Wavelet fasalin: kayyade aikace-aikace misali

Zuwan m dijital kyamarori ya nufi da cewa babban ɓangare na mazaunan duniya, ko da kuwa shekaru da kuma jima'i, ya samu al'ada kama da kowane mataki da kuma sa su images a kan jama'a nuni a social networks. Bugu da ƙari, idan da a baya iyali photo archive da aka sanya a cikin wannan album, a yau shi kunshi daruruwan hotuna. Domin sauƙaƙe ajiya da kuma watsa a fadin cibiyoyin sadarwa bukatar wani dijital image na nauyi raguwa. Don wannan karshen, hanyoyin da ake amfani da su ne bisa daban-daban lissafi mai tsauri, ciki har da wani wavelet canza. Mene ne shi, gaya mana labarin.

Me ne mai dijital image

Kayayyakin bayanai a cikin kwamfuta da aka wakilta a cikin nau'i na lambobin. A sauki sharuddan, a auki hoto tare da wani dijital na'ura, shi ne a tebur a cikin abin da Kwayoyin suna shiga dabi'u na kowane daga cikin pixel launi. Idan ya zo ga wani monochrome image, to, suna da maye gurbinsu da luminance dabi'u daga tazara [0, 1], inda 0 aka yi amfani da su koma ga baki, da kuma 1 - fari. Wasu launuka suna ba fractional lambobi, amma tare da su m aiki, don haka cikin kewayon aka mika da darajar zaba daga cikin tazara tsakanin 0 da 255. Me ne wannan? Yana da sauki! Tare da wannan zabi a cikin binary misali ga shigar da luminance na kowane pixel bukatar daidai da daya byte. Babu shakka cewa da yawa daga memory ake bukata don adana ma wani karamin image. Alal misali, hoton size of 256 x 256 pixels daukan 8 Kbytes.

A 'yan kalmomi game da image matsawa hanyoyin

Lalle ne kowa da kowa ya gani da matalauta ingancin da hotuna inda akwai hargitsi a cikin nau'i na rectangles na wannan launi, wanda ake kira kayayyakin gargajiya. Sun bayyana a sakamakon da ake kira lossy matsawa. Yana iya rage nauyin da image, duk da haka, babu shakka zai tasiri a kan ta quality.

Domin lossy matsawa Algorithms sun hada da:

• JPEG. Wannan shi ne ta zuwa yanzu daya daga cikin mafi m lissafi mai tsauri. Ya dogara ne a kan yin amfani da mai hankali cosine canza. A ãdalci ya kamata a lura da cewa akwai zaɓuɓɓuka saboda JPEG Yin lossless matsawa. Wadannan sun hada da Lossless JPEG da JPEG-LS.
• JPEG 2000. A algorithm da ake amfani a kan mobile dandamali, da kuma dogara ne a kan aikace-aikace na wani mai hankali wavelet canza.
• fractal matsawa. A wasu lokuta, shi ba ka damar samun images of kyau kwarai inganci ko da karfi matsawa. Duk da haka, saboda matsalolin da mallakar wannan hanyar ci gaba da zama m.

Lossless matsawa Algorithms yi da:

• RLE (amfani da primary Hanyar cikin TIFF format, BMP, TGA).
• LZW (amfani da GIF format).
• LZ-Huffman (amfani da PNG format).

Fourier fasalin

Kafin juya zuwa ga wavelet, shi ya sa hankali domin gano related ayyuka, ta kwatanta coefficients na fadada daga cikin na farko bayanai cikin na farko da aka gyara, watau. E. masu jituwa vibrations da daban-daban mitoci. A wasu kalmomin, da Fourier fasalin - na musamman da kayan aiki a haɗa mai hankali da kuma ci gaba da halittu.

Yana kama da wannan:

A inversion dabara aka rubuta kamar haka:

Mene ne wani wavelet

Baya da wannan sunan boyewa a ilmin lissafi aiki, wanda ba ka damar nazarin daban-daban mita gyara na gwajin bayanai. Its jadawali ne undulation wanda mawadãta rage-rage zuwa 0 daga asalin. A general amfani ne wavelet coefficients m na game sigina.

