Wavelet ukuguqula: nokumisela umzekelo isicelo

Ukufika lwe khamera engaxabisi kuthethe ukuba inxalenye enkulu abemi umhlaba, kungajongwanga budala ngesondo, iye fumene ngumkhwa kwakhe ngakunye nyathelo kwaye ufake imifanekiso yazo ziyaxhonywa zikarhulumente social networks. Ngaphezu koko, ukuba ngaphambili photo usapho yokugcina yafakwa kule album enye, namhlanje iqulathe amakhulu imifanekiso. Ukwenzela ukulungiselela ukugcinwa kunye transmission kuzo zonke iinethiwekhi ifuna umfanekiso wekhompyutha yokunciphisa weight. Ukuza kuthi ga ngoku, iindlela zisetyenziswa ukuba zisekelwe ubuchule eyahlukeneyo, kuquka wavelet ukuguqula. Yintoni na, xelela inqaku lethu.

Yintoni a umfanekiso wedijithali

ulwazi Visual kwi computer imelwe ngohlobo amanani. Ngamagama alula, ifoto wayephethwe isixhobo i-digital, i itafile apho iiseli wangena amaxabiso nganye umbala wayo pixel. Xa kufikwa umfanekiso ezinombala, ngoko ke indawo ziinqobo luminance ukusuka lokuphumla [0, 1], apho 0 lisetyenziswa ukubhekisela abamnyama, yaye-1 - ezimhlophe. Ezinye imibala banikwa amanani iqhezu, kodwa nabo nzima ukusebenza, ngoko ke uluhlu sandisiwe kunye ixabiso okhethiweyo ukusuka lekhefu phakathi 0 no 255. Kutheni na le nto? Yinto elula! Olo khetho kwi ukumelwa yokubini usebenzisa ikhowudi kwi luminance ye pixel nganye kufuna kanye byte enye. Kucacile ukuba eninzi inkumbulo efunekayo ukugcina nkqu umfanekiso encinane. Umzekelo, ubungakanani umfanekiso 256 x 256 pixels kuthatha Kbytes 8.

A amagama ambalwa malunga ngeendlela umfanekiso ucinezelo

Ngokuqinisekileyo wonke umbonile nomgangatho ophantsi imifanekiso apho kukho ukuphazamiseka ngohlobo namaxande umbala ofanayo, ezo zibizwa ngokuba zakudala. Bona ngenxa ucinezelo ebizwa njalo-lossy kuvuka. It unga nciphisa ngokubaluleka ubunzima mfanekiso, nangona kunjalo, kuya entla nefuthe ubulunga bayo.

Kuba lossy ubuchule ucinezelo ziquka:

• JPEG. Le yeyona ngomnye ubuchule athandwa kakhulu. Oku kusekelwe ukusetyenziswa cosine ekhethekileyo ukuguqula. Kubulungisa kufanele kuqatshelwe ukuba kukho iindlela JPEG lossless abenza ucinezelo. Ezi ziquka Lossless JPEG kunye JPEG-LS.
• JPEG 2000. I algorithm kusetyenziswa kumaqonga mobile, kwaye zisekelwe phezu ukusetyenziswa kwezinto wavelet ekhethekileyo ukuguqula.
• ucinezelo Fractal. Kwezinye iimeko, it ikuvumela ukuba ukufumana imifanekiso Obusemagqabini ubunjani nkqu ucinezelo olomeleleyo. Kodwa ke, ngenxa yeengxaki kunye nokukhuselwa kokuqamba yale ndlela kuyaqhubeka ukuba exotic.

ubuchule ucinezelo Lossless ezenziwa:

• RLE (zisetyenziswa njengeyona ndlela iphambili kwifomati TIFF, BMP, TGA).
• LZW (asetyenziswe kwi format GIF).
• LZ-Huffman (asetyenziselwa format PNG).

Fourier ukuguqula

Ngaphambi waguqukela wavelet, iyavakala ukuba ukuhlola imisebenzi enxulumene, ezichaza okuza solwandiso ulwazi sokuqala zibe kumacandelo aphantsi, okt. Intlokoma E. harmonic kunye ezitsho ezahlukeneyo. Ngamanye amazwi, le Fourier ukuguqula - isixhobo esisodwa yokudibanisa kanisa obubobu kunye ngokuqhubekayo.

