jpeg , except in older Internet Explorer versions, which provides a MIME typeimage / pjpeg when uploading JPEG images. [4] JPEG files usually have an extension .jpg or .jpeg .

JPEG / JFIF supports a maximum image size of 65,535 x 65,535 pixels, [5] which up to 4 giga pixels a ratio of 1: 1.

The JPEG standard

“JPEG” stands for Joint Photographic Experts Group, the name of the committee that created the JPEG standard and also other coding standards still image. The “Joint” was in ISO TC97 WG8 and CCITT SGVIII. In 1987, ISO TC 97 was ISO / IEC JTC1 and in 1992 the CCITT became ITU-T. Currently on the JTC1 side JPEG is one of the two subsets of the ISO / IEC Joint Technical Committee 1, Subcommittee 29, Working Group 1 (ISO / IEC JTC 1 / SC 29 / WG 1) – title Coding of still images . [6 ] [7] [8] on the ITU-T-side ITU-T SG16 is the respective body. The original JPEG group was organized in 1986, [9] which is the first JPEG standard in 1992, which was approved in September 1992 as ITU-T Recommendation T.81 [10] and in 1994 as ISO / IEC 10918-1 .

The JPEG standard specifies the codec, which determines how an image is compressed into a stream of bytes and back decompressed in an image, but not the file format which is used to contain this flow. [11] The Exif and JFIF standards, the most frequently used file defining exchange formats of JPEG compressed images.

JPEG standards are officially listed as Information technology – Digital compression and coding of continuous-tone still images . ISO / IEC 10918 is made up of the following components:

DIGITAL COMPRESSION AND CODING OF CONTINUOUS-TONE STILL IMAGES – PARTS [7] [9] [12]
Part ISO / IEC standard ITU-T Rec. First public release date Last modification Title Description
Part 1 ISO / IEC 10918-1: 1994 T.81 (09/92) September 18, 1992 Requirements and guidelines
Part 2 ISO / IEC 10918-2: 1995 T.83 (11/94) November 11, 1994 compliance testing rules and checks for software compliance (Part 1)
part 3 ISO / IEC 10918-3: 1997 T.84 (07/96) July 3, 1996 April 1, 1999 extensions series expansions of the part 1, including to improve the file format SPIFF
part 4 ISO / IEC 10918-4: 1999 T.86 (06/98) 18 June 1998 June 29, 2012 Registration of JPEG profiles, SPIFF profiles SPIFF tags, SPIFF color spaces, APPN markers SPIFF compression types and Registration Authorities (REGAUT) Ways to extend some of the parameters for JPEG
part 5 ISO / IEC 10918-5: 2013 T.871 (05/11) May 14, 2011 JPEG File Interchange Format (JFIF) A popular format that the de facto file format for images encoded been by the JPEG standard. In 2009, the JPEG committee formally established an ad hoc group to standardize JFIF JPEG part 5.[13]
part 6 ISO / IEC 10918-6: 2013 T.872 (06/12) June 2012 Applicable to printing systems Specifies a subset of features and application tools for the exchange of images encoded according to ISO / IEC 10918-1 for printing.

ECMA TR / 98 specifies the JPEG File Interchange Format (JFIF); the first edition was published in June 2009.[14]

typical usage

The JPEG compression algorithm is at its best on photographs and paintings of realistic scenes with smooth variations of tone and color. For use of the Internet, wherein the amount of data that are used for an image is important, JPEG is very popular. JPEG / Exif is also saved the most common form by digital cameras.

JPEG on the other hand may be less suitable for line drawings and other textual or iconic graphics, where the sharp contrasts can cause noticeable artifacts between adjacent pixels. Such images may be better stored in a lossless graphics format such as TIFF, POISON, PNG, or raw. The JPEG standard actually includes a lossless coding mode, but is not supported in most products.

Because the typical use of JPEG is a lossy compression method, which slightly reduces the image fidelity, it should not be used in scenarios where the exact representation of the data is required (such as some scientific and medical imaging applications and certain technical processing work).

JPEG is not suitable for files undergo multiple operations, such as some image quality will usually be lost each time going the image is decompressed and compressed again, especially if the image is cropped or shifted, or if the encoding parameters are changed – see the digital generation loss for more informatie.Om prevent this, an image can be changed or can be stored to be changed in the future in a lossless format, exported as JPEG copies for distribution.

JPEG compression

JPEG uses a lossy form of compression on the basis of the discrete cosine transform (DCT). This mathematical operation converts each frame / field of the video source of the spatial (2D) domain in the frequency domain (aka transform domain). A perceptual model based loosely on the human psycho-visual system ignores high frequency information, ie sharp transitions in intensity and hue. In the transform domain, will further reduce information called quantization. More simply put, quantization is a method for the optimal reduction of a large number of scale (with different times that each number) into a smaller and the transform domain is a suitable representation of the image, because the high-frequency coefficients, which contribute less to the general image than other coefficients, are typically small values with a high compressibility. The quantized coefficients are then sequenced and lossless packed into the output bitstream. Almost all software implementations of JPEG permit user control over the compression ratio (as well as other optional parameters), allowing the user to trade off picture quality for smaller file size. In embedded applications (such as miniDV, making a similar DCT compression scheme), the parameters are pre-selected and for the application.

The compression method is usually lossy, leaving some original data is lost and can not be restored, any loss of image quality. An optional lossless mode defined by the JPEG standard. However, this mode is not widely supported in products.

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 are displayed during the download over a slow connection, allowing a reasonable preview after receiving only a portion of the data. However, support for progressive JPEG is not universal. If progressive JPEG by programs that do not support (such as versions of Internet Explorer are provided for Windows 7) [15] The software displays the picture until it is fully downloaded.

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

lossless editing

See also: jpegtran

A number of changes to a JPEG image may be carried out loss of charge (ie, without recompression and the related loss of quality) as long as the image size a multiple of 1 MCU block (Minimum Coded Unit) (usually 16 pixels in both directions, for the 4: 2: 0 chroma sampling ). Utilities that implement this under jpegtran,with user interface Jpeg Crop, and JPG_TRANSFORM plugin IrfanView.

Blocks can be rotated in steps of 90 degrees, mirrored in the horizontal, vertical and diagonal axes and moved about in the image. Not all the blocks of the original image is to be used in the modified one.

The top and left edges of a JPEG should be on an 8 x 8 pixel block boundary, but the bottom and right edges do not have to. This limits the possible lossless crop operations, and also prevents flips and rotations of an image whose bottom or right is not on a block boundary for all channels (because the border would end at the top or left, where – as mentioned above – a block boundary is for the applicable).

Rotations where the image is not a multiple of 8 or 16, which value is dependent on the chroma subsampling, not loss-free. Such an image rotation ensures that the blocks are recalculated making quality. [16]

When using lossless cropping, if the bottom or right side of the crop area is not on a block boundary than the rest of the data of the partial blocks used in the trimmed still file, and can be recovered. It is also possible to convert between baseline and progressive formats without quality loss, since the only difference is the order in which the coefficients included in the dossier.

Moreover, can be merged lossless JPEG images, as long as they are stored 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” format rarely used, mainly because of the difficulty of programming encoders and decoders to fully implement all aspects of the standard and because of certain shortcomings of the standard:

  • color definition
  • Component recording sub-sampling
  • Pixel Aspect Ratio definition.

Several additional standards have been developed to address these problems. The first of these, released in 1992, was JPEG File Interchange Format (JFIF or) followed in recent years by Exchangeable Image File Format (EXIF) and ICC color profiles. Both formats make use of the actual JIF byte layout, which consists of severalmarkers , but in addition, make use of one of the JIF standard extension points, namely, the application markers: JFIF used APP0, while Exif used APP1. Within these segments of the file, which were for future use in the JIF standard and are not read by it, adding these standards specific metadata.

Thus, in some respects, JFIF is a cutdown version of the standard JIF because they will be certain restrictions (such as not allowing all of the different coding modes), while in other respects is an extension of JIF due to the added metadata. The documentation suggests the original JFIF standard: [17]

JPEG File Interchange Format is a minimal file format JPEG bitstreams allows to switch between a wide variety of platforms and applications. This minimal format does not include the advanced features of TIFF JPEG specification or application-specific file format. Nor should it, for the sole purpose of this simplified format is to allow for the exchange of JPEG compressed images.

Image files employing JPEG compression are generally “JPEG”, and stored in variants of the JIF format. Most image capture devices (such as digital cameras) that outputs JPEG are actually creating files in the Exif format, the format that the camera industry standardized metadata uitwisseling.Aan the other hand, since the Exif standard does not color profiles allow to stand, the most image editing software stores JFIF in JPEG format, and also the APP1 segment from the Exif file in order to record the metadata in a near-compliant manner; JFIF standard has been interpreted somewhat flexible. [18]

Strictly speaking, the JFIF and Exif standards are not compatible because each requires the marker segment (APP0 or APP1, respectively) first appear. In practice, most JPEG files contain a JFIF marker segment precedes the Exif header. This allows older readers to correctly handle the older format JFIF segment, while newer readers decode the following Exif segment, requiring less stringent that they first appear.

JPEG file extensions

The most common file extensions for files employing JPEG compression .jpg and .jpeg , although .jpe, .jfif and .jif also be used. It is also possible for JPEG data to be embedded in other formats – TIFF encrypted files on a JPEG image as often embed thumbnail of the main image; MP3 and JPEG files can contain a 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 using a non-linear transformation, the dynamic range of an 8-bit JPEG file stops is approximately 11; See gamma curve.

Syntax and structure

A JPEG consists of a series of segments, each of which begin with a marker , each of which begins with a byte 0xFF followed by a byte which is which marker. Some markers consist of only these two bytes; others are followed by two bytes (high then low) with an indication of the length of the marker-specific payload data that follows. (The length includes two bytes for the length, but not the two bytes for the marking.) Some of the markers, followed by entropy encoded data; The duration of this marker does not include the entropy coded data. Note that successive bytes are 0xFF used as stuffing bytes for padding purposes, although this only fill byte padding would have to take place once for markers immediately after entropy-encoded scan data (see B.1.1.2 JPEG specification section for details and E.1.2 ; specifically “In all cases where markers are added after the compressed data, optionally enter 0xFF bytes, the label can precede”).

The entropy encoded data, after any byte 0xFF, 0x00 a byte is inserted at the encoder for the next byte, so that it seems not a marker as not provided, framing errors occur. Decoders should 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 data payload marker. However, note that entropy coded data has a pair of markers of his own; Reset the particular markers (0xD0 to 0xD7), which are used to isolate independent chunks of entropy coded data decoding parallel encoders as possible and free to these markers regularly again place (although not all encoders).

COMMON JPEG MARKERS [19]
short name bytes payload Name Comments
SO I 0xFF, 0xD8 no Start Of Image
SOF0 0xFF, 0xC0 variable size Start Of Frame (baseline DCT) Indicates that this is a DCT-based JPEG base line, and specifies the width, height, number of components, and subsampling component (for example, 4: 2: 0).
Sof2 0xFF, 0xC2 variable size Start Of Frame (progressive DCT) Indicates that the progressive DCT-based JPEG, and specifies the width, height, number of components, and component subsampling (eg 4: 2: 0).
DHT 0xFF, 0xC4 variable size Define Huffman (s) Specifies one or more Huffman tables.
DQT 0xFF, 0xDB variable size Define Quantization Table (s) Specifies one or more quantization tables.
DRI 0xFF, 0xDD 4 bytes Define Restart Interval Specifies the interval between RST n markers in macro blocks. This marking is followed by two bytes in which the fixed size, so that it can be treated like any other variable size segment.
SOS 0xFF, 0xDA variable size Start Of Scan Starts a top-to-bottom scan of the image. In the initial situation DCT JPEG images, there is generally a single scan. Progressive DCT JPEG images typically contain multiple scans. This marking determines which data segment will contain, and is immediately followed by entropy coded data.
RSTn 0xFF, 0xDn ( n= 0..7) no restart Inserted in each case r macroblocks, wherein r is to be set in the restart interval by a DRI marker. Do not use if there is no DRI marker.The low three bits of the tag code cycle value 0-7.
APPn 0xFF, 0xE n variable size application-specific For example, an Exif JPEG file uses an APP1 marker to store metadata in a structure that is closely based on established TIFF.
COM 0xFF, 0xFE variable size commentary Includes a text commentary.
EOI 0xFF, 0xD9 no End Of Image

There are other Start Of Frame markers that introduce other types of JPEG encoding.

For several vendors could use the same APP n Marker type of application-specific markers often begin with a standard or vendor name (eg “Exif” or “Adobe”) or any other identification string.

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

JPEG codec example

Although a JPEG file can be encoded in various ways, it is usually done JFIF coding. The code consists of several steps:

  1. The appearance of the colors in the image is converted from RGB to Y’C B C R , consisting of one luma component (Y ‘), which is the brightness, and two chroma components (C B and C R ), which is color. This step is sometimes over beaten.
  2. The resolution of the chroma data is reduced, usually by a factor of 2 or 3. This shows that the eye is less sensitive to fine color details than brightness fine details.
  3. The image is divided into blocks of 8 x 8 pixels, and for each block, wherein each of the Y, C B and CR data subjected to the discrete cosine transform (DCT), which was developed in 1974 by N. Ahmed, T. Natarajan and KR Rao; see Citation 1 on the discrete cosine transform. A DCT is similar to a Fourier transformation in the sense that it produces a type of spatial frequency spectrum.
  4. The amplitudes of the frequency components are quantized. Human eye is much more sensitive to small variations in color or brightness over large areas than the strength of high-frequency brightness variations. Therefore, the magnitude of the high frequency components is stored with an accuracy lower than the low frequency components. The quality setting of the encoder (e.g., 50 or 95 on a scale of 0-100 in the Independent JPEG Group library [20] ) will affect the extent to which decreases the resolution of each frequency component. If too low quality setting is used, the high-frequency components are removed completely.
  5. The resulting data for all 8 x 8 blocks further compressed using a lossless algorithm, a variant of Huffman coding.

The decoding process reverses these steps, with the exception of the quantization , as it is irreversible. In the remainder of this section, the encryption and decryption processes in more detail.

encoding

Many of the options are not often used in the JPEG standard, and as mentioned above, most image software uses the simpler JFIF format when creating a JPEG file, which among other things specifies the encryption method. Here follows a brief description of one of the most common encoding methods, when applied to an input 24 which is 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 must be converted from RGB into a different color space called Y’C B C R (or, colloquially, YCbCr). It has three components Y, C B and C R : Y ‘component in the brightness of a pixel, and the C B and C Rcomponents represent the chrominance (broken down into blue and red components). This is basically the same as used color space by digital color television and digital video such as video DVD’s, and is similar to the way in which color is represented in analog PAL video and MAC (they do not analog NTSC, which is used YIQ color space). The Y’C B C R color space conversion allows for a greater compression without a significant influence on the perceptual image quality (or more perceptual image quality for the same compression). The compression is more efficient, because the brightness information, what is more important is restricted to the final perceptual quality of the image to a single channel. This corresponds more closely to the perception of color in the human visual system. The color transformation also enhances compression by statistical Decorrelation.

A special conversion into Y’C B C R is specified in the standard JFIF and must be done to affect the resulting JPEG maximum compatibility. However, some JPEG implementations in “high quality” mode this step does not apply and the color information to keep the place RGB color model, [ citation needed ] , where the image is stored in a separate channels for red, green and blue brightness components. This results in less efficient compression, and would probably not be used if the file is particularly important.

downsampling

As a result of the densities of color and brightness-sensitive receptors in the human eye, the human being can be seen considerably more fine detail in the brightness of an image (a component of the Y ‘) than in the hue and the color saturation of an image (CB and Cr components). With the help of this knowledge, encoders may be designed to more efficiently compress images.

The transformation in the Y’C B C R color model allows the next usual step, which is the spatial resolution of the Cb and Cr components (called “decrease downsampling” or “chroma sampling”). The proportions in which the down-sampling is usually done for JPEG images are 4: 4: 4 (no downsampling), 4: 2: 2 (reduction by a factor of 2 in the horizontal direction), or (usually) 4: 2: 0 (reduction by a factor of 2 in both the horizontal and vertical directions). For the rest of the compression process are Y, Cb and Cr separately and integrated in a similar manner.

split Block

After subsampling, each channel should be divided into 8 × 8 blocks. Depending chroma sampling delivers this Minimum Coded Unit (MCU) blocks of size 8 x 8 (4: 4: 4 – no subsampling), 16 x 8 (4: 2: 2), or more usually 16 × 16 (4: 2: 0 ). In video compression MCUs are called macro blocks.

If the data of a channel does not result in an integer number of blocks then the encoder, the remaining space of the partial blocks having a shape of dummy data in. Filling the edges with a solid color (eg black) can make ringing artifacts along the visible part of the border; repeating the edge pixels is a technique that reduces (but not necessarily completely eliminate) such as artifacts, and more advanced boundary filling techniques may also be used.

discrete cosine transformation

The 8 × 8 sub-picture displayed in 8-bit grayscale

Then, each 8 x 8 blocks of each component (Y, Cb, Cr) is converted into a frequency domain representation, with a normalized two-dimensional type II discrete cosine transform (DCT), introduced by N. Ahmed, T. Natarajan, and KR Rao in 1974 ; see Citation 1 on the discrete cosine transform. The DCT is sometimes called “type-II DCT” in the context of a family of transformations mentioned indiscrete cosine transform, and the corresponding inverse (IDCT) is referred to as “type-III DCT”.

As an example may be about 8 x 8 8-bit sub-image:

{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr 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 {matrix}} \ right].}\ Left [{\ begin {matrix} {} rrrrrrrr 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 {matrix }} \ right].

Before computing the DCT of the 8 x 8 block, the values are shifted from a positive set on the centered to zero. drop an 8-bit for each item in the original block in the range {\ Display Style [0255]}[0255] . The center of the range (in this case, the value 128) is subtracted from each item, a range of data which is centered on zero to produce, so that the modified range {\ Display Style [-128,127]}[-128 127] . This step reduces the dynamic range of reasons DCT processing stage which follows. (Apart from the difference in the dynamic range within the DCT phase, this step is mathematically equivalent to subtracting 1024 the DC coefficient after the execution of the transformation – which is a better way to be the operation on some architectures, since it includes the performance of one subtraction rather than 64.)

This step leads to the following values:

{\ Display Style g = {\ begin {matrix} {c} x \\\ lung right arrow left \\\ [{\ begin {matrix} {} rrrrrrrr -76 and -73 and -67 and -62 and -58 and -67 and -64 and -55 \ \ -65 and -69 and -73 and -38 and -19 and -43 and -59 and -56 \\ – 66 and -69 and -60 and -15 & 16 and -24 & -62 and -55 \\ – 65 and -70 and -57 and -6 & 26 & -22 and -58 and -59 \ \ -61 and -67 and -60 and -24 and -2 and -40 and – 60 and -58 \\ – 49 & -63 and -68 and -58, and -51 and -60, and -70 and -53 \\ – 43 & -57 and -64 and -69, and -73 and -67 & – 63 & -45 \\ – 41 & -49 and -59 and -60 and -63 and -52 and -50 and -34 \ end {matrix}} \ right] \ end {matrix}} {\ Bigg \ downarrow} y}.g = {\ begin {matrix} {c} x \\\ lung right arrow left \\\ [{\ begin {matrix} {} rrrrrrrr -76 and -73 and -67 and -62 and -58 and -67 and -64 and -55 \\ - 65 and -69 and -73 and -38 and -19 and -43 and -59 and -56 \\ - 66 and -69 and -60 and -15 & 16 & -24 and -62 and -55 \\ - 65 and -70 and -57 and -6 & 26 & -22 and -58 and -59 \\ - 61 and -67 and -60 and -24 and -2 and -40 and -60 and - 58 \\ - 49 & -63 and -68 and -58 and -51 and -60 and -70 and -53 \\ - 43 & -57 and -64 and -69 and -73 and -67 and -63 and - 45 \\ - 41 & -49 and -59 and -60 and -63 and -52 and -50 and -34 \ end {matrix}} \ right] \ end {matrix}} {\ Bigg \ downarrow} y.

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

The DCT transforms a 8 x 8 block of input values a linear combination of these 64 patterns. The cartridges are referred to as the two-dimensional DCT basic functions , and the output values are referred to as transform coefficients . The horizontal index {\ Display Style u}YOU and the vertical index {\ Display Style v}v .

{\ Display Style \ G_ {u, v} = {\ frac {1} {4}} \ alpha (u) \ alpha (v) \ sum _ {x = 0} ^ {7} \ sum _ {y = 0 } ^ {7} G_ {x, y} \ cos \ left [{\ frac {(2x + 1) you \ pi} {16}} \ right] \ cos \ left [{\ frac {(2y + 1) v \ pi} {16}} \ right]}\ G_ {u, v} = {\ frac {1} {4}} \ alpha (u) \ alpha (v) \ sum _ {x = 0} ^ {7} \ sum _ {y = 0} ^ { 7} G_ {x, y} \ cos \ left [{\ frac {(2x + 1) you \ pi} {16}} \ right] \ cos \ left [{\ frac {(2y + 1) v \ pi {16}}} \ right]

true

  • {\ Display Style \ u}\ u is the horizontal spatial frequency, the integers {\ Display Style \ 0 \ Leq you <8}\ 0 \ Leq you <8 .
  • {\ Display Style \ v}\ v is the vertical spatial frequency, the integers {\ Display Style \ 0 \ Leq v <8}\ 0 \ v Leq <8 .
  • {\ Display Style \ alpha (u) = {\ begin {cases} {\ frac {1} {\ sqrt {2}}} and {\ mbox {if}} u = 0 \\ 1 and {\ mbox {otherwise }} \ end {cases}}}\ Alpha (u) = {\ begin {cases} {\ frac {1} {\ sqrt {2}}} and {\ mbox {if}} u = 0 \\ 1 and {\ mbox {else}} \ end {cases}} is a normalizing scale factor to make the transformation orthonormal
  • {\ Display Style \ G_ {x, y}}\ G_ {x, y} is the pixel value at the coordinates {\ Display Style \ (x, y)}\ (X, y)
  • {\ Display Style \ G_ {u, v}}\ G_ {u, v} is the DCT coefficient at coordinates {\ Display Style \ (u, v).}\ (U, v).

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

{\ Display Style G = {\ begin {matrix} {c} you \\\ lung right arrow left \\\ [{\ begin {matrix} {} & rrrrrrrr -415.38 -30.19 and -61.20 and 27, 24 and 56.12 and -20.10 & – 2:39 and 0:46 & 4:47 \\ -21.86 and -60.76 & 10:25 & 13:15 and -7.09 and -8.54 and 4.88 \\ – 46.83 and 7.37 and 77.13 and -24.56 and -28.91 and 9.93 and 5.42 and -5.65 \\ – 12:07 & 48.53 & 34.10 and -14.76 and -10.24 & 6.30 and 1.83 and 1.95 \\ & 12:12 -6.55 and -13.20 and -3.95 and -1.87 and -2.79 and 1.75 and 3.14 \\ – 7 73 and 2.91 and 2.38 and -5.94 and -2.38 and 0.94 and 4.30 and 1.85 \\ – 1.03 and 0.18 and 0.42 and -2.42 and -0.88 and -3.02 and -0.66 \\ & 4.12 – 0.17 and 0.14 and -1.07 and -4.19 and -1.17 and -0.10 & 0.50 and 1.68 \ end {matrix}} \ right] \ end {matrix}} {\ Bigg \ downarrow} v.}G = {\ begin {matrix} {c} you \\\ lung right arrow left \\\ [{\ begin {matrix} {} & rrrrrrrr -415.38 -30.19 and -61.20 and 27.24 and 56 12 and -20.10 and -2.39 & 0. 46 \\ & 4:47 -21.86 and -60.76 & 10:25 & 13:15 and -7.09 and -8.54 and 4.88 \\ - 46.83 & 7.37 and 77.13 and -24.56 and -28.91 and 9.93 and 5.42 and -5.65 \\ - 48.53 & 12 & 07 & 34.10 -14.76 and -10 24 and 6.30 and 1.83 and 1.95 \\ & 12:12 -6.55 and -13.20 and -3.95 and -1.87 and -2.79 and 1.75 and 3.14 \\ - 7.73 and 2.91 and 2.38 and -5.94 and -2.38 and 0.94 and 4.30 and 1.85 \\ - 1.03 and 0.18 and 0.42 and - 2.42 and -0.88 and -3.02 and -0.66 \\ & 4.12 - 0.17 and 0.14 and -1.07 and -4.19 and -1.17 and -0 10 & 0 0.50 and 1.68 \ end {matrix}} \ right] \ end {matrix}} {\ Bigg \ downarrow} v.

Note the top left corner entry with the relatively large size. This is the DC coefficient (also called the constant component), which defines the basic color of the whole block. The remaining 63 coefficients, the AC coefficients (also known as the alternating components). [21] The advantage of the DCT is the tendency for the majority of the aggregate signal in a corner of the result, as is shown above. The quantization step for this purpose, while at the same time accentuates follow reduce the overall size of the DCT coefficients, which results in the entropy signal which can easily efficiently compress phase.

The DCT temporarily increases the bit depth of the data, since the DCT coefficients an 8-bit / component to be up to 11 bits or more (depending on reliability of the DCT calculation) store. This codec can force 16-bit numbers temporarily to keep these coefficients, doubling the display at this point; These values are typically reduced to 8-bit values which are the quantization step. The temporary increase in size at this stage, no performance concern for most JPEG implementations, since usually only a very small part of the image is stored completely DCT shape at any time during the image encoding or decoding process.

quantization

The human eye is good at distinguishing small differences in brightness over a relatively large surface area, but not as good at distinguishing the precise strength of a high-frequency brightness variation. This makes it possible to greatly reduce the amount of information in the high frequency components. This is done by simply any component in the frequency domain divided by a constant for that component, and rounded to the nearest whole number. This rounding operation is the only lossy operation in the entire process (except chroma sampling) where the DCT calculation is performed with a sufficiently high precision. As a result of this is usually the case that many of the higher frequency components rounded to zero, and much of the rest become small positive or negative numbers, which represent far fewer bits to.

The elements in the quantization matrix regulate the compression ratio, produce larger values greater compression. A typical quantization matrix (for a quality of 50% as in the original JPEG standard) is as follows:

{\ Display Style 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 }.}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 calculated with

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

where {\ Display Style G}G the quantized DCT coefficients is; {\ Display Style Q}Q is the quantization above;and {\ Display Style B}B is the quantized DCT coefficients.

Use of this quantization matrix with the DCT coefficient matrix from above resulting in:

Left: final image is built up from a series of basic functions. Right: each DCT basis functions that comprise the image and the corresponding weight coefficient. Middle: the basic functions, multiplied by the coefficient: this component is added to the ultimate beeld.Voor clarity, the 8 × 8 macroblock in this example magnified 10X using bilinear interpolation.
{\ Display Style B = \ left [{\ begin {matrix} {} rrrrrrrr -26 and -3 and -6 & 2 & 2 & -1 & 0 & 0 \\ 0 and -2 and -4 and 1 & 1 & 0 0 & & \\ 0 – 3 & 1 & 5 & -1 & -1 & 0 0 & & \\ 0 – 3 & 1 & 2 & -1 & 0 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 \ end {matrix}} \ right].}B = \ left [{\ begin {matrix} {} rrrrrrrr -26 and -3 and -6 & 2 & 2 & -1 & 0 & 0 \\ 0 and -2 and -4 and 1 & 1 & 0 & 0 & 0 \\ - 3 & 1 & 5 & -1 & -1 & 0 0 & & \\ 0 - 3 & 1 & 2 & -1 & 0 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 \ end {matrix}} \ right].