Wavelet spectrograms ne daban-daban daga al'ada Fourier a jere, tun daban-daban siffofin hade bakan sakonni da su boko bangaren.

Wavelet canji

Wannan hanya na siginar hira (ayyuka) ba shi da fassara daga wani lokaci a cikin lokaci-mita misali.

Don wavelet canji ya yiwu, ga m wavelet aiki, wadannan yanayi dole ne a hadu:

• Idan saboda wasu aiki ψ (t) -Fourier fasalin yana da tsari

cewa yanayin dole ne gamsu:

Bugu da kari:

• Wavelet dole ne mai iyaka da makamashi.
• shi ya zama integrable m, kuma da m support.
• wavelet dole ne a sarrafa biyu a mita da kuma a lokaci (sarari).

iri

A ci gaba da wavelet fasalin da ake amfani da Game da sakonni. Yafi ban sha'awa shi ne da mai hankali analogue. Bayan duk, shi za a iya amfani da bayanai da aiki a kwakwalwa. Duk da haka, matsala ta taso a cewa dabara domin wani mai hankali fiberboard ba za a iya samu ta hanyar sauki dace discretization dabarbari DNP.

A warware wannan matsala da aka samu ta hanyar Daubechies, wanda ya iya zabi wani Hanyar gina jerin orthogonal wavelets, kowanne daga wanda aka ayyana ta guntun yawan coefficients. Daga baya sauri lissafi mai tsauri da aka halitta, kamar da algorithm Malla. A aikace a decompose ko don mayar da ake bukata domin yin ayyukan CN, inda N - samfurin tsawon, kuma tare da - da yawan coefficients.

Vayvlet Haar

Don damfara wani image, shi wajibi ne a sami wani tsari tsakanin ta data, kuma mafi kyau ma idan shi zai zama dogon sarƙoƙi na zeros. Wannan shi ne inda shi zai iya zama da amfani a cikin wavelet fasalin algorithm. Duk da haka, mu ci gaba da duba aiki hanyoyin domin.

Da farko wajibi ne a tuna da cewa images asubahin m pixels ne yawanci halin da kananan adadin. Ko akwai hotuna a real shafukan da kaifi, contrasting bambance-bambance da haske, suka zauna kawai a kananan rabo daga image. A matsayin misali, sama a kan san gwajin Lenna tsarkiya image. Idan muka dauki wani matrix na luminance na ta pixels, sa'an nan da wani ɓangare na farko line zai bayyana a matsayin wani jerin lambobi 154, 155, 156, 157, 157, 157, 158, 156.

za ka iya amfani da abin da ake kira Delta Hanyar samun zeros zuwa gare shi. Don yin wannan, ci gaba ne kawai na farko number, da kuma ga wasu dauka kawai da bambance-bambance na kowanne daga baya daya tare da alamar "+" ko "-".

A sakamakon haka ne a jerin 154,1,1,1,0,0,1, -2.

A hasara na Delta-tsarinsa ne wadanda ba Locality. A wasu kalmomin, ba shi yiwuwa a yi kawai wani yanki na da jerin da kuma gano abin da Haske shi ne shigar wanda ke aiki, decoded, idan ba duk na dabi'u a gaban shi.

Don shawo kan wannan hasara, yawan ne zuwa kashi nau'i-nau'i, kuma kowane ne rabin Naira Miliyan Xari (v. A) da kuma rabin bambanci (v. D), m. F. Ga (154,155) (156,157) (157,157) (158,156) da (154.5, 0,5) (156.5,0.5) (157,0.0), (157, -1.0). A wannan yanayin, shi ne ko da yaushe zai yiwu a sami darajar da biyu lambobi a cikin wata biyu.

A general, da mai hankali wavelet fasalin na siginar S, muna da:

Wannan hanya haka daga mai hankali hali na ci gaba da wavelet canza, Haar kuma yadu amfani a fannoni daban daban na data aiki da kuma matsawa.

matsawa

Kamar yadda aka ambata riga, daya daga cikin aikace-aikace na wavelet fasalin algorithm ne JPEG 2000 matsawa Hanyar yin amfani da Haar bisa translation vector na biyu pixels a cikin X kuma Y vector (X + Y) / 2, kuma (X - Y) / 2. Shi ya ishe ninka na farko vector a matrix kasa.

