JPEG 2000

JPEG 2000 or ISO/CEI 15444-1 is a common standard of the ISO and UIT-T. It is a standard of compression of images defined by the committee Joint Photographic Experts Group . JPEG 2000 is able to work with or without losses, using a transformation into ondelette S (mathematical method of analysis of the signal). In irreversible compression, JPEG 2000 is more powerful than the method of Compression JPEG ISO/CEI 10918-1 (the traditional JPEG). One thus obtains files of a lower weight for a quality of equal image. Moreover, contours Nets and contrasted are returned better.

The standard is divided into 12 under-parts. Although name JPEG 2000 covers the whole of these under-parts, it is in general with the first part that one refers, the “system main part”. JPEG standardizes only the algorithm and the format of decoding. The process of coding is left free with the competition of the industrialists and academics, since the produced image is décodable by a standard decoder. The standard proposes a set of files of tests called files of conformance which make it possible to check that a decoder respects the standard strictly. A decoder is then known as in conformity if it is able to decode all the files of conformance. It is the object of part 4 of the standard.

Left 1: system center of coding
Left 2: extensions
Left 3: Motion JPEG 2000
Left 4: conformance
Left 5: knowledge robot
Left 6: compound image spins format
Partie 7:
Partie 8 was abandoned: JPSEC safety
Left 9: JPIP interactive protocol
Left 10: Volumetric JP3D imagery
Left 11: JPWL wireless
Left 12: ISO Base Media Spins Format (common with MPEG-4)

Performances in compression of JPEG 2000, although better than JPEG with low flow are not revolutionists. They are rather the multitude of new characteristics the such Scalabilité, the areas of interest, resistance to the errors of transmission, coding without losses, the fickleness of the organization of the data, as well as the various extensions aiming at an application (interactivity, safety, without wire, etc) which make the interest of the standard.

From its advanced functionalities, its capacity to manage the images of big size, as well as excellent performances with high banc, JPEG 2000 has a strong potential for the professionals of the image. Its career in the general public is on the other hand likely to be less brilliant than that of its predecessor JPEG.

General principle

The process of coding follows a traditional diagram of modification of the statistical properties of the data source by a change of space by a transform, before quantification of the coefficients resulting from this transform then entropic Codage. The innovations compared to JPEG from the compression point of view are the use of a transform in ondelettes, which offers a natural Scalabilité, but especially of an entropic algorithm of very sophisticated coding. This one is strongly based on the algorithm EBCOT of David Taubman. It consists of a regrouping and a modeling of the coefficients ondelettes which provide to a arithmetic Codeur adaptive a binary stream having the adequate statistical properties.

It follows a stage of allowance of flow which makes it possible to respect the target flow, and whose work is facilitated by the partitioning of the binary stream formed by EBCOT. The last stage is syntactic working of the codestream JPEG 2000, with the formation of the packages, then syntax high level, particularly abundant in JPEG 2000.

In standard JPEG a 2000 codestream is the whole of the data formed by the data compressed images gathered in packages as well as high level syntax: headings of tiles, heading the main thing.
To note that the Métadonnées format of file JP2 do not form part of the codestream. JP2 encapsulates codestream JPEG 2000 in a format of file.

Pretreatment

Cd. level shift

The first stage, very simple, consists in transforming the values of the pixels into signed values. Typically, one passes from a representation from 255 to 127, in order to have a signal centered around zero.

Transform color

The transform color is optional. It consists in passing from space color of the image of origin (RVB in general) to space color YUV (1 brightness, 2 chrominances) more adapted for compression because the 3 components are much correlated.

Two transforms are specified: irreversible ( ICT for Irreversible Component Transform ), with real coefficients, and reversible ( RCT for Reversible Component Transform ) with whole coefficients. The interest of the RCT is to be used in combination with the reversible transform in ondelette 5/3 for compression without losses.

Although the RCT can be used for coding with losses, in fact generally the ICT is used because it gives better results.

Transform in ondelette

The transform is carried out on each tile of each component. It is carried out on a dyadic grid, i.e each iteration of the filters of analysis is followed of a Décimation by 2. It breaks up the image into $3N_L+1$ sub-bands where $N_L$ is the number of levels of decomposition (the iteration count of the filters of analysis). The standard envisages a maximum number of levels of decomposition of 32.

