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quantization image processing wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 color quantization 2 grayscale quantization 3 frequency quantization for image compression toggle frequency quantization for image compression subsection 3 1 quantization matrices 4 see also 5 references toggle the table of contents quantization image processing 3 languages català español bahasa indonesia edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia lossy compression technique this article needs more citations please help improve this article by adding citations to reliable sources unsourced material may be challenged and removed find sources quantization image processing news newspapers books scholar jstor november 2012 learn how and when to remove this message quantization involved in image processing is a lossy compression technique achieved by compressing a range of values to a single quantum discrete value when the number of discrete symbols in a given stream is reduced the stream becomes more compressible for example reducing the number of colors required to represent a digital image makes it possible to reduce its file size specific applications include dct data quantization in jpeg and dwt data quantization in jpeg 2000 color quantization edit main article color quantization color quantization reduces the number of colors used in an image this is important for displaying images on devices that support a limited number of colors and for efficiently compressing certain kinds of images most bitmap editors and many operating systems have built in support for color quantization popular modern color quantization algorithms include the nearest color algorithm for fixed palettes the median cut algorithm and an algorithm based on octrees it is common to combine color quantization with dithering to create an impression of a larger number of colors and eliminate banding artifacts grayscale quantization edit grayscale quantization also known as gray level quantization is a process in digital image processing that involves reducing the number of unique intensity levels shades of gray in an image while preserving its essential visual information this technique is commonly used for simplifying images reducing storage requirements and facilitating processing operations in grayscale quantization an image with n intensity levels is converted into an image with a reduced number of levels typically l levels where l n the process involves mapping each pixel s original intensity value to one of the new intensity levels one of the simplest methods of grayscale quantization is uniform quantization where the intensity range is divided into equal intervals and each interval is represented by a single intensity value let s say we have an image with intensity levels ranging from 0 to 255 8 bit grayscale if we want to quantize it to 4 levels the intervals would be 0 63 64 127 128 191 and 192 255 each interval would be represented by the midpoint intensity value resulting in intensity levels of 31 95 159 and 223 respectively the formula for uniform quantization is q x x δ δ δ 2 displaystyle q x left lfloor frac x delta right rfloor times delta frac delta 2 where q x is the quantized intensity value x is the original intensity value δ is the size of each quantization interval let s quantize an original intensity value of 147 to 3 intensity levels original intensity value x 147 desired intensity levels l 3 we first need to calculate the size of each quantization interval δ 255 l 1 255 3 1 127 5 displaystyle delta frac 255 l 1 frac 255 3 1 127 5 using the uniform quantization formula q x 147 127 5 127 5 127 5 2 displaystyle q x left lfloor frac 147 127 5 right rfloor times 127 5 frac 127 5 2 q x 1 15294118 127 5 127 5 2 displaystyle q x left lfloor 1 15294118 right rfloor times 127 5 frac 127 5 2 q x 1 127 5 63 75 191 25 displaystyle q x 1 times 127 5 63 75 191 25 rounding 191 25 to the nearest integer we get q x 191 displaystyle q x 191 so the quantized intensity value of 147 to 3 levels is 191 frequency quantization for image compression edit 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 rapidly varying brightness variation this fact allows one to reduce the amount of information required by ignoring 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 as human vision is also more sensitive to luminance than chrominance further compression can be obtained by working in a non rgb color space which separates the two e g ycbcr and quantizing the channels separately 1 quantization matrices edit a typical video codec works by breaking the picture into discrete blocks 8 8 pixels in the case of mpeg 1 these blocks can then be subjected to discrete cosine transform dct to calculate the frequency components both horizontally and vertically 1 the resulting block the same size as the original block is then pre multiplied by the quantization scale code and divided element wise by the quantization matrix and rounding each resultant element the quantization matrix is designed to provide more