Discrete cosine transform: Difference between revisions

Revision as of 02:56, 11 December 2023

Revision as of 00:31, 31 December 2023

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===Visual media standards===

The DCT-II, is an important [[image compression]] technique. It is used in image compression standards such as [[JPEG]], and [[video compression]] standards such as [[H.26x]], [[MJPEG]], [[MPEG]], [[DV (video format)|DV]], [[Theora]] and [[Daala]]. There, the two-dimensional DCT-II of <math>N \times N</math> blocks are computed and the results are [[Quantization (signal processing)|quantized]] and [[Entropy encoding|entropy coded]]. In this case, <math>N</math> is typically 8 and the DCT-II formula is applied to each row and column of the block. The result is an 8&nbsp;× 8 transform coefficient array in which the <math>(0,0)</math> element (top-left) is the DC (zero-frequency) component and entries with increasing vertical and horizontal index values represent higher vertical and horizontal spatial frequencies.

The integer DCT, an integer approximation of the DCT,<ref name="Britanak2010"/><ref name="Stankovic"/> is used in [[Advanced Video Coding]] (AVC),<ref name="Wang">{{cite journal |last1=Wang |first1=Hanli |last2=Kwong |first2=S. |last3=Kok |first3=C. |title=Efficient prediction algorithm of integer DCT coefficients for H.264/AVC optimization |journal=IEEE Transactions on Circuits and Systems for Video Technology |date=2006 |volume=16 |issue=4 |pages=547–552 |doi=10.1109/TCSVT.2006.871390|s2cid=2060937 }}</ref><ref name="Stankovic"/> introduced in 2003, and [[High Efficiency Video Coding]] (HEVC),<ref name="apple"/><ref name="Stankovic"/> introduced in 2013. The integer DCT is also used in the [[High Efficiency Image Format]] (HEIF), which uses a subset of the [[HEVC]] video coding format for coding still images.<ref name="apple"/> AVC uses 4&nbsp;x 4 and 8&nbsp;x 8 blocks. HEVC and HEIF use varied block sizes between 4&nbsp;x 4 and 32&nbsp;x 32 [[pixels]].<ref name="apple"/><ref name="Stankovic"/> {{As of|2019}}, AVC is by far the most commonly used format for the recording, compression and distribution of video content, used by 91% of video developers, followed by HEVC which is used by 43% of developers.<ref name="Bitmovin">{{cite web |url=https://cdn2.hubspot.net/hubfs/3411032/Bitmovin%20Magazine/Video%20Developer%20Report%202019/bitmovin-video-developer-report-2019.pdf |title=Video Developer Report 2019 |website=[[Bitmovin]] |year=2019 |access-date=5 November 2019}}</ref><!--[[User:Kvng/RTH]]-->

====Image formats====

{| class="wikitable"

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! [[Image compression]] standard !! Year !! Common applications

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| [[JPEG]]<ref name="Stankovic"/> ||1992|| The most widely used [[image compression]] standard<ref name="Hudson">{{cite journal |last1=Hudson |first1=Graham |last2=Léger |first2=Alain |last3=Niss |first3=Birger |last4=Sebestyén |first4=István |last5=Vaaben |first5=Jørgen |title=JPEG-1 standard 25 years: past, present, and future reasons for a success |journal=[[Journal of Electronic Imaging]] |date=31 August 2018 |volume=27 |issue=4 |pages=1 |doi=10.1117/1.JEI.27.4.040901|doi-access=free }}</ref><ref>{{cite web |title=The JPEG image format explained |url=https://home.bt.com/tech-gadgets/photography/what-is-a-jpeg-11364206889349 |website=[[BT.com]] |publisher=[[BT Group]] |access-date=5 August 2019 |date=31 May 2018}}</ref> and digital [[image format]],.<ref name="Baraniuk">{{cite news |last1=Baraniuk |first1=Chris |title=Copy protections could come to JPegs |url=https://www.bbc.co.uk/news/technology-34538705 |access-date=13 September 2019 |work=[[BBC News]] |agency=[[BBC]] |date=15 October 2015}}</ref>

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| [[JPEG XR]] ||2009|| [[Open XML Paper Specification]]

|-

| [[WebP]] ||2010|| A graphic format that supports the [[lossy compression]] of [[digital images]]. Developed by [[Google]].

|-

| [[High Efficiency Image Format]] (HEIF) ||2013|| [[Image file format]] based on [[HEVC]] compression. It improves compression over JPEG,<ref name="apple">{{cite web |last1=Thomson |first1=Gavin |last2=Shah |first2=Athar |title=Introducing HEIF and HEVC |url=https://devstreaming-cdn.apple.com/videos/wwdc/2017/503i6plfvfi7o3222/503/503_introducing_heif_and_hevc.pdf |publisher=[[Apple Inc.]] |year=2017 |access-date=5 August 2019}}</ref> and supports [[animation]] with much more efficient compression than the [[animated GIF]] format.<ref>{{cite web |title=HEIF Comparison - High Efficiency Image File Format |url=https://nokiatech.github.io/heif/comparison.html |publisher=[[Nokia Technologies]] |access-date=5 August 2019}}</ref>

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| [[Better Portable Graphics|BPG]] ||2014||Based on [[HEVC]] compression

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| [[JPEG XL]]<ref name="jxl">{{Cite web |url=http://ds.jpeg.org/whitepapers/jpeg-xl-whitepaper.pdf |title=JPEG XL White Paper |last1=Alakuijala | first1=Jyrki |last2=Sneyers |first2=Jon |last3=Versari |first3=Luca |last4=Wassenberg |first4=Jan |access-date=14 Jan 2022 |date=22 January 2021 |website=JPEG Org. |archive-date=2 May 2021 |archive-url=https://web.archive.org/web/20210502025653/http://ds.jpeg.org/whitepapers/jpeg-xl-whitepaper.pdf |url-status=live |quote=Variable-sized DCT (square or rectangular from 2x2 to 256x256) serves as a fast approximation of the optimal decorrelating transform.}}</ref> ||2020|| A royalty-free raster-graphics file format that supports both lossy and lossless compression.

|}<!--[[User:Kvng/RTH]]-->

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====Video formats====

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| [[MPEG-1]] Video<ref name="Rao">{{cite book | last1 = Rao | first1 = K.R. | author-link1 = K. R. Rao | last2 = Hwang | first2 = J. J. | date = 1996-07-18 | title = Techniques and Standards for Image, Video, and Audio Coding | language = en | publisher = Prentice Hall | at = JPEG: Chapter 8; H.261: Chapter 9; MPEG-1: Chapter 10; MPEG-2: Chapter 11 | isbn = 978-0133099072 | lccn = 96015550 | oclc = 34617596 | ol = OL978319M | s2cid = 56983045 | df = dmy-all}}</ref> ||1993|| [[Digital video]] distribution on [[CD]] or [[Internet video]]

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| [[MPEG-2 Video]] (H.262)<ref name="Rao"/> ||1995|| Storage and handling of [[digital images]] in broadcast applications, [[digital television]], [[HDTV]], cable, satellite, high-speed [[Internet]], [[DVD]] video distribution

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| [[DV (video format)|DV]] ||1995|| [[Camcorders]], [[digital cassettes]]

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{{See|Compression artifact}}

A common issue with DCT compression in [[digital media]] are blocky [[compression artifacts]],<ref name="Katsaggelos">{{cite book |last1=Katsaggelos |first1=Aggelos K. |last2=Babacan |first2=S. Derin |last3=Chun-Jen |first3=Tsai |title=The Essential Guide to Image Processing |date=2009 |publisher=[[Academic Press]] |isbn=9780123744579 |pages=349–383|chapter=Chapter 15 - Iterative Image Restoration}}</ref> caused by DCT blocks.<ref name="Alikhani">{{cite web |last1=Alikhani |first1=Darya |title=Beyond resolution: Rosa Menkman's glitch art |url=http://postmatter.merimedia.com/articles/archive-2012-2016/2015/51-rosa-menkman/ |website=POSTmatter |date=April 1, 2015 |access-date=19 October 2019 |archive-date=19 October 2019 |archive-url=https://web.archive.org/web/20191019082218/http://postmatter.merimedia.com/articles/archive-2012-2016/2015/51-rosa-menkman/ |url-status=dead }}</ref> The DCT algorithm can cause block-based artifacts when heavy compression is applied. Due to the DCT being used in the majority of [[digital image]] and [[video coding standards]] (such as the [[JPEG]], [[H.26x]] and [[MPEG]] formats), DCT-based blocky compression artifacts are widespread in [[digital media]]. In a DCT algorithm, an image (or frame in an image sequence) is divided into square blocks which are processed independently from each other, then the DCT of these blocks is taken, and the resulting DCT coefficients are [[Quantization (signal processing)|quantized]]. This process can cause blocking artifacts, primarily at high [[data compression ratio]]s.<ref name="Katsaggelos"/> This can also cause the "[[mosquito noise]]" effect, commonly found in [[digital video]] (such as the MPEG formats).<ref>{{cite web |title=Mosquito noise |url=https://www.pcmag.com/encyclopedia/term/55914/mosquito-noise |website=[[PC Magazine]] |access-date=19 October 2019}}</ref>

DCT blocks are often used in [[glitch art]].<ref name="Alikhani"/> The artist [[Rosa Menkman]] makes use of DCT-based compression artifacts in her glitch art,<ref name="Menkman">{{cite book |last1=Menkman |first1=Rosa |title=The Glitch Moment(um) |url=https://networkcultures.org/_uploads/NN%234_RosaMenkman.pdf |publisher=Institute of Network Cultures |isbn=978-90-816021-6-7 |date=October 2011 |access-date=19 October 2019}}</ref> particularly the DCT blocks found in most [[digital media]] formats such as [[JPEG]] [[digital images]] and [[MP3]] [[digital audio]].<ref name="Alikhani"/> Another example is ''Jpegs'' by German photographer [[Thomas Ruff]], which uses intentional [[JPEG]] artifacts as the basis of the picture's style.<ref>{{cite book|chapter=jpegs|first=Thomas|last=Ruff|title=Aperture|date=May 31, 2009|page=132|publisher=Aperture |isbn=9781597110938}}</ref><ref>{{cite web|url=http://jmcolberg.com/weblog/2009/04/review_jpegs_by_thomas_ruff/|title=Review: jpegs by Thomas Ruff|first=Jörg|last=Colberg|date=April 17, 2009}}</ref>

==Informal overview==