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

{\ Display Style \ mathrm {by} \ left ({\ frac {-415.37} {16}} \ right) = \ mathrm {by} \ left (-25.96 \ right) = -. 26}\ Mathrm {by} \ left ({\ frac {-415.37} {16}} \ right) = \ mathrm {by} \ left (-25.96 \ right) = - 26.

Note that most of the higher frequency elements of the sub-block (for example, by an x or y spatial frequency higher than 4) is compressed to zero values.

entropy

Main article: Entropy Encoding

Zigzag ordering of JPEG Parts

Entropy is a special form of lossless data compression. It comes to controlling of the image components in a “zigzag” To enable the use of run-length encoding (RLE) algorithm that groups of similar frequencies to each other, the insertion length encoding of zeros, and then using Huffman coding on what remains .

The JPEG standard also makes it possible, but not required, decoders in order to support the use of arithmetic coding, which mathematically superior to Huffman coding. However, rarely use this feature, because it was historically under patents require royalty-bearing licenses, and because it slower to encode and decode compared to Huffman coding. Arithmetic coding typically makes files about 5-7% lower.

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

The zig-zag sequence for the above quantized coefficients are shown below. (The format shown is only for ease of understanding / view.)

-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 -the block is represented by {\ Display Style B_ {i}}Bi} , and positions are represented within each block by {\ Display Style (p, q)}(P, q) where {\ Display Style p = 0,1, …, 7}p = 0,1, ..., 7 and { \ Display Style q = 0,1, …, 7}q = 0,1, ..., 7 , Then, each coefficient of the DCT is image can be represented as {\ Display Style B_ {i} (p, q)}B_ {i} (p, q) . So in the above diagram, the order of encoding pixels (the i -the block) is {\ Display Style B_ {i} (0,0)}B_ {i} (0,0) , {\ Display Style B_ {i} (0,1)}B_ {i} (0.1) , {\ Display Style B_ {i} (1,0)}B_ {i} (1,0) , {\ Display Style B_ {i} (2,0)}B_ {i} (2.0) , {\ Display Style B_ {i} (1,1)}B_ {i} (1,1) , {\ Display Style B_ {i} (0.2 )}B_ {i} (0.2) , {\ Display Style B_ i} {(0,3)}B_ {i} (0.3) , {\ Display Style B_ i} {(1,2)}B_ {i} (1,2) and so on.

Baseline sequential JPEG coding and decoding processes

This coding mode is base line sequential coding. Baseline JPEG also supports progressive encoding. While sequential code encoding coefficients of a block at a time (in zigzag), progressive encoding encodes equal situated batch coefficients of all the blocks in one go (a scan ), followed by the next set of coefficients of all the blocks, enzovoort.Bijvoorbeeld, if the image is divided in N 8 x 8 blocks {\ Display Style B_ {0}, {1} B-, B- {2}, …, B_ {n-1}}{\ Display Style B_ {0}, {1} B-, B- {2}, ..., B_ {n-1}} , Then a third scan progressive encoding encoding DC component, {\ display Style B_ i} {(0,0)}B_ {i} (0,0) for all the blocks, that is to say, for all {\ display Style i = 0,1,2, …, N-1}i = 0,1,2, ..., N-1 , in the first scan. This is followed by the second scan coding with a pair of components (assuming four components they {\ Display Style B_ i} {(0,1)}B_ {i} (0.1) to {\ Display Style B_ i} {(1,1)}B_ {i} (1,1), still in a zig-zag way) coefficients of all blocks (ie, the order is: {\ Display Style B_ {0} (0.1), B_ {0} (1.0) B- {0} (2.0) B- {0} ( 1,1), B_ {1} (0, 1), B_ 1} {(1,0), …, N} B_ {(2,0), B_ N} {(1,1)}{\ Display Style B_ {0} (0.1), B_ {0} (1.0) B- {0} (2.0) B- {0} (1.1), B_ {1} (0, 1), B_ 1} {(1,0), ..., N} B_ {(2,0), B_ N} {(1,1)} ), followed all remained coefficients of all the blocks in the last scan.

It should be noted that as soon as all similar situated coefficients are encoded, and then encode the next position is located next to the zigzag traversal as shown in the figure above. It was found that the output value Progressive JPEG coding often provides better compression compared to baseline sequential JPEG because of the possibility of different Huffman tables (see below) tuned to different frequencies on each “scan” or “pass” (which consists Similar-located coefficients), but the difference is not too large.

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

To encode the aforesaid coefficient generated pattern, JPEG uses Huffman coding. The JPEG standard provides general-purpose Huffman tables; encoders can also choose Huffman tables optimized for the actual frequency distributions in images are encoded to generate.

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

  • x is the non-zero quantized AC coefficient.
  • Loop Length the number of zeros that came to these 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 zeros came before the last AC coefficient. With this information, two symbols are created:

symbol 1 symbol 2
(Loop duration, SIZE) (AMPLITUDE)

Both the runlength and SIZE is resting on the same byte, which means that each contains only four pieces of information. The higher bits of handling the number of zeros, while the lower bits represent the number of bits required to encode the value of x .

As a direct implication of Symbol 1 are only able to store information with respect to the first 15 zeros preceding the non-zero AC coefficient. However, JPEG defines two special Huffman code words. One is for the termination of the series prematurely when the remaining coefficients to zero (the so-called “End-of-Block” or “EPO”), and another when the run of zeros goes beyond 15 in order to achieve a non-zero AC coefficient. In that case, 16 zeros encountered before a particular non-zero AC coefficient symbol 1 is “special” encoded as: (15, 0) (0).

The overall process continues until “EPO” – marked with (0, 0) – is reached.

To this end, the sequence is from earlier is:

(0, 2) (- 3); (1, 2) (- 3); (0, 2) (- 2); (0, 3) (- 6); (0, 2) (2); (0, 3) (- 4); (0, 1) (1); (0, 2) (- 3); (0, 1) (1);
(0, 1) (1); (0, 3) (5); (0, 1) (1); (0, 2) (2); (0, 1) (- 1); (0, 1) (1); (0, 1) (- 1); (0, 2) (2); (5, 1) (- 1);
(0, 1) (- 1); (0, 0).

(The first value in the matrix, -26, is the DC coefficient, is not encoded in the same way, see above.).

From here made frequency calculations based on events of the coefficients. In our example, block most of the quantized coefficients small quantities which are not immediately preceded by a zero coefficient. This more common cases, it will be represented by a shorter code words.

Compression ratio and artifacts

This image shows the pixels that differ between a non-compressed image and the same image quality JPEG compressed with a setting of 50. Darker means a larger difference is. Pay particular attention to the changes occurring in the vicinity of sharp edges and with a block-like shape.

