JPEG 2000

JPEG 2000 decomposes the image into a multiple resolution representation in the course of its compression process. This pyramid representation can be put to use for other image presentation purposes beyond compression.

These features are more commonly known as progressive decoding and signal-to-noise ratio (SNR) scalability. JPEG 2000 provides efficient code-stream organizations which are progressive by pixel accuracy and by image resolution (or by image size). This way, after a smaller part of the whole file has been received, the viewer can see a lower quality version of the final picture. The quality then improves progressively through downloading more data bits from the source.

Like the Lossless JPEG standard,[4] the JPEG 2000 standard provides both lossless and lossy compression in a single compression architecture. Lossless compression is provided by the use of a reversible integer wavelet transform in JPEG 2000.

Like JPEG 1992, JPEG 2000 is robust to bit errors introduced by noisy communication channels, due to the coding of data in relatively small independent blocks.

The JP2 and JPX file formats allow for handling of color-space information, metadata, and for interactivity in networked applications as developed in the JPEG Part 9 JPIP protocol.

JPEG 2000 supports bit depths of 1 to 38 bits per component. Supported color spaces include monochrome, 3 types of YCbCr, sRGB, PhotoYCC, CMY(K), YCCK and CIELab. It also later added support for CIEJab, e-sRGB, ROMM, YPbPr and others.[5]

Full support for transparency and alpha planes.

Initially images have to be transformed from the RGB color space to another color space, leading to three components that are handled separately. There are two possible choices:

1. Irreversible Color Transform (ICT) uses the well known BT.601 YC_BC_R color space. It is called "irreversible" because it has to be implemented in floating or fix-point and causes round-off errors. The ICT shall be used only with the 9/7 wavelet transform.
2. Reversible Color Transform (RCT) uses a modified YUV color space (almost the same as YC_GC_O) that does not introduce quantization errors, so it is fully reversible. Proper implementation of the RCT requires that numbers be rounded as specified and cannot be expressed exactly in matrix form. The RCT shall be used only with the 5/3 wavelet transform. The transformations are:

${\displaystyle {\begin{array}{rl}Y&=&\left\lfloor {\frac {R+2G+B}{4}}\right\rfloor$ ;\\C_{B}&=&B-G;\\C_{R}&=&R-G;\end{array}}\qquad {\begin{array}{rl}G&=&Y-\left\lfloor {\frac {C_{B}+C_{R}}{4}}\right\rfloor ;\\R&=&C_{R}+G;\\B&=&C_{B}+G.\end{array}}}

If R, G, and B are normalized to the same precision, then numeric precision of C_B and C_R is one bit greater than the precision of the original components. This increase in precision is necessary to ensure reversibility. The chrominance components can be, but do not necessarily have to be, downscaled in resolution; in fact, since the wavelet transformation already separates images into scales, downsampling is more effectively handled by dropping the finest wavelet scale. This step is called multiple component transformation in the JPEG 2000 language since its usage is not restricted to the RGB color model.[25]

After color transformation, the image is split into so-called tiles, rectangular regions of the image that are transformed and encoded separately. Tiles can be any size, and it is also possible to consider the whole image as one single tile. Once the size is chosen, all the tiles will have the same size (except optionally those on the right and bottom borders). Dividing the image into tiles is advantageous in that the decoder will need less memory to decode the image and it can opt to decode only selected tiles to achieve a partial decoding of the image. The disadvantage of this approach is that the quality of the picture decreases due to a lower peak signal-to-noise ratio. Using many tiles can create a blocking effect similar to the older JPEG 1992 standard.

CDF 5/3 wavelet used for lossless compression.

An example of the wavelet transform that is used in JPEG 2000. This is a 2nd-level CDF 9/7 wavelet transform.

These tiles are then wavelet-transformed to an arbitrary depth, in contrast to JPEG 1992 which uses an 8×8 block-size discrete cosine transform. JPEG 2000 uses two different wavelet transforms:

1. irreversible: the CDF 9/7 wavelet transform (developed by Ingrid Daubechies).[26] It is said to be "irreversible" because it introduces quantization noise that depends on the precision of the decoder.
2. reversible: a rounded version of the biorthogonal Le Gall–Tabatabai (LGT) 5/3 wavelet transform[27][26][28] (developed by Didier Le Gall and Ali J. Tabatabai).[29] It uses only integer coefficients, so the output does not require rounding (quantization) and so it does not introduce any quantization noise. It is used in lossless coding.