resolution to more perceivable frequency components over less perceivable components usually lower frequencies over high frequencies in addition to transforming as many components to 0 which can be encoded with greatest efficiency many video encoders such as divx xvid and 3ivx and compression standards such as mpeg 2 and h 264 avc allow custom matrices to be used the extent of the reduction may be varied by changing the quantizer scale code taking up much less bandwidth than a full quantizer matrix 1 this is an example of dct coefficient matrix 415 33 58 35 58 51 15 12 5 34 49 18 27 1 5 3 46 14 80 35 50 19 7 18 53 21 34 20 2 34 36 12 9 2 9 5 32 15 45 37 8 15 16 7 8 11 4 7 19 28 2 26 2 7 44 21 18 25 12 44 35 48 37 3 displaystyle begin bmatrix 415 33 58 35 58 51 15 12 5 34 49 18 27 1 5 3 46 14 80 35 50 19 7 18 53 21 34 20 2 34 36 12 9 2 9 5 32 15 45 37 8 15 16 7 8 11 4 7 19 28 2 26 2 7 44 21 18 25 12 44 35 48 37 3 end bmatrix a common quantization matrix is 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 displaystyle 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 dividing the dct coefficient matrix element wise with this quantization matrix and rounding to integers results in 26 3 6 2 2 1 0 0 0 3 4 1 1 0 0 0 3 1 5 1 1 0 0 0 4 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 displaystyle begin bmatrix 26 3 6 2 2 1 0 0 0 3 4 1 1 0 0 0 3 1 5 1 1 0 0 0 4 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 bmatrix for example using 415 the dc coefficient and rounding to the nearest integer r o u n d 415 16 r o u n d 25 9375 26 displaystyle mathrm round left frac 415 16 right mathrm round left 25 9375 right 26 typically this process will result in matrices with values primarily in the upper left low frequency corner by using a zig zag ordering to group the non zero entries and run length encoding the quantized matrix can be much more efficiently stored than the non quantized version 1 see also edit image segmentation image based meshing range segmentation references edit 1 2 3 4 5 john wiseman an introduction to mpeg video compression https web archive org web 20111115004238 http www john wiseman com technical mpeg_tutorial htm 1 v t e data compression methods lossless type entropy adaptive coding arithmetic asymmetric numeral systems golomb huffman adaptive canonical modified range shannon shannon fano shannon fano elias tunstall unary universal exp golomb fibonacci gamma levenshtein dictionary byte pair encoding lempel ziv 842 lz4 lzjb lzo lzrw lzss lzw lzwl snappy other bwt ctw cm delta incremental dmc dpcm grammar re pair sequitur ldct mtf paq ppm rle hybrid lz77 huffman deflate lzx lzs lz77 ans lzfse lz77 huffman ans zstandard lz77 huffman context brotli lzss huffman lha lzh lz77 range lzma lzham rle bwt mtf huffman bzip2 lossy type transform discrete cosine transform dct mdct dst fft wavelet daubechies dwt spiht predictive dpcm adpcm lpc acelp celp lar lsp wlpc motion compensation estimation vector psychoacoustic audio concepts bit rate abr cbr vbr companding convolution dynamic range latency nyquist shannon theorem sampling silence compression sound quality speech coding sub band coding codec parts a law μ law dpcm adpcm dm ft fft lpc acelp celp lar lsp wlpc mdct psychoacoustic model image concepts chroma subsampling coding tree unit color space compression artifact image resolution macroblock pixel psnr quantization standard test image texture compression methods chain code dct deflate fractal klt lp rle wavelet daubechies dwt ezw spiht video concepts bit rate abr cbr vbr display resolution frame frame rate frame types interlace video characteristics video quality codec parts dct dpcm deblocking filter lapped transform motion compensation estimation vector wavelet daubechies dwt theory compressed data structures compressed suffix array fm index entropy information theory timeline kolmogorov complexity prefix code quantization rate distortion redundancy symmetry smallest grammar problem community hutter prize people mark adler david a huffman phil katz smith steven w 2003 digital signal processing a practical guide for engineers and scientists demystifying technology series amsterdam boston newnes isbn 978 0 7506 7444 7 retrieved from https en wikipedia org w index php title quantization_ image_processing oldid 1370491179 categories lossy compression algorithms image compression data compression hidden categories articles with short description short description is different from wikidata articles needing additional references from november 2012 all articles needing additional references this page was last edited on 21 august 2026 at 12 05 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms may apply by using this site you agree to the terms of use and privacy policy wikipedia is a registered trademark of the wikimedia foundation inc a non profit organization privacy policy about wikipedia disclaimers contact wikipedia legal safety contacts code of conduct developers statistics cookie statement mobile view search search toggle the table of contents quantization image processing 3 languages add topic