In computing, JPEG is a commonly used standard method of Data compression photographic images. The file format which employs this compression is commonly also called JPEG; the most common file extensions for this format are .jpeg, .jfif, .jpg, .JPG, or .JPE although .jpg is the most common on all platforms. The name stands for Joint Photographic Experts Group. JPEG itself specifies only how an image is transformed into a stream of bytes, but not how those bytes are encapsulated in any particular storage medium. A further standard, created by the Independent JPEG Group, called JFIF (JPEG File Interchange Format) specifies how to produce a file suitable for computer storage and transmission (such as over the Internet) from a JPEG stream. In common usage, when one speaks of a "JPEG file" one generally means a JFIF file, or sometimes an Exif JPEG file. There are, however, other JPEG-based file formats, such as JNG. JPEG/JFIF is the most common format used for storing and transmitting photographs on the World Wide Web. It is ''not'' as well suited for line drawings and other textual or iconic graphics because its compression method performs badly on these types of images (the PNG and GIF formats are in common use for that purpose; GIF, having only 8 bits per pixel is not well suited for colour photographs, but PNG may have as much or more detail than JPEG). The MIME media type for JFIF is ''image/jpeg'' (defined in RFC 1341). ==Encoding== Many of the options in the JPEG standard are little used. Here is a brief description of one of the more common methods of encoding when applied to an input that has 24 bits per pixel (eight each of RGB color model). This particular option is a lossy data compression method. ===Color space transformation=== First, the image is converted from RGB color model into a different color space called YUV. This is similar to the color space used by NTSC and PAL color television transmission. The Y component represents the brightness of a pixel, and the U and V components together represent the hue and saturation (not respectively). This part is useful because the human eye can see more detail in the Y component than in the others. ===Downsampling=== The above transformation enables the next step, which is to reduce the U and V components (called "downsampling" or "chroma subsampling"). The ratios at which the downsampling can be done on JPEG are YUV 4:4:4 (no downsampling), YUV 4:2:2 (decimate by factor of 2 in horizontal direction), and most commonly YUV 4:2:0 (decimate by factor of 2 in horizontal and vertical directions). For the rest of the compression process, Y, U and V are processed separately and in a very similar manner. ===Discrete cosine transform=== Next, each component (Y, U, V) of the image is "tiled" into sections of eight by eight pixels each, then each tile is converted to frequency space using a two-dimensional discrete cosine transform (DCT). If one such 8×8 8-bit subimage is: : which is then shifted by 128 results in : and then taking the DCT and rounding to the nearest integer results in : Note the rather large value of the top-left corner. This is the DC coefficient. ===Quantization=== The human eye is fairly good at seeing small differences in brightness over a relatively large area, but not so good at distinguishing the exact strength of a high frequency brightness variation. This fact allows one to get away with greatly reducing the amount of information in the high frequency components. This is done by simply dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer. This is the main lossy operation in the whole process. As a result of this, it is typically the case that many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers. A common quantization matrix is: : Using this quantization matrix with the DCT coefficient matrix from above results in: : For example, using −415 (the DC coefficient) and rounding to the nearest integer : ===Entropy coding=== Entropy coding is a special form of lossless data compression. It involves arranging the image components in a "zigzag" order that groups similar frequencies together, inserting length coding zeros, and then using Huffman coding on what is left. The JPEG standard also allows, but does not require, the use of arithmetic coding which is mathematically superior to Huffman coding. However, this feature is rarely used as it is covered by patents and because it is much slower to encode and decode compared to Huffman coding. Arithmetic coding typically makes files about 5% smaller. The zig-zag sequence for the above quantized coefficients would be: −26, −3, 0, −3, −3, −6, 2, −4, 1 −4, 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 JPEG has a special Huffman code word for ending the sequence prematurely when the remaining coefficients are zero. Using this special code word, EOB, the sequence becomes −26, −3, 0, −3, −3, −6, 2, −4, 1 −4, 1, 1, 5, 1, 2, −1, 1, −1, 2, 0, 0, 0, 0, 0, −1, −1, EOB ===Compression ratio and artifacts=== The resulting compression ratio can be varied according to need by being more or less aggressive in the divisors used in the quantization phase. Ten to one compression usually results in an image that can't be distinguished by eye from the original. 