The wavelet transforms are implemented by the lifting scheme or by convolution.

After the wavelet transform, the coefficients are scalar-quantized to reduce the number of bits to represent them, at the expense of quality. The output is a set of integer numbers which have to be encoded bit-by-bit. The parameter that can be changed to set the final quality is the quantization step: the greater the step, the greater is the compression and the loss of quality. With a quantization step that equals 1, no quantization is performed (it is used in lossless compression).

The result of the previous process is a collection of sub-bands which represent several approximation scales. A sub-band is a set of coefficients—real numbers which represent aspects of the image associated with a certain frequency range as well as a spatial area of the image.

The quantized sub-bands are split further into precincts, rectangular regions in the wavelet domain. They are typically sized so that they provide an efficient way to access only part of the (reconstructed) image, though this is not a requirement.

Precincts are split further into code blocks. Code blocks are in a single sub-band and have equal sizes—except those located at the edges of the image. The encoder has to encode the bits of all quantized coefficients of a code block, starting with the most significant bits and progressing to less significant bits by a process called the EBCOT scheme. EBCOT here stands for Embedded Block Coding with Optimal Truncation. In this encoding process, each bit plane of the code block gets encoded in three so-called coding passes, first encoding bits (and signs) of insignificant coefficients with significant neighbors (i.e., with 1-bits in higher bit planes), then refinement bits of significant coefficients and finally coefficients without significant neighbors. The three passes are called Significance Propagation, Magnitude Refinement and Cleanup pass, respectively.

In lossless mode all bit planes have to be encoded by the EBCOT, and no bit planes can be dropped.

The bits selected by these coding passes then get encoded by a context-driven binary arithmetic coder, namely the binary MQ-coder (as also employed by JBIG2). The context of a coefficient is formed by the state of its eight neighbors in the code block.

The result is a bit-stream that is split into packets where a packet groups selected passes of all code blocks from a precinct into one indivisible unit. Packets are the key to quality scalability (i.e., packets containing less significant bits can be discarded to achieve lower bit rates and higher distortion).

Packets from all sub-bands are then collected in so-called layers. The way the packets are built up from the code-block coding passes, and thus which packets a layer will contain, is not defined by the JPEG 2000 standard, but in general a codec will try to build layers in such a way that the image quality will increase monotonically with each layer, and the image distortion will shrink from layer to layer. Thus, layers define the progression by image quality within the code stream.

The problem is now to find the optimal packet length for all code blocks which minimizes the overall distortion in a way that the generated target bitrate equals the demanded bit rate.

While the standard does not define a procedure as to how to perform this form of rate–distortion optimization, the general outline is given in one of its many appendices: For each bit encoded by the EBCOT coder, the improvement in image quality, defined as mean square error, gets measured; this can be implemented by an easy table-lookup algorithm. Furthermore, the length of the resulting code stream gets measured. This forms for each code block a graph in the rate–distortion plane, giving image quality over bitstream length. The optimal selection for the truncation points, thus for the packet-build-up points is then given by defining critical slopes of these curves, and picking all those coding passes whose curve in the rate–distortion graph is steeper than the given critical slope. This method can be seen as a special application of the method of Lagrange multiplier which is used for optimization problems under constraints. The Lagrange multiplier, typically denoted by λ, turns out to be the critical slope, the constraint is the demanded target bitrate, and the value to optimize is the overall distortion.

Packets can be reordered almost arbitrarily in the JPEG 2000 bit-stream; this gives the encoder as well as image servers a high degree of freedom.

Already encoded images can be sent over networks with arbitrary bit rates by using a layer-progressive encoding order. On the other hand, color components can be moved back in the bit-stream; lower resolutions (corresponding to low-frequency sub-bands) could be sent first for image previewing. Finally, spatial browsing of large images is possible through appropriate tile and/or partition selection. All these operations do not require any re-encoding but only byte-wise copy operations.