Idan maki more, dauki mafi matrix, wanda aka shirya a kan wani diagonal matrix H. Saboda haka, da farko vector da kansa ta tsawon aka sarrafa a nau'i-nau'i.

tacewa

A sakamakon "rabin Miliyan Xari" - ne talakawan luminance dabi'u na pixels a nau'i-nau'i. Wannan shi ne darajar a lokacin da ya tuba zuwa hoton kamata ba shi da wani kwafin, rage a 2 sau. A wannan rabin Miliyan Xari kaddarance haske, t. E. "tace" bazuwar bursts na dabi'u da kuma yi kamar yadda mita tacewa.

Yanzu bari magance masu nuna bambanci. Suna "ware" interpixel "bursts", cire m bangaren, watau. E. "tace" dabi'u a low mitoci.

Ko daga sama Haar wavelet fasalin ga "dummies" kuma shi ya zama a bayyane yake cewa yana da wani biyu daga CD da raba wani alama kashi biyu aka gyara: da high mita da kuma low mita. kawai a sake-gama da wadannan abubuwa zuwa samu asali sigina.

misali

Misali muna so mu damfara da m (gwajin image Lenna). Ka yi la'akari da misalin na wavelet canza matrix na pixel brightnesses. A high-mita bangaren na image ne ke da alhakin nuna lafiya daki-daki, kuma ya bayyana amo. Amma ga low-mita, shi ya ƙunshi bayani game da siffar fuskar da santsi gradients da haske.

Features photos na mutum ji ne irin wannan cewa karshen ne mafi muhimmanci bangaren. Wannan yana nufin cewa a lokacin da matsa a wasu ɓangare na high-mita data za a iya jefar da. The fiye da haka, saboda shi yana da ƙasa da darajar da aka shigar wanda ke aiki mafi compactly.

Don kara mataki na matsawa za a iya amfani da sau da yawa Haar canji zuwa low-mita data.

A amfani da biyu-girma iri-iri

Kamar yadda aka ambata riga, da dijital image a kwamfuta ne a cikin wani nau'i na matrix na intensities dabi'u na ta pixels. Saboda haka, ya kamata mu yi sha'awar a cikin wani biyu-girma Haar wavelet canza. Don aiwatar da shi wajibi ne kawai a yi ta girma hira domin kowane jere da kowane shafi na matrix na intensities na pixels a cikin hoton.

Dabi'u kusa da sifili, za a iya jefar da ba tare da gagarumin lalacewar da decoded image. Wannan tsari ne da aka sani a matsayin quantization. Kuma a wannan mataki na bayanai da aka rasa. Af, da yawan nullable dalilai iya canza, game da shi, daidaitawa da mataki na matsawa.

Duk wadannan matakai haifar da cewa matrix an samu wanda ya ƙunshi manyan yawa na 0. Ya kamata a rubuta layi da layin a cikin wani rubutu fayil da kuma damfara wani archiver.

dikodi mai

A kishiya canji a cikin image a kan wadannan algorithm:

• Yana unpacks wani archive.
• shafi kishiya Haar canza.
• A decoded image ne tuba a cikin wani matrix.

Abũbuwan amfãni idan aka kwatanta da JPEG

было сказано, что он основан на ДКП. A lokacin da la'akari da algorithm hadin gwiwa daukar hoto Masana Group aka gaya masa cewa shi ne tushen on DCT. Wannan hira ne da za'ayi a tubalan (8 x 8 pixels). A sakamakon haka, idan wani karfi matsawa a kan rage image zama appreciable block tsarin. A lokacin matsawa amfani wavelets irin wannan matsala ne mãsu fakowa ba. Duk da haka, amo iya bayyana daban-daban irin wanda da bayyanar ripples kusa gefuna. An yi imani da cewa irin wannan kayayyakin gargajiya a kan talakawan kasa m fiye da "murabba'ai" wanda aka halitta a lokacin da yin amfani da JPEG algorithm.

Yanzu da ka san abin da wavelets ne abin da suka kasance, da abin da m amfani a gare su da aka samu a fagen aiki da kuma compressing dijital images.