The original image

The compressed 8 × 8 squares are visible in the scale-up photo, along with other visual artifacts of the lossy compression

The resulting compression ratio can be varied according to need by used more or less aggressive in the dividers in the quantization phase. Ten to one compression usually results in an image that can not be distinguished with the naked eye of the original. A compression ratio of 100: 1 is usually possible, but there will be apparent artifacted compared to the original. The appropriate level of compression depends on the use to which the image is brought.

EXTERNAL IMAGE
Illustration of the rim expressed [22]

Those who use the World Wide Web may be familiar with the irregularities known as its compression artifacts that appear in JPEG images in the form of noise around contrast edges (especially curves and angles), or “angular” can take pictures. This is caused by the quantization step of the JPEG algorithm. They are especially noticeable around sharp corners between contrasting colors (text is a good example, because it contains many such corners). The analog artifacts in MPEG video are referred to as mosquito noise, because the resulting “edge rush” and disturbing dots that change time, like swarms of mosquitoes around the object.[22] [23]

These artifacts can be reduced by choosing a lower pressure; they can be avoided completely by storing of an image by means of a lossless format, but this will result in a larger file. The images are created using ray-tracing programs strikingly angular shapes on the ground. Certain low-intensity compression artifacts may be acceptable if only the viewing of the images, but it can be stressed when the image is then processed, usually up to unacceptable quality. Consider the example below, showing the effect of compression on an edge detection processing step.

Image lossless compression lossy compression
original Lossless circle.png Lossy circle.jpg
Processed by
Canny edge detector
Lossless-circle-canny.png Lossy-circle-canny.png

Some software allows the user to the amount by which the individual blocks are compressed vary. Stronger compression is applied to parts of the image that show less artifacts. In this way, it is possible to reduce manual JPEG file with less loss of quality.

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

decoding

Decrypt the image from all of the above reversed.

Of DCT coefficient matrix (after addition of the difference of the DC coefficient back)

{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr -26 and -3 and -6 & 2 & 2 & -1 & 0 & 0 \\ 0 and -2 and -4 and 1 & 1 & 0 & 0 & 0 \\ – 3 & 1 & 5 & -1 & -1 & 0 0 & & \\ 0 – 3 & 1 & 2 & -1 & 0 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 \ end {matrix}} \ right]}\ Left [{\ begin {matrix} {} rrrrrrrr -26 and -3 and -6 & 2 & 2 & -1 & 0 & 0 \\ 0 and -2 and -4 and 1 & 1 & 0 & 0 & 0 \\ - 3 & 1 & 5 & -1 & -1 & 0 0 & & \\ 0 - 3 & 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 {matrix}} \ right]

and the taking of the entry-by-entry product with the quantization matrix of the above results in

{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr -416 and -33 and -60 & 32 & 48 & -40 & 0 & 0 \\ 0 and -24 and -56 & 19 & 26 & 0 & 0 & 0 \\ – 42 & 13 & 80 & -24 and -40 & 0 & 0 & 0 \\ – 42 & 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 {matrix}} \ right]}\ Left [{\ begin {matrix} {} rrrrrrrr -416 and -33 and -60 & 32 & 48 & -40 & 0 & 0 \\ 0 and -24 and -56 & 19 & 26 & 0 & 0 & 0 \\ - 42 & 13 & 80 & -24 and -40 & 0 & 0 & 0 \\ - 42 & 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 {matrix}} \ right]

which is very similar to the original DCT coefficient matrix for the top-left portion.

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

{\ Display Style F_ {x, y} = {\ frac {1} {4}} \ sum _ {u = 0} ^ {7} \ sum _ {v = 0} ^ {7} \ alpha (u) \ alpha (v) F_ {u, v} \ cos \ left [{\ frac {(2x + 1) you \ pi} {16}} \ right] \ cos \ left [{\ frac {(2y + 1) v \ pi} {16}} \ right]}F_ {x, y} = {\ frac {1} {4}} \ sum _ {u = 0} ^ {7} \ sum _ {v = 0} ^ {7} \ alpha (u) \ alpha (v ) F_ {u, v} \ cos \ left [{\ frac {(2x + 1) you \ pi} {16}} \ right] \ cos \ left [{\ frac {(2y + 1) v \ pi} {16}} \ right]

true

  • {\ Display Style \ x}\ x is the pixel row, the integers {\ Display Style \ 0 \ Leq x <8}\ 0 \ Leq x <8 .
  • {\ Display Style \ y}\ y is the pixel column of integers {\ Display Style \ 0 \ Leq y <8}\ 0 \ Leq y <8 .
  • {\ Display Style \ \ alpha (h)}\ \ Alpha (u) as defined above, for the integers {\ Display Style \ 0 \ Leq you <8}\ 0 \ Leq you <8 .
  • {\ Display Style \ F_ {u, v}}\ F_ {u, v} is the reconstructed approximate coefficient at coordinates {\ Display Style \ (u, v).}\ (U, v).
  • {\ Display Style \ F_ {x, y}}\ F_ {x, y} is the reconstructed pixel value at the coordinates {\ Display Style \ (x, y)}\ (X, y)

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

Notice the slight differences between the original (top) and decompressed image (below), which can be seen most easily in the bottom left corner.
{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr -66 and -63 and -71 and -68 and -56 and -65 and -68 and -46 \\ – 71 and -73 and -72 and – 46 and -20 and -41 and -66 and -57 \ \ -70 and -78 and -68 and -17 & 20 & -14 and -61 and -63 \\ – 63 and -73 and -62 and -8 & 27 & -14 and -60 and -58 \\ – 58 & -65 and -61 and -27 and -6 and -40 and -68 and -50 \ \ -57 and -57 and -64 and -58 and -48 and -66 and -72 and -47 \\ – 53 and -46 and -61 and -74 and -65 and -63 and -62 and -45 \\ – 47 & -34 and -53 and -74 and -60 and -47 and – 47 & -41 \ end {matrix}} \ right]}\ Left [{\ begin {matrix} {} rrrrrrrr -66 and -63 and -71 and -68 and -56 and -65 and -68 and -46 \\ - 71 and -73 and -72 and -46 and - 20 and -41 and -66 and -57 \\ - 70 and -78 and -68 and -17 & 20 & -14 and -61 and -63 \\ - 63 and -73 and -62 and -8 & 27 & -14 and -60 and -58 \\ - 58 & -65 and -61 and -27 and -6 and -40 and -68 and -50 \\ - 57 and -57 and -64 and -58 and -48 and -66 and -72 and -47 \\ - 53 and -46 and -61 and -74 and -65 and -63 and -62 and -45 \\ - 47 & -34 and -53 and -74 and -60 and -47 and -47 and -41 \ end {matrix}} \ right]

and the addition of 128 to each item

{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr 62 & 65 & 57 & 60 & 72 & 63 & 60 & 82 \\ 57 & 55 & 56 & 82 & 108 & 87 & 62 & 71 \\ 58 & 50 & 60 & 111 & 148 & 114 & 67 & 65 \\ 65 & 55 & 66 & 120 & 155 & 114 & 68 & 70 \\ 70 & 63 & 67 & 101 & 122 & 88 & 60 & 78 \\ 71 & 71 & 64 & 70 & 80 & 62 & 56 & 81 \\ 75 & 82 & 67 & 54 & 63 & 65 & 66 & 83 \\ 81 & 94 & 75 & 54 & 68 & 81 & 81 & 87 \ end {matrix}} \ right].}\ Left [{\ begin {matrix} {} rrrrrrrr 62 & 65 & 57 & 60 & 72 & 63 & 60 & 82 \\ 57 & 55 & 56 & 82 & 108 & 87 & 62 & 71 \\ 58 & 50 & 60 & 111 & 148 & 114 & 67 & 65 \\ 65 & 55 & 66 & 120 & 155 & 114 & 68 & 70 \\ 70 & 63 & 67 & 101 & 122 & 88 & 60 & 78 \\ 71 & 71 & 64 & 70 & 80 & 62 & 56 & 81 \\ 75 & 82 & 67 & 54 & 63 & 65 & 66 & 83 \\ 81 & 94 & 75 & 54 & 68 & 81 & 81 & 87 \ end {matrix }} \ right].

This is the extracted subimage. In general, it can provide the decompression process values outside of the original input voltage range of {\ Display Style [0255]}[0255] . If this happens, the decoder must be cut to keep the output values they are 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 (see figures to the right) by the difference (original – uncompressed) results in the following error values:

{\ Display Style \ left [{\ begin {matrix} {} rrrrrrrr -10 and -10 & 4 & 6 & -2 and -2 and -9 \\ 4 & 6 & 4 & 8 & -1 & 1 and -2 & 7 & 1 \\ 4 & 9 & 8 & 2 and -4 and -10 and -1 and 8 \\ – 2 & 3 and 5 & 2 & -1 & -8 & 2 & – \\ 1 – 3 and -2 & 1 & 3 & 4 & 0 & 8 & 8 -8 \\ & -6 and -4 and -3 -0 & 6 & & 2 & \\ -6 and 10 -11 and -3 and 5 – 8 & -4 and -1 & -0 \\ 6 and -15 and -6 & 14 & -3 and -5 and -3 and 7 \ end {matrix}} \ right]}\ Left [{\ begin {matrix} {} rrrrrrrr -10 and -10 & 4 & 6 & -2 and -2 and -9 \\ 4 & 6 & 4 & 8 & -1 & 1 and 2 & 7 & 1 \\ 4 & 9 & 8 & 2 and -4 and -10 and -1 and 8 \\ - 2 & 3 and 5 & 2 & -1 & -8 & 2 & \\ -1 and -2 & -3 1 & 3 & 4 & 8 & 0 \\ & -8 8 -4 & -6 & & & -0 -3 & 6 & 2 & \\ -6 and 10 -11 and -3 & 5 & 8 & - -1 & 4 & 6 & \\ -0 -15 -6 & 14 & -3 and -5 and -3 and 7 \ end {array}} \ right]

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

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

required accuracy

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

  • a maximum of one single difference for each pixel component
  • low mean square error for each 8 × 8-pixel block
  • very low average error on each 8 × 8-pixel block
  • very low mean square error over the entire image
  • extremely low average error over the entire image

These claims are tested on a large number of randomized input images to deal with the worst cases. The former IEEE 1180-1990 standard contained a number of similar accuracy requirements. The precision has implications for the implementation of decoders, and it is essential because some coding processes (particularly used for encoding sequences of images as MPEG) should be able to build a reference decoded image to the encoder side. Every 8-bit per pixel precision-component-output, dequantization and inverse DCT support transformations are typically carried out with at least 14-bit precision in the 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 left corner of the image, and how the contrasting lines become fuzzy. The very high compression ratio seriously affect the quality of the image, although the overall color and image form still recognizable. The accuracy of colors less burden (for a human eye), then the accuracy of contours (based on luminance). This justifies the fact that the images must first be converted into a color model to the luminance of the chromatic information separates prior to sampling of the chromatic surfaces (which can also operate at a lower quality quantization) to maintain the accuracy of the luminance plane with more information bits.

sample pictures

For more information, the 24-bit image would uncompressed RGB bitmap below (73 242 pixels) 219 726 bytes (excluding all other information headers) needed. The file sizes listed below include the internal JPEG information headers and some meta-data. For the highest quality images (Q = 100) requires approximately 8.25 bits per color pixel. On grayscale images, a minimum of 6.5 bits per pixel is enough (a similar Q = 100 color quality information requires about 25% more coded bits). The highest quality image below (Q = 100) is coded by nine bits per color pixel, the image of medium quality (Q = 25) uses one bit per pixel color. For most applications, the quality factor should not go lower than 0.75 bit per pixel (Q = 12.5), as can be seen the image of low quality on. The image on the lowest quality used only 0.13 bit per pixel, and gives a very poor color.This is useful when the image will be displayed in a significantly reduced size. A method for making better quantization matrices for a given picture quality via PSNR instead of the Q-factor is described in Minguillon & Pujol (2001). [24]

NOTE: THE ABOVE IMAGES ARE NOT IEEE / CCIR / EBU  TEST IMAGES AND THE ENCODER SETTINGS ARE NOT SPECIFIED OR IS UNAVAILABLE.
Image Quality Size (bytes) compression ratio commentary
For example, JPG JPEG RIP 100.jpg The highest quality (Q = 100) 83261 2.6: 1 Extremely small artifacts
For example, JPG JPEG RIP 050.jpg High quality (Q = 50) 15138 15: 1 First signs of subimage artifacts
For example, JPG JPEG RIP 025.jpg Medium quality (Q = 25) 9553 23: 1 Stronger artifacts; loss of high frequencies,
For example, JPG JPEG RIP 010.jpg Low quality (Q = 10) 4787 46: 1 Severe high-frequency loss; artifacts subimage boundaries ( “macro-blocking”) are obvious
For example, JPG JPEG RIP 001.jpg Lowest quality (Q = 1) 1523 144: 1 Extreme loss of color and detail; The leaves are almost unrecognizable

The average quality photo uses only 4.3% of the storage space required for the uncompressed image, but has little noticeable loss of detail or visual artefacten.Echter, 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 specific limitation of JPEG for this is the non-overlapping 8 x 8 block transform structure. More modern designs, such as JPEG 2000 enJPEG XR exhibit a degradation of the quality as the bit consumption decreases – with the aid of transformations with a larger spatial extent of the lower frequency coefficients and by the use of overlapping transform basis functions.

 

Lossless compression further

Emerged from 2004-2008 new research on ways to further compress the data in JPEG images without changing the represented image. [25] [26] [27] [28] This has applications in scenarios where the original image is only available in JPEG format and size must be reduced for archiving or verzending.Standard general-purpose compression tools can not significantly compress JPEG files.