Kubonakala ngathi le nto:

Ifomula inversion ibhalwe ngolu hlobo lulandelayo:

Yintoni a wavelet

Emva lo gama lufihla umsebenzi zezibalo, nto leyo evumela ukuba sihlaziye amacandelo ahlukeneyo amaza data zovavanyo. igrafu lixabiso undulation wakhe awo uyehla uye kuma-0 kude imvelaphi. Xa nomdla jikelele ke okuza wavelet wagqiba umqondiso ezifunekayo.

spectrograms Wavelet yahlukile Fourier oluqhelekileyo spectra, ekubeni iinkalo ezahlukeneyo ezinxulumene Imiqondiso spectrum ne candelo lwabo temporal.

inguqu Wavelet

Le ndlela ukuguqulwa uphawu (imisebenzi) ivumela ukuba ukuguqulela ukusuka kwixesha kwi ukumelwa ixesha rhoqo.

Ukuze wavelet nguquko kunokwenzeka, kuba ehambelana umsebenzi wavelet, le miqathango ilandelayo kufuneka kuhlangatyezwane:

• Ukuba for ezinye umsebenzi ψ (t) -Fourier ukuguqula unalo ifomu

ukuba imeko kufuneka kwaneliswa:

Ukongeza:

• Wavelet kufuneka ube namandla sokuzalwa;
• kufanele kube integrable eqhubekayo kwaye inkxaso compact;
• wavelet kufuneka yenzelwe kokubini oluqukuqelayo kunye kwangethuba (kwisithuba).

iintlobo

A wavelet eqhubekayo ukuguqula isetyenziselwa imiyalezo zichaphazelekayo. Kakhulu ezinomdla kakhulu yi-analogu yalo ekhethekileyo. Ngapha koko, oku kusetyenziswa ulwazi processing computer. Noko ke, kuvela ingxaki ukuba Ifomula a fiberboard obubobu awukho obulula ezifanelekileyo ifomula discretization DNP.

Isisombululo sale ngxaki Ndifunyenwe Daubechies, owaba nako ukukhetha indlela yokwakha uthotho wavelets orthogonal, nganye echazwe linani anesiphelo okuza. Kamva ubuchule fast zadalwa, ezifana algorithm Malla. Kwisicelo sayo sezimali ukuba ukubola okanye ukubuyisela umyalelo ezifunekayo ukwenza imisebenzi cn, apho N - ubude isampula, kunye ne - inani okuza.

Vayvlet Haar

Ukuze compress umfanekiso, kuyimfuneko ukuba ukufumana njalo ethile phakathi idatha yaso, kwaye nokuba ngcono ukuba iya kuba imixokelelwane elide amaqanda. Oku kulapho kunokuba luncedo ukuba wavelet nokuguqula algorithm. Nangona kunjalo, siya kuqhubeka kwakhona iindlela zokusebenza ukuze.

Okokuqala kubalulekile ukukhumbula ukuba imifanekiso elubengezelo pixels ezikufutshane kudla iphawulwa imali encinane. Nokuba kukho imifanekiso kwiziza ngokwenene ezibukhali, abenza umahluko ukukhanya, asezikhundleni kuphela inxalenye encinane mfanekiso. Ngokomzekelo, ukuthatha phezu eyaziwa uvavanyo Lenna umfanekiso imibala. Xa sithatha matrix of luminance of pixels zayo, ngoko kuya kuvela inxalenye kumgca wokuqala njenge ukulandelelana kwamanani 154, 155, 156, 157, 157, 157, 158, 156.

ungenza isicelo ekuthiwa-Delta indlela ukufumana amaqanda kulo. Ukuze wenze oku, ugcine kuphela inani lokuqala, nangenxa abanye kuphela somahluko nganye ezidlulileyo kunye umqondiso "+" okanye "-".

Isiphumo ulandelelwano 154,1,1,1,0,0,1, -2.

A engxakini ogudle-encoding kwalo non-asekuhlaleni. Ngamanye amazwi, akunakwenzeka ukuba kuphela iqhekeza ulandelelwano ufumanise yintoni kukuqaqamba ukuba ufakwe, decoded, ukuba ayizizo zonke amaxabiso phambi kwakhe.

Ukoyisa lo nokubi, inani yahlulahlulwe ngababini kwaye ngasinye isiqingatha sum of (v. A) kunye nesiqingatha umahluko (v. D), m. F. Ngenxa (154,155) (156,157) (157,157) (158,156) kufuneka (154.5, 0,5) (156.5,0.5) (157,0.0), (157, -1.0). Kulo mzekelo, kunokwenzeka kusoloko ukufumana ixabiso amanani amabini kwisibini.

Ngokubanzi, i wavelet obubobu okuguqula yomqondiso S, kufuneka:

Lendlela lulandelayo kwimeko ezahlukene ze wavelet rhoqo ukuguqula, Haar kunye esisetyenziswa ngokubanzi kwiinkalo ezahlukeneyo lweenkcukacha kunye ucinezelo.

ucinezelo

Njengoko sele kukhankanyiwe, omnye izicelo ze wavelet ukuguqula algorithm i JPEG 2000 ucinezelo indlela usebenzisa Haar ngokusekelwe translation kumda wesangqa ye pixel ezimbini kwi-X kunye Y kumda wesangqa (X + Y) / 2 (X - Y) / 2. Kwanele zande kumda wesangqa okokuqala kule matrix ngezantsi.

Ukuba iindawo, thabatha matrix ngakumbi, apho acwangcise phezu matrix H. oxwesileyo Ngoko ke, kumda wesangqa sokuqala ngaphandle ubude balo kusingathwa ngababini.

izihluzi

Oku kubangela "isiqingatha-mali" - ke amaxabiso luminance avareji pixels ngababini. Elo lixabiso xa eziguqulelwe kumfanekiso kufuneka amnike ikopi, lancitshiswa ngamaxesha-2. Kulo Kwisiqingatha-mali avareji ukukhanya, t. E. "ecociweyo" Ungqabhuko random lwamaxabiso bazo zize zibe izihluzi rhoqo.

Ngoku makhe ukuhlangabezana nezo zibonisa umahluko. Bona ke "ikude" interpixel "Ungqabhuko", ukususa icandelo rhoqo, okt. E. "ecociweyo" amaxabiso kwi ezitsho eliphantsi.

Nokuba ukusuka ngentla Haar wavelet okuguqula "Dummies" kuba kucacile ukuba iperi okucoca gqiphu umqondiso ibe amacandelo amabini: aqhelekileyo kunye njalo. nje re-bamanyane ezi zinto ukuze bafumane uphawu yokuqala.

umzekelo

Masithi sifuna compress ifoto (umfanekiso uvavanyo Lenna). Cinga nje ngomzekelo wavelet ukuguqula matrix of brightnesses pixel. Icandelo eliphezulu-rhoqo umfanekiso inoxanduva ebonisa iinkcukacha entle kwaye ichaza ingxolo. Njengoko ngokuba ephantsi kwamaza, kuba iqulathe ulwazi malunga imilo kobuso kunye ukuthambeka agudileyo ukuqaqamba.

Iimpawu iifoto umbono abantu abanjalo ukuba yokugqibela yingxenye ebaluleke ngakumbi. Oku kuthetha ukuba xa zixinaniswe inxalenye ethile ye data eziphakamileyo-rhoqo nga ishenxiswe. Ngakumbi ke kuba elinexabiso ngaphantsi yaye ufakwe ngakumbi oyimbumba.

Ukunyusa izinga ucinezelo nga tirhisiwaka izihlandlo eziliqela Haar yenguqu ukuya data ephantsi-rhoqo.

Ukusetyenziswa kwimiboniso onamacala amabini

Njengoko sele kukhankanyiwe, umfanekiso wedijithali kwi computer sele ngohlobo matrix of intensities amaxabiso pixels zayo. Ngoko ke, simele sibe nomdla kwi Haar okuntlandlo-mbini wavelet ukuguqula. Ukwenza kuyimfuneko nje ukwenza uguqulo yayo mbini ukuba kumqolo ngamnye kunye umhlathi ngamnye matrix le intensities of pixels kumfanekiso.

Imilinganiselo kufutshane zero, ukuze zilahlwe ngaphandle umonakalo elibalulekileyo kumfanekiso decoded. Le nkqubo yaziwa ngokuba quantization. Kwaye ngeli thuba le nkcazelo ilahlekileyo. Hi ndlela leyi, inani lemiba nullable ingatshintsha, ngokwenjenjalo ngokulungelanisa imeko izinga ucinezelo.

Zonke ezi manyathelo kukhokelela ukuba isizalo ifunyenwe equlethe izixa ezikhulu 0. Kufuneka umgca ebhalwe umgca njengefayile-yokubhaliweyo kwaye compress nