Wavelet uguqule: sokunquma Ngokwesibonelo isicelo

Ukufika kombuso engabizi khamera kuye kwasho ukuthi ingxenye enkulu abakhileyo iplanethi, kungakhathaliseki ubudala noma ucansi, usezuze umkhuba ukuba liyobamba yakhe ngaso sonke wafaka izithombe zabo obala umphakathi in the amanethiwekhi zenhlalo. Ngaphezu kwalokho, uma ngaphambili isithombe somndeni ingobo yomlando yafakwa ku-albhamu efanayo, namuhla liqukethe amakhulu izithombe. Ukuze kube lula isitoreji kanye ne-transmission kuwo wonke amanethiwekhi adinga isithombe sedijithali isisindo ukunciphisa. Kuze kube yimanje, izindlela ezisetshenzisiwe zisekelwe algorithm ezihlukahlukene kuhlanganise nesithombe wavelet uguqule. Kuyini, tshela i-athikili yethu.

Kuyini isithombe sedijithali

Imininingwane Visual kule khompyutha amelwe ngesimo izinombolo. Ngamagama alula, isithombe esithathwe nedivaysi digital, yitafula lapho amaseli afakiwe amagugu ngayinye kwe-pixel yayo umbala. Uma kuziwa umfanekiso ezinombala ofanayo, bese esikhundleni iLuminance amanani asuka isikhawu [0, 1], lapho 0 isetshenziswa ubheke omnyama, futhi 1 - omhlophe. Okunye imibala zinikwa izinombolo wamaqhuzu, kodwa nabo sezimiso ukusebenza, ngakho ibanga enwetshiwe futhi lenani elikhethiwe kusukela isikhawu kuka-0 no 255. Kungani lokhu? Kulula! Nale lizikhethele ukumelwa kanambambili lokufaka ikhodi le iLuminance ka-pixel elingu ngayinye idinga ncamashi eyodwa ibhayithi. Kusobala ukuthi eziningi memory iyadingeka ukugcina ngisho isithombe encane. Ngokwesibonelo, usayizi wesithombe 256 x 256 Amaphikseli kuthatha 8 Kbytes.

A amazwi ambalwa mayelana nezindlela isithombe kokucindezelwa

Ngokuqinisekile wonke umuntu oye wabona ikhwalithi embi izithombe lapho ehlanekezelwe ngesimo calandze nangebala, ababiziweyo zobuciko. Kuphakama ngenxa okubizwa ngokuthi kokucindezelwa skrini esingaqinile. Kungaba kakhulu ukunciphisa isisindo yesithombe, Nokho, ngaso nakanjani nomthelela kukhwalithi.

Ukuze skrini esingaqinile kokucindezelwa algorithm zihlanganisa:

• JPEG. Lokhu iyona omunye algorithm ethandwa kakhulu. Kusekelwe ukusetshenziswa cosine ngokuqhubekayo uguqule. Uzokwenza kufanele kuphawulwe ukuthi kukhona okukhethwa kukho JPEG lossless abacula kokucindezelwa. Lezi zihlanganisa esingaqinile JPEG futhi JPEG-LS.
• JPEG 2000. algorithm isetshenziswa ezisekelweni mobile, futhi esekelwe isicelo wavelet ngokuqhubekayo uguqule.
• kokucindezelwa Fractal. Kwezinye izimo, it ikuvumela ukuba bathole izithombe eliphezulu ngisho ne kokucindezelwa eqinile. Nokho, ngenxa yezinkinga Nelungelo Lokwenza le ndlela uyaqhubeka ukuba angavamile.

Esingaqinile kokucindezelwa algorithm eyenziwa:

• RLE (ezazisetshenziswa njengomhlatshelo indlela eyinhloko ngefomethi TIFF, BMP, TGA).
• LZW (elisetshenziswa i-GIF format).
• LZ-Huffman (esetshenziselwa PNG).

Fourier uguqule

Ngaphambi kokuvala kuya wavelet, kunengqondo ukuhlola imisebenzi ahlobene, echaza okuza wokwanda ulwazi sokuqala ku izingxenye aphansi, isb. E. Harmonic kunyakaza nge amaza ezahlukene. Ngamanye amazwi, lo Fourier uguqule - ithuluzi eliyingqayizivele yokuxhuma imihlaba ngokuqhubekayo futhi okuqhubekayo.

Kubonakala sengathi lokhu:

Ifomula kombhala kulotshiwe kanje:

Uyini wavelet

Ngemuva leli gama efihla umsebenzi zezibalo, okuyinto ikuvumela ukuba sihlaziye ezahlukene izingxenye imvamisa idatha yokuhlola. igrafu yayo kuyinto undulation kabani amplitude Sehlile 0 kude umsuka. Ngo interest jikelele kukhona okuza wavelet kunqunywa isignali ebalulekile.

spectrograms Wavelet zihlukile ezivamile Fourier spectra, kusukela izici ezihlukahlukene ezihlobene amasignali spectrum nge ingxenye yabo yesikhashana.

ukuguqulwa Wavelet

Le ndlela isignali ukuguqulwa (imisebenzi) kuyivumela ukuhumusha kusuka isikhathi ukumelwa isikhathi imvamisa.

Ukuze wavelet ukuguqulwa kwakunokwenzeka, ngokuba elihambisana umsebenzi wavelet, kumele izimo ezilandelayo kuhlangatshezwane nazo:

• Uma kwabanye ψ umsebenzi (t) -Fourier uguqule ine uhlobo

ukuthi isimo kufanele aneliswe:

Ngaphezu kwalokho:

• Wavelet kumele abe namandla ezilinganiselwe;
• kufanele kube integrable okuqhubekayo futhi zisekelwa compact;
• wavelet kumele yenziwe yaba yasendaweni kokubili imvamisa futhi ngesikhathi (space).

izinhlobo

A wavelet okuqhubekayo uguqule osetshenziselwa amasignali abafanele. ezithakazelisayo kakhulu kangakanani Analogue yayo leyehlukene. Phela, ingasetshenziswa i-information processing computer. Nokho, inkinga ephakama ukuthi ifomula okwesikhathi fiberboard leyehlukene ayikwazi etholwe elula ezifanele discretization amafomula DNP.

Isixazululo sale nkinga, sitholwe Daubechies, owakwazi ukhethe indlela ukwakha uchungechunge wavelets orthogonal, ngasinye sazo kuchazwe inombolo ezilinganiselwe ka okuza. Kamuva ama-algorithm okusheshayo zadalwa, ezifana algorithm Malla. Ngo isicelo yayo ukubola noma ukubuyisela oda edingekayo ukwenza imisebenzi CN, lapho N - isampula obuphelele, futhi - isibalo okuza.

Vayvlet Haar

Cindezela isithombe, kubalulekile ukuthola njalo ezithile phakathi idatha yayo, futhi ngisho kangcono uma kuyoba amaketanga olude amaqanda. Lapha kulapho ke kungaba usizo kuya wavelet uguqule algorithm. Nokho, siqhubeka ubuyekeze izindlela zokusebenza ukuze.

Okokuqala kubalulekile ukukhumbula ukuthi izithombe ukukhanya Amaphikseli eduze ngokuvamile elinesimo esincane. Ngisho noma kukhona izithombe kumasayithi sangempela abukhali, siziqhathanise ukwahluka ukugqama, hlala kuphela ingxenye encane isithombe. Njengoba isibonelo, ukuthatha test eyaziwa Lenna isithombe ukwenza mhlophe. Uma sithatha a matrix iLuminance pixels bayo, abese ingxenye komugqa wokuqala lizovela ukulandelana kweenomboro 154, 155, 156, 157, 157, 157, 158, 156.

ungafaka isicelo okubizwa ngokuthi i-delta indlela yokuthola amaqanda kuso. Ukuze wenze lokhu, ukugcina kuphela Inombolo yokuqala, futhi abanye abanikeze kuphela umehluko ngayinye sangaphambilini uphawu "+" noma "-".

Imiphumela iba yinhlanganisela yokukhandleka ukulandelana 154,1,1,1,0,0,1, -2.

A Ububi delta-wekhodi akunakudluliswa endawo. Ngamanye amazwi, akunakwenzeka ukuthatha kuphela nocezu ukulandelana futhi uthole ukuthi yini ukukhanya okukhulu ke ufakwe, ukukhishwa, uma kungesona sonke amagugu phambi kwakhe.

Ukuze unqobe lo kusimo, inombolo uhlukaniswe ngazimbili kanye ngamunye zimaphakathi isamba (v. A) kanye nengxenye umehluko (v. D), m. F. Ukuze (154,155) (156,157) (157,157) (158,156) kufanele (154.5, 0,5) (156.5,0.5) (157,0.0), (157, -1.0). Kulokhu, kuba njalo kungenzeka ukuthola ukubaluleka izinombolo ezimbili pair.

Ngokuvamile, le wavelet ngokuqhubekayo uguqule we S isignali, sinazo:

Le ndlela elandelayo kusukela kwenzeka ngokuqhubekayo of wavelet okuqhubekayo uguqule, Haar futhi asetshenziswa kabanzi emikhakheni ehlukahlukene idatha kusebenziswe futhi kokucindezelwa.

kokucindezelwa

Njengoba sekushiwo, omunye izicelo wavelet uguqule algorithm iyona JPEG 2000 kokucindezelwa indlela usebenzisa Haar esekelwe Vector ukuhunyushwa Amaphikseli amabili e-X Y Vector (X + Y) / 2 futhi (X - Y) / 2. Kwanele uphindaphinde Vector kokuqala kuleli matrix ngezansi.

Uma amaphuzu ngaphezulu, thatha-matrix ngaphezulu, okuyinto ahlelwe kwi idayagonali-matrix H. Ngakho-ke, vector kokuqala ngokuzimela Ubude baso kusingathwa ngazimbili.

izihlungi

I kwaphumela "isigamu-sum" - emaphakathi iLuminance amagugu pixels ngababili. Lokho ukubaluleka lapho aguqulwa esithombeni kufanele umnike kona ikhophi, encishisiwe ezikhathini 2. Kulesi isigamu-sum okulinganiselwa ku ukukhanya, t. E. "ehlungiwe" Ukuvutha ongacabangi izindinganiso zawo isenzo njengoba imvamisa izihlungi.

Manje ake ukubhekana nalezo Ukubonisa umehluko. Basuke "isehlane" interpixel "Ukuvutha", kokukhipha ingxenye njalo, isb. E. "ehlungiwe" amagugu at imisindo ephansi.

Ngisho kusukela ngenhla Haar wavelet okuguqula "dummies" kuba sobala ukuthi i-pair of izihlungi ezihlukanisa isiginali ku tincenye letimbili: high imvamisa futhi imvamisa low. umane kabusha hlanganani lezi zinto ukuthola isignali yasekuqaleni.

Ngokwesibonelo

Ake sithi sifuna cindezela isithombe (lesithombe sokuhlola Lenna). Cabanga ngesibonelo wavelet zidlulisela matrix kwe-pixel brightnesses. Uphiko ephezulu imvamisa yesithombe unesibopho ukubonisa imininingwane emihle futhi uchaza umsindo. Ngokuqondene ongaphakeme-imvamisa, iqukethe ulwazi mayelana ukuma ebusweni futhi gradients abushelelezi ukugqama.

Izici izithombe okuqonda ezingabantu yokuthi wesibili ingxenye ezibaluleke kakhudlwana. Lokhu kusho ukuthi uma onomfutho ingxenye ethile idatha ephezulu imvamisa kungenziwa kulahliwe. Ikakhulukazi ngoba sibaluleke kancane futhi ifakwe ngaphezulu ubumbene.

Ukuze wandise degree of kokucindezelwa singasetshenziswa izikhathi eziningana Haar ukuguqulwa idatha ephansi imvamisa.

Ukusetshenziswa afanayo mgudumbili

Njengoba sekuphawuliwe, isithombe sedijithali in computer kukhona ngesimo a matrix kwemibala amagugu pixels yayo. Ngakho, kufanele sibe nesithakazelo endaweni Haar mgudumbili wavelet uguqule. Ukuqalisa kubalulekile nje ukwenza ukuguqulwa ntathu wemigqa ngayinye futhi kukholomu matrix we kwemibala pixels esithombeni ngasinye.

Amanani esondele ku-zero, kungenziwa alahlwe ngaphandle umonakalo ebalulekile ukuze isithombe Decoded. Le nqubo ibizwa ngokuthi quantization ezaziwayo. Futhi kulesi sigaba imininingwane elahlekile. By the way, inombolo yezinto nullable zingashintsha, kanjalo ngokulungisa degree of kokucindezelwa.

Zonke lezi zinyathelo kuholele ukuthi matrix etholwe equkethe esiningi 0. Kumele umugqa eyabhalwa umugqa in ifayela text futhi cindezela noma iyiphi archiver.

emagama

Ukuguqulwa ephambene esithombeni algorithm ezilandelayo:

• It unpacks ingobo yomlando;
• osebenza ephambene Haar uguqule;
• Isithombe Decoded iguqulwe ibe matrix.

Izinzuzo kuqhathaniswa JPEG

было сказано, что он основан на ДКП. Uma sicabanga algorithm Joint Ubuciko bezithombe Ochwepheshe Iqembu watshelwa ukuthi kusekelwe DCT. Lokhu ukuguqulwa wenziwa amabhlogo (8 x 8 Amaphikseli). Ngenxa yalokho, uma kokucindezelwa elinamandla isithombe encishisiwe iba appreciable block isakhiwo. Phakathi kokucindezelwa usebenzisa wavelets inkinga enjalo engekho. Nokho, umsindo zingavela uhlobo oluhlukile ezithinta ukubukeka enyakaza emhlabeni imiphetho. Kukholakala ukuthi zobuciko efanayo ngokwesilinganiso obunganakekile kuka "izikwele" okuyinto zidalwe lapho usebenzisa i-JPEG algorithm.

Manje ngoba sewuyazi ukuthi lokho wavelets kukhona lokho abayikho nalokho okusebenzayo ukusetshenziswa ngabo watholakala emkhakheni kusebenziswe futhi ukugxisha izithombe digital.