100 to one compression is usually possible, but will look distinctly Compression artifact compared to the original. The appropriate level of compression depends on the use to which the image will be put. Those who use the World Wide Web may be familiar with the irregularities known as compression artifacts that appear in JPEG digital images. These are due to the quantization step of the JPEG algorithm. They are especially noticeable around eyes in pictures of faces. They can be reduced by choosing a lower level of image compression; they may be eliminated by saving an image using a Lossless data compression file format, though for photographic images this will usually result in a larger file size. ===Decoding=== Decoding to display the image consists of doing all the above in reverse. Taking the DCT coefficient matrix (after adding the difference of the DC coefficient back in) : and multiplying it by the quantization matrix from above results in : which closely resembles the original DCT coefficient matrix for the top-left portion. Taking the inverse DCT results in an image with values (still shifted down by 128) {| border="1" width="256" align="right" |- |
|- | Notice the slight differences between the original (top) and decompressed image (bottom) which is most readily seen in the bottom-left corner. |} : and adding 128 to each entry : This is the uncompressed subimage and can be compared to the original subimage (also see images to the right) by taking the difference (original - uncompressed) results in error values : with an average absolute error of about 5 values per pixels (i.e., ). The error is most noticeable in the bottom-left corner where the bottom-left pixel becomes darker than the pixel to its immediate right. == Usage == JPEG is at its best on photographs and paintings of realistic scenes with smooth variations of tone and color. In this case it usually performs much better than purely lossless methods while still giving a good looking image (in fact it will produce a much higher quality image than other common methods such as GIF which are lossless for drawings and iconic graphics but require severe quantization for full-color images). === Photographs === JPEG compression artifacts blend well into photographs with detailed non-uniform textures, allowing higher compression ratios.
The mid-quality photo uses only one sixth the storage space but has no noticeable loss of detail and artifacts. However, once a certain threshold of compression is passed, compressed images show increasingly visible defects. See the article on rate distortion theory for a mathematical explanation of this threshold effect. ==Other lossy encoding formats== Newer lossy methods, particularly wavelet compression, perform even better in these cases. However, JPEG is a well established standard with plenty of software available, including free software, so it continues to be heavily used as of 2005. Also, many wavelet algorithms are patented, making it difficult or impossible to use them freely in many software projects. The JPEG committee has now created its own wavelet-based standard, JPEG 2000, which is intended to eventually supersede the original JPEG standard. ==Potential patent issues== In 2002 Forgent Networks asserted that it owns and will enforce patent rights on the JPEG technology, arising from a patent that had been filed in 1986 (). The announcement has created a furor reminiscent of Unisys' attempts to assert its rights over the GIF image compression standard. The JPEG committee investigated the patent claims in 2002 and found that they were invalidated by prior art. [http://www.jpeg.org/newsrel1.html] Others have also concluded that Forgent doesn't have a patent that covers JPEG. [http://web.archive.org/web/20040817154508/www.algovision-luratech.com/company/news/patentquarrel.jsp?OnlineShopId=164241031081525276] Nevertheless, between 2002 and 2004 Forgent was able to obtain about $90 million by licensing their patent to some 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 goal of invalidating the patent. The JPEG committee has as one of its explicit goals that their standards be implementable without payment of license fees, and they have secured appropriate license rights for their upcoming JPEG 2000 standard from over 20 large organizations. ==See also== *Image compression *JPEG 2000 *Motion JPEG *Graphics editing program *GDI#GDI.2B (mentions jpeg exploit) *Comparison of layout engines (graphics) ==External links== *[http://www.jpeg.org/ Official JPEG site] *[http://www.faqs.org/faqs/jpeg-faq/ JPEG FAQ] *[http://www.wotsit.org/search.asp?page=5&s=graphics Wotsit.org's entry] on the JPEG format *[http://www.w3.org/Graphics/JPEG/itu-t81.pdf ITU T.81 JPEG compression] (Portable document format) *[http://www.w3.org/Graphics/JPEG/jfif3.pdf JFIF File Format] (Portable document format) *[ftp://ftp.uu.net/graphics/jpeg/wallace.ps.gz The JPEG Still Picture Compression Standard, Summary by Gregory K. Wallace] * [http://www.fho-emden.de/~hoffmann/jpeg131200.pdf JPEG Compression (Gernot Hoffman)] Lossy compression algorithms Graphics file formats
There was a computer virus alert earlier this year regarding the JPEG format. Evidently, there's some way to hide a virus in a jpeg file, and have the virus activate when the jpeg is loaded in a typical viewer. This would be good info to include, but I would want to research and verify the details first. Perhaps someone will beat me to it? User:Wesley :There is some weird virus that attaches itself to JPEG files. (Un)fortunately, JPEG files cannot be executed on any computer I know of, so the virus will never be activated. The writer might as well have written a computer virus that attaches itself to lamp shades, that would have the same effect. See [http://www.theregister.co.uk/content/archive/25718.html].--branko ::Unless there's a buffer overrun or similar exploit for some commonly-used JPEG decoder library... -- User:The Anome 09:22, 1 Sep 2004 (UTC) :::iirc there was (iirc it was in a microsoft implementation) User:Plugwash 20:48, 2 Apr 2005 (UTC) ==graphics== If you would like to use some graphic for this topic. There's an online [http://www.poltran.com/ Polish-English translator] that does one sentence at a time, though results can be sketchy. (unsigned comment by user:Ke4roh :anything that uses the % sign when describing jpeg quality has no credibility whatsoever sorry User:Plugwash 20:48, 2 Apr 2005 (UTC) ==external link== Are you sure the "Compress JPG and GIF images" link is appropriate for this article? The site looks quite commercial, but I didn't delete it since I didn't know if someone put it there on purpose or if was simply vandalism. User:TheListener :mmm link didn't work at all for me i'll try it again later. User:Plugwash 20:48, 2 Apr 2005 (UTC) ==typo to be fixed== In the example 8 by 8 matrix to be put through the jpeg compression algorithm, there is something wrong with the entry 68 in row 6, column 6, because subtracting 128 does not give the asserted result -65 in the next displayed matrix. It is not clear which of the two matrices is wrong, except that the discrete cosine transform result matches the second matrix rather than the first. These matrices, with same inconsistency, also appear in the second edition of the Gonzalez/Woods book Digital Image Processing, second editon, page 499. Hopefully the author of this page can clear up the inconsistency. ---- 24.118.95.84 (sig added by Cburnett) :How's that now? User:Cburnett 03:58, Apr 19, 2005 (UTC) ::Not sure. Which of the two numbers was wrong? ---- 24.118.95.84 (sig added by Cburnett) :::You'll have to go into the history and check. I re-ran all the numbers and just pasted them in. User:Cburnett 02:11, Apr 20, 2005 (UTC) :::: I contacted the original author of the example to determine which of the numbers to correct. The correct fix is to 63. ---- 24.118.95.84 (sig added by Cburnett) ::::: You're point is irrelevant as everything is based on the matrix here. Changing them requires changing of *ALL* the numbers. There are enough discrepancies in Gonzalez & Woods numbers that I didn't copy the numbers but generated them on my own. ::::: So stop reverting as you're invalidating all the numbers. User:Cburnett 22:47, Apr 22, 2005 (UTC) ::::::OK. Fine. That's what I wanted to know - that you had recalculated them all. I was in the process of writing code to do it myself, for the same reason you gave, but I am happy to have it done by you. ==The matrix reformatted?