It is possible to use two types of transforms in ondelettes in JPEG 2000.

the ondelette 5/3 or of Gall is a ondelette whose coefficients of the filters of analysis are whole. There are 5 coefficients for the low-pass filter and 3 for the high-pass. These filters allow a perfect rebuilding and can be used for a compression without losses.
the ondelette 9/7 or of Daubechies is with real coefficients, with 9 coefficients for the low-pass one and 7 for the high-pass one. It allows better performances that the 5/3 in terms of compression but is also more complex.

JPEG 2000 allows the implementation of these filters is by traditional a convolution or the method of the “face lift”.

Cutting in tiles

In certain cases, it can be interesting to cut out the image in tiles (of English bast : tile, square). It is simply about a rectangular image division, cutting to be specified, which is generally used to compress images of big size. The tiles are then a means of reducing memory complexity for the coder as for the decoder, while working on independent under-images. The tiles can have a visual impact: one perceives sometimes the terminals of the tiles (horizontal lines and verticals on the image).

By defect, the whole image is regarded as only one tile.

Quantification

Standard JPEG 2000 uses a uniform scalar quantifier at dead zone. The vectorial Quantification although theoretically more powerful is regarded as too expensive. The uniform scalar quantifier is on the contrary extremely simple of implementation and inexpensive.

The interest of the dead zone comes from the very many coefficients ondelettes not-null but close to zero. These coefficients only bring very little of relevant information, and their entropic coding would imply an important overcost within sight of gained quality. The dead zone thus makes it possible to get rid of these coefficients by quantifying them to zero.

Entropic coding

August 1st

Allowance of flow

August 1st

Working and syntax

In terminology JPEG a 2000 package consists of a heading and regrouping of the entropic data associated with a tile, a layer of quality, a component, a resolution and a Precinct. For a monochromic image (1 component) compressed with the default options (1 tile, 1 precinct, 1 layer of quality and 5 resolutions) the number of packages is thus of 5.

The order of the packages is important because it determines progressiveness. According to whether a space progressiveness is wished, by layer of quality, or even by component, the order of the packages will be different to allow a progressive decoding according to the selected method.

It should be noted that a package can be empty, i.e it does not have there entropic data which correspond to this private individual precinct, in this layer of quality, this component, this resolution. This can arrive on small images on-cut out by tiles and precincts.

Areas of interest

An area of interest (KING for Area Off Interest) is an area of the image which is coded with a highher degree of accuracy, in general because this area presents an private interest (ex: face, plate number…). This highher degree of accuracy is done with the detriment of the other zones of the image which then are compressed ata lower rate and thus degraded. The selection of the KING is made by the user, therefore in general manually, but there exist algorithms which allow an automatic extraction of the KING. These algorithms do not form part of JPEG 2000.

Resistance to the errors

An originality of JPEG 2000 is to include tools of resistance to the errors of transmission. The problem comes primarily from the arithmetic coder because only one erroneous bit involves the decoding of a bad sequence.

By defect, arithmetic coding acts indeed on a Code-block. In the event of error (only one erroneous bit is enough) it is the whole of the Code-block which is lost. In order to limit the effects of these errors, the standard proposes several tools, whose philosophy is primarily to compartmentalize the words of codes or to reduce their length in order to avoid the propagation of the errors or to limit their effects.

The tools proposed are the following:

Marker of segment : These markers are inserted after each plan of bit and are coded arithmetically. Their good decoding indicates that the plan of current bit was correctly decoded. Conversely, if the marker is not found, the plan of bit will be regarded as erroneous and thus removed.
Termination with each master key : It is a means of limiting the propagation of the errors, by compartmentalizing the data in a fine way (with each master key). The arithmetic decoder can thus continue decoding in the event of error.
Marker of resynchronisation (SOP/EPH) : These two markers indicate the beginning and the end of each package and allow the decoder to synchronize themselves thanks to the number of package included in these markers. They are here markers of syntax (arithmetically uncoded) and whose management is specific to each decoder.

To note that these tools are not enough for a transmission without wire. Specific methods were developed in part 11 of the standard, JPEG 2000 Wireless (JPWL).

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