Typically, such arrangements take advantage of improvements in the naive scheme for coding of DCT coefficients, which do not take into account:

  • Correlations between magnitudes of adjacent coefficients in the same block;
  • Correlations between variables of the same coefficient of adjacent blocks;
  • Correlations between variables 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 scale factor. Known systems for lossless coding of continuous tone images are applied to achieve something better compression than Huffman coded DPCM uses JPEG.

Some standard rarely used options are already in JPEG format to improve the efficiency of coding the DCT coefficients coding Arithmetic option and the progressive Codeermogelijkheid (with lower bitrates produces because values independently coded for each coefficient and each coefficient a significantly different distribution). Modern methods improved these techniques by the order coefficients group coefficients of greater size each other, [25] by using neighboring coefficients and blocks new coefficient values predict [27]divide blocks or coefficients between a small number of independently coded models based on their statistics and adjacent values ; [26] [27] . and recently by decoding blocks predict next blocks in the spatial domain and encoding these predictions to generate DCT coefficients [28]

Typically, such methods may compress existing JPEG files between 15 and 25 percent, and JPEG compressed at low quality settings, can produce improvement up to 65%. [27] [28]

A freely available tool called packJPG [29] is based on the 2007 paper “Enhanced Redundancy Reduction for JPEG files.”

Derived formats for stereoscopic 3D

JPEG stereoscopic

An example of a stereoscopic file .jps

JPS is a stereoscopic image JPEG used for creating 3D effects from 2D images. It contains two static images, one for the left eye and one for the right eye; coded as two adjacent images in a JPG file. Stereoscopic JPEG (JPS, expansion .jps) is a JPEG-based format for stereoscopic images. [30] [31] It has a range of configurations that are stored in the tag field JPEG APP3, but usually contains an image of double width that two images of identical size in squint (ie left frame on the right half of the image and vice versa) side-by-side formation.This file format can be seen as a JPEG without special software, or can be processed for display in other modes.

JPEG Multi-Picture Format

JPEG Multi-Picture Format (MPO, extension .mpo) is a JPEG-based format for multi-view images. It includes combining two or more JPEG files with each other. [32] [33] There are also special EXIF fields describing his goal. This is used by the Fujifilm FinePix Real 3D W1 camera, the Panasonic Lumix DMC-TZ20, DMC-TZ30, DMC-TZ60 and DMC-TS4 (FT4), Sony DSC-HX7V, HTC Evo 3D, the JVC GY-HMZ1U AVCHD / MVC expansion camcorder and the 3D camera Nintendo 3DS. In recent years, due to the increasing use of stereoscopic images, much effort has been spent by the scientific community to develop algorithms for stereoscopic image compression. [34] [35]

patent issues

In 2002, Forgent Networks asserted that it owned and would enforce patent rights on the JPEG technology, arising from a patent filed on October 27 1986 and was granted on October 6, 1987 (US Patent 4,698,672). The announcement created a rage reminiscent of Unisys’ attempts to protect its rights over the POISON-image compression standard.

The JPEG committee investigated the patent application in 2002 and felt that they were invalidated by prior art. [36] Others have also concluded that Forgent patent which JPEG had covered. [37] Nevertheless, between 2002 and 2004 Forgent was able to around US $ 105 million gain by licensing their patent about 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 aim invalidate the patent. In addition, Microsoft launched a separate lawsuit against Forgent in April 2005. [38] 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. [39] On May 26 , 2006, the USPTO found the patent void on the basis of the prior art. The USPTO also found that Forgent knew about the state of the art, and do not tell the Patent Office, making an appeal to the patent to recover very little chance of success. [40]

Forgent also possesses a similar patent granted by the European Patent Office in 1994, but it is unclear how enforceable. [41]

As of October 27, 2006, 20-year term appears US patent to have expired, and in November 2006, Forgent agreed to leave the enforcement of patent claims against using the JPEG standard. [42]

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

Beginning in August 2007, another company, Global Patent Holdings, LLC claimed that its patent (US Patent 5,253,341), published in 1993, is violated by downloading JPEG images on either a website or via email. If not null, this patent applies to any website that displays JPEG images. The patent arose [ clarification needed ] in July 2007 after a seven-year re-examination by the US Patent and Trademark Office, which was revoked all of the original claims of the patent, but an additional claim (claim 17) was confirmed. [43]

In the first two lawsuits in response to the new research, both filed in Chicago, Illinois, Global Patent Holdings sued the Green Bay Packers, CCC, Motorola, Apple, Orbitz, OfficeMax, Caterpillar, Kraft and Peapod as defendants. A third lawsuit was filed on December 5, 2007 in South Florida at ADT Security Services, AutoNation, Florida Crystals Corp., HearUSA, MovieTickets.com, Ocwen Financial Corp. and Tire Kingdom, and a fourth lawsuit on January 8, 2008 in South Florida at the Boca Raton Resort & Club. A fifth lawsuit was filed against Global Patent Holdings in Nevada. That lawsuit was filed by Zappos.com, Inc., which was allegedly threatened by Global Patent Holdings, and seeking a judicial declaration that the ‘341 patent is invalid and not infringed.

Global Patent Holdings had also suing use of the ‘341 patent or threatening outspoken critics of broad software patents, including Gregory Aharonian [44] and the anonymous operator of a website blog known as the “Patent Troll Tracker.” [45] on December 21 2007, patent attorney Vernon Francissen Chicago asked the US patent and Trademark Office to re-examine the only remaining claim of the ‘341 patent on the basis of the new state of the art. [46]

On March 5, 2008, the US Patent and Trademark Office agreed to the ‘341 patent reexamined find that the new state of the art raised substantial new questions concerning the validity of the patent. [47] In light of the investigation, the suspected offenders in four of the five pending lawsuits have filed motions to suspend their business (stay) until the completion of the US patent and revision of the ‘341 patent and Trademark Office programs. On April 23, 2008, a judge presided over the two lawsuits in Chicago, Illinois granted the motions in those cases. [48] On July 22 2008, the European Patent Office issued the first “Office Action” of the second re-examination finding the claim invalid based on nineteen different grounds. [49] on november 24, 2009, a new research license was issued canceling all claims.

Beginning in 2011 and continuing as of early 2013, an entity known as Princeton Digital Image Corporation,[50] , located in East Texas, began persecuting large numbers of companies for alleged infringement of US Patent 4,813,056. Princeton claims that the JPEG compression standard is infringing the ‘056 patent and has a large number of websites, retailers, camera and the unit sued manufacturers and resellers. The patent was originally owned and assigned to General Electric. The patent expired in December 2007, but Princeton has a large number of companies sued for “past violations” of this patent. (According to US patent law, a patent holder can sue for “past infringement ‘to six years for filing a lawsuit so that Princeton would remain theoretically sue companies until December 2013) As of March 2013, Princeton had suits pending of New York and Delaware against more than 55 companies. Involvement of General Electric in the suit is unknown, although court records show that the patent assigned to Princeton in 2009 and retains certain rights to the patent. [51]

implementations

A very important application of a JPEG codec is the free programming library libjpeg of the Independent JPEG Group. It was first published in 1991 and is important for the success of the standard. [52] This library or a direct derivative thereof is used in numerous applications.