== The numerical matrices are in what looks to me like a *terribly* old-fashioned font (probably through association with similar fonts I've seen in antiquated schoolbooks). They're also so wide that when viewed at 800 pixels width (which I often do when using a Favorites or History sidebar in IE6) the right hand side of some tables disappears behind the images on the right. User:Lee M 00:39, 3 May 2005 (UTC) :A lot of web viewers sitll use 800x600; it's about 30% of the browsing public. Time to fix it. User:Samboy 09:02, 3 May 2005 (UTC) :yeah its mediawiki math markup being rendered as png :maybe there is some other way to do the matrixes that will work better (is there any particular reason for them to look like maths matrixes rather than more generic grids of numbers?) User:Plugwash 10:14, 3 May 2005 (UTC) ::As the author of the data, you're going to have to explain to me the difference between a matrix and a "grid of numbers". ::Regarding the "*terribley* old-fashioned font", do you never read any math articles? Like covariance matrix or List of integrals of rational functions. It's TeX. User:Cburnett 14:21, May 3, 2005 (UTC) :::I think we should use a different font than the one TeX uses; it doesn't look that great against the sans-serif font what we use for articles. User:Samboy 04:41, 16 May 2005 (UTC) ::::This is the incorrect place for such a discussion... User:Cburnett 23:11, May 22, 2005 (UTC) :Imo the issue at hand here is if its appropriate to use matrix math markup for a table of numbers that afaict has basically nothing to do with matrix algebra etc. User:Plugwash 12:22, 23 May 2005 (UTC) ::A matrix ''IS'' a table of numbers. MATLAB stores images as matrices and there's really no difference between a 2-D array and a matrix. Simply because the subimages in question are not used as linear algebra matrices will not compel me to agree to switch to another form of ''representation'' of the same numbers. User:Cburnett 16:16, May 25, 2005 (UTC)
#redirectJPEG
See other meanings of words starting from letter:
Words begining with Jpeg:
JPEG
JPEG
Jpeg
JPEG-2000
JPEG2000
Jpegtran
JPEG_2000
JPEG_file_format
JPEG_File_Interchange_Format
JPEG_Image
JPEG
In computing, JPEG is a commonly used standard method of Data compression photographic images. The file format which employs this compression is commonly also called JPEG; the most common file extensions for this format are .jpeg, .jfif, .jpg, .JPG, or .JPE although .jpg is the most common on all platforms. The name stands for Joint Photographic Experts Group. JPEG itself specifies only how an image is transformed into a stream of bytes, but not how those bytes are encapsulated in any particular storage medium. A further standard, created by the Independent JPEG Group, called JFIF (JPEG File Interchange Format) specifies how to produce a file suitable for computer storage and transmission (such as over the Internet) from a JPEG stream. In common usage, when one speaks of a "JPEG file" one generally means a JFIF file, or sometimes an Exif JPEG file. There are, however, other JPEG-based file formats, such as JNG. JPEG/JFIF is the most common format used for storing and transmitting photographs on the World Wide Web. It is ''not'' as well suited for line drawings and other textual or iconic graphics because its compression method performs badly on these types of images (the PNG and GIF formats are in common use for that purpose; GIF, having only 8 bits per pixel is not well suited for colour photographs, but PNG may have as much or more detail than JPEG). The MIME media type for JFIF is ''image/jpeg'' (defined in RFC 1341). ==Encoding== Many of the options in the JPEG standard are little used. Here is a brief description of one of the more common methods of encoding when applied to an input that has 24 bits per pixel (eight each of RGB color model). This particular option is a lossy data compression method. ===Color space transformation=== First, the image is converted from RGB color model into a different color space called YUV. This is similar to the color space used by NTSC and PAL color television transmission. The Y component represents the brightness of a pixel, and the U and V components together represent the hue and saturation (not respectively). This part is useful because the human eye can see more detail in the Y component than in the others. ===Downsampling=== The above transformation enables the next step, which is to reduce the U and V components (called "downsampling" or "chroma subsampling"). The ratios at which the downsampling can be done on JPEG are YUV 4:4:4 (no downsampling), YUV 4:2:2 (decimate by factor of 2 in horizontal direction), and most commonly YUV 4:2:0 (decimate by factor of 2 in horizontal and vertical directions). For the rest of the compression process, Y, U and V are processed separately and in a very similar manner. ===Discrete cosine transform=== Next, each component (Y, U, V) of the image is "tiled" into sections of eight by eight pixels each, then each tile is converted to frequency space using a two-dimensional discrete cosine transform (DCT). If one such 8×8 8-bit subimage is: : which is then