This image shows the (accentuated) difference between an image saved as JPEG 2000 (quality 50%) and the original.

Comparison of JPEG, JPEG 2000, JPEG XR, and HEIF at similar file sizes.

Compared to the previous JPEG standard, JPEG 2000 delivers a typical compression gain in the range of 20%, depending on the image characteristics. Higher-resolution images tend to benefit more, where JPEG 2000's spatial-redundancy prediction can contribute more to the compression process. In very low-bitrate applications, studies have shown JPEG 2000 to be outperformed[30] by the intra-frame coding mode of H.264. Good applications for JPEG 2000 are large images, images with low-contrast edges – e.g., medical images.

JPEG 2000 is much more complicated in terms of computational complexity in comparison with JPEG standard. Tiling, color component transform, discrete wavelet transform, and quantization could be done pretty fast, though entropy codec is time-consuming and quite complicated. EBCOT context modelling and arithmetic MQ-coder take most of the time of JPEG 2000 codec.

On CPU the main idea of getting fast JPEG 2000 encoding and decoding is closely connected with AVX/SSE and multithreading to process each tile in a separate thread. The fastest JPEG 2000 solutions utilize both CPU and GPU power to get high performance benchmarks.[31][32]

Although the JPEG 2000 format supports lossless encoding, it is not intended to completely supersede today's dominant lossless image file formats.

In 2005, a JPEG 2000–based image browsing protocol, called JPIP was published as ISO/IEC 15444-9.[38] Within this framework, only selected regions of potentially huge images have to be transmitted from an image server on the request of a client, thus reducing the required bandwidth.

JPEG 2000 data may also be streamed using the ECWP and ECWPS protocols found within the ERDAS ECW/JP2 SDK.

Motion JPEG 2000, (MJ2), originally defined in Part 3 of the ISO Standard for JPEG2000 (ISO/IEC 15444-3:2002,) as a standalone document, has now been expressed by ISO/IEC 15444-3:2002/Amd 2:2003 in terms of the ISO Base format, ISO/IEC 15444-12 and in ITU-T Recommendation T.802.[39] It specifies the use of the JPEG 2000 format for timed sequences of images (motion sequences), possibly combined with audio, and composed into an overall presentation.[40][41] It also defines a file format,[42] based on ISO base media file format (ISO 15444-12). Filename extensions for Motion JPEG 2000 video files are .mj2 and .mjp2 according to RFC 3745.

It is an open ISO standard and an advanced update to MJPEG (or MJ), which was based on the legacy JPEG format. Unlike common video formats, such as MPEG-4 Part 2, WMV, and H.264, MJ2 does not employ temporal or inter-frame compression. Instead, each frame is an independent entity encoded by either a lossy or lossless variant of JPEG 2000. Its physical structure does not depend on time ordering, but it does employ a separate profile to complement the data. For audio, it supports LPCM encoding, as well as various MPEG-4 variants, as "raw" or complement data.[43]

Motion JPEG 2000 (often referenced as MJ2 or MJP2) is considered as a digital archival format[44] by the Library of Congress though MXF_OP1a_JP2_LL (lossless JPEG 2000 wrapped in MXF operational pattern 1a) is preferred by the LOC Packard Campus for Audio-Visual Conservation.

ISO/IEC 15444-12 is identical with ISO/IEC 14496-12 (MPEG-4 Part 12) and it defines ISO base media file format. For example, Motion JPEG 2000 file format, MP4 file format or 3GP file format are also based on this ISO base media file format.[45][46][47][48][49]

The Open Geospatial Consortium (OGC) has defined a metadata standard for georeferencing JPEG 2000 images with embedded XML using the Geography Markup Language (GML) format: GML in JPEG 2000 for Geographic Imagery Encoding (GMLJP2), version 1.0.0, dated 2006-01-18.[50] Version 2.0, entitled GML in JPEG 2000 (GMLJP2) Encoding Standard Part 1: Core was approved 2014-06-30.[50]

JP2 and JPX files containing GMLJP2 markup can be located and displayed in the correct position on the Earth's surface by a suitable Geographic Information System (GIS), in a similar way to GeoTIFF and GTG images.