shifted by 128 results in : and then taking the DCT and rounding to the nearest integer results in : Note the rather large value of the top-left corner. This is the DC coefficient. ===Quantization=== The human eye is fairly good at seeing small differences in brightness over a relatively large area, but not so good at distinguishing the exact strength of a high frequency brightness variation. This fact allows one to get away with greatly reducing the amount of information in the high frequency components. This is done by simply dividing each component in the frequency domain by a constant for that component, and then rounding to the nearest integer. This is the main lossy operation in the whole process. As a result of this, it is typically the case that many of the higher frequency components are rounded to zero, and many of the rest become small positive or negative numbers. A common quantization matrix is: : Using this quantization matrix with the DCT coefficient matrix from above results in: : For example, using −415 (the DC coefficient) and rounding to the nearest integer : ===Entropy coding=== Entropy coding is a special form of lossless data compression. It involves arranging the image components in a "zigzag" order that groups similar frequencies together, inserting length coding zeros, and then using Huffman coding on what is left. The JPEG standard also allows, but does not require, the use of arithmetic coding which is mathematically superior to Huffman coding. However, this feature is rarely used as it is covered by patents and because it is much slower to encode and decode compared to Huffman coding. Arithmetic coding typically makes files about 5% smaller. The zig-zag sequence for the above quantized coefficients would be: −26, −3, 0, −3, −3, −6, 2, −4, 1 −4, 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 JPEG has a special Huffman code word for ending the sequence prematurely when the remaining coefficients are zero. Using this special code word, EOB, the sequence becomes −26, −3, 0, −3, −3, −6, 2, −4, 1 −4, 1, 1, 5, 1, 2, −1, 1, −1, 2, 0, 0, 0, 0, 0, −1, −1, EOB ===Compression ratio and artifacts=== The resulting compression ratio can be varied according to need by being more or less aggressive in the divisors used in the quantization phase. Ten to one compression usually results in an image that can't be distinguished by eye from the original. 100 to one compression is usually possible, but will look distinctly Compression artifact compared to the original. The appropriate level of compression depends on the use to which the image will be put. Those who use the World Wide Web may be familiar with the irregularities known as compression artifacts that appear in JPEG digital images. These are due to the quantization step of the JPEG algorithm. They are especially noticeable around eyes in pictures of faces. They can be reduced by choosing a lower level of image compression; they may be eliminated by saving an image using a Lossless data compression file format, though for photographic images this will usually result in a larger file size. ===Decoding=== Decoding to display the image consists of doing all the above in reverse. Taking the DCT coefficient matrix (after adding the difference of the DC coefficient back in) : and multiplying it by the quantization matrix from above results in : which closely resembles the original DCT coefficient matrix for the top-left portion. Taking the inverse DCT results in an image with values (still shifted down by 128) {| border="1" width="256" align="right" |- |
|- | Notice the slight differences between the original (top) and decompressed image (bottom) which is most readily seen in the bottom-left corner. |} : and adding 128 to each entry : This is the uncompressed subimage and can be compared to the original subimage (also see images to the right) by taking the difference (original - uncompressed) results in error values : with an average absolute error of about 5 values per pixels (i.e., ). The error is most noticeable in the bottom-left corner where the bottom-left pixel becomes darker than the pixel to its immediate right. == Usage == JPEG is at its best on photographs and paintings of realistic scenes with smooth variations of tone and color. In this case it usually performs much better than purely lossless methods while still giving a good looking image (in fact it will produce a much higher quality image than other common methods such as GIF which are lossless for drawings and iconic graphics but require severe quantization for full-color images). === Photographs === JPEG compression artifacts blend well into photographs with detailed non-uniform textures, allowing higher compression ratios.
The mid-quality photo uses only one sixth the storage space but has no noticeable loss of detail and artifacts. However, once a certain threshold of compression is passed, compressed images show increasingly visible defects. See the article on rate distortion theory for a mathematical explanation of this threshold effect. ==Other lossy encoding formats== Newer lossy methods, particularly wavelet compression, perform even better in these cases. However, JPEG is a well established standard with plenty of software available, including free software, so it continues to be heavily used as of 2005. Also, many wavelet algorithms are patented, making it difficult or impossible to use them freely in many software projects. The JPEG committee has now created its own wavelet-based standard, JPEG 2000, which is intended to eventually supersede the original JPEG standard. ==Potential patent issues== In 2002 Forgent Networks asserted that it owns and will enforce patent rights on the JPEG technology, arising from a patent that had been filed in 1986 (). The announcement has created a furor reminiscent of Unisys' attempts to assert its rights over the GIF image compression standard. The JPEG committee investigated the patent claims in 2002 and found that they were invalidated by prior art. [http://www.jpeg.org/newsrel1.html] Others have also concluded that Forgent doesn't have a patent that covers JPEG. [http://web.archive.org/web/20040817154508/www.algovision-luratech.com/company/news/patentquarrel.jsp?OnlineShopId=164241031081525276] Nevertheless, between 2002 and 2004 Forgent was able to obtain about $90 million by licensing their patent to some 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 goal of invalidating the patent. The JPEG committee has as one of its explicit goals that their standards be implementable without payment of license fees, and they have secured appropriate license rights for their upcoming JPEG 2000 standard from over 20 large organizations. ==See also== *Image compression *JPEG 2000 *Motion JPEG *Graphics editing program *GDI#GDI.2B (mentions jpeg exploit) *Comparison of layout engines (graphics) ==External links== *[http://www.jpeg.org/ Official JPEG site] *[http://www.faqs.org/faqs/jpeg-faq/ JPEG FAQ] *[http://www.wotsit.org/search.asp?page=5&s=graphics Wotsit.org's entry] on the JPEG format *[http://www.w3.org/Graphics/JPEG/itu-t81.pdf ITU T.81 JPEG compression] (Portable document format) *[http://www.w3.org/Graphics/JPEG/jfif3.pdf JFIF File Format] (Portable document format) *[ftp://ftp.uu.net/graphics/jpeg/wallace.ps.gz The JPEG Still Picture Compression Standard, Summary by Gregory K. Wallace] * [http://www.fho-emden.de/~hoffmann/jpeg131200.pdf JPEG Compression (Gernot Hoffman)] Lossy compression algorithms Graphics file formats
JPEG
There was a computer virus alert earlier this year regarding the JPEG format. Evidently, there's some way to hide a virus in a jpeg file, and have the virus activate when the jpeg is loaded in a typical viewer. This would be good info to include, but I would want to research and verify the details first. Perhaps someone will beat me to it? User:Wesley :There is some weird virus that attaches itself to JPEG files. (Un)fortunately, JPEG files cannot be executed on any computer I know of, so the virus will never be activated. The writer might as well have written a computer virus that attaches itself to lamp shades, that would have the same effect. See [http://www.theregister.co.uk/content/archive/25718.html].--branko ::Unless there's a buffer overrun or similar exploit for some commonly-used JPEG decoder library... -- User:The Anome 09:22, 1 Sep 2004 (UTC) :::iirc there was (iirc it was in a microsoft implementation) User:Plugwash 20:48, 2 Apr 2005 (UTC) ==graphics== If you would like to use some graphic for this topic. There's an online [http://www.poltran.com/ Polish-English translator] that does one sentence at a time, though results can be sketchy. (unsigned comment by user:Ke4roh :anything that uses the % sign when describing jpeg quality has no credibility whatsoever sorry User:Plugwash 20:48, 2 Apr 2005 (UTC) ==external link== Are you sure the "Compress JPG and GIF images" link is appropriate for this article? The site looks quite commercial, but I didn't delete it since I didn't know if someone put it there on purpose or if was simply vandalism. User:TheListener :mmm link didn't work at all for me i'll try it again later. User:Plugwash 20:48, 2 Apr 2005 (UTC) ==typo to be fixed== In the example 8 by 8 matrix to be put through the jpeg compression algorithm, there is something wrong with the entry 68 in row 6, column 6, because subtracting 128 does not give the asserted result -65 in the next displayed matrix. It is not clear which of the two matrices is wrong, except that the discrete cosine transform result matches the second matrix rather than the first. These matrices, with same inconsistency, also appear in the second edition of the Gonzalez/Woods book Digital Image Processing, second editon, page 499. Hopefully the author of this page can clear up the inconsistency. ---- 24.118.95.84 (sig added by Cburnett) :How's that now? User:Cburnett 03:58, Apr 19, 2005 (UTC) ::Not sure. Which of the two numbers was wrong? ---- 24.118.95.84 (sig added by Cburnett) :::You'll have to go into the history and check. I re-ran all the numbers and just pasted them in. User:Cburnett 02:11, Apr 20, 2005 (UTC) :::: I contacted the original author of the example to determine which of the numbers to correct. The correct fix is to 63. ---- 24.118.95.84 (sig added by Cburnett) ::::: You're point is irrelevant as everything is based on the matrix here. Changing them requires changing of *ALL* the numbers. There are enough discrepancies in Gonzalez & Woods numbers that I didn't copy the numbers but generated them on my own. ::::: So stop reverting as you're invalidating all the numbers. User:Cburnett 22:47, Apr 22, 2005 (UTC) ::::::OK. Fine. That's what I wanted to know - that you had recalculated them all. I was in the process of writing code to do it myself, for the same reason you gave, but I am happy to have it done by you. ==The matrix reformatted?== The numerical matrices are in what looks to me like a *terribly* old-fashioned font (probably through association with similar fonts I've seen in antiquated schoolbooks). They're also so wide that when viewed at 800 pixels width (which I often do when using a Favorites or History sidebar in IE6) the right hand side of some tables disappears behind the images on the right. User:Lee M 00:39, 3 May 2005 (UTC) :A lot of web viewers sitll use 800x600; it's about 30% of the browsing public. Time to fix it. User:Samboy 09:02, 3 May 2005 (UTC) :yeah its mediawiki math markup being rendered as png :maybe there is some other way to do the matrixes that will work better (is there any particular reason for them to look like maths matrixes rather than more generic grids of numbers?) User:Plugwash 10:14, 3 May 2005 (UTC) ::As the author of the data, you're going to have to explain to me the difference between a matrix and a "grid of numbers". ::Regarding the "*terribley* old-fashioned font", do you never read any math articles? Like covariance matrix or List of integrals of rational functions. It's TeX. User:Cburnett 14:21, May 3, 2005 (UTC) :::I think we should use a different font than the one TeX uses; it doesn't look that great against the sans-serif font what we use for articles. User:Samboy 04:41, 16 May 2005 (UTC) ::::This is the incorrect place for such a discussion... User:Cburnett 23:11, May 22, 2005 (UTC) :Imo the issue at hand here is if its appropriate to use matrix math markup for a table of numbers that afaict has basically nothing to do with matrix algebra etc. User:Plugwash 12:22, 23 May 2005 (UTC) ::A matrix ''IS'' a table of numbers. MATLAB stores images as matrices and there's really no difference between a 2-D array and a matrix. Simply because the subimages in question are not used as linear algebra matrices will not compel me to agree to switch to another form of ''representation'' of the same numbers. User:Cburnett 16:16, May 25, 2005 (UTC)
Jpeg
#redirectJPEG
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JA | JB | JC | JD | JE | JF | JG | JH | JI | JK | JL | JM | JN | JO | JP | JR | JS | JT | JU | JW | JX | JY | JZ |Words begining with Jpeg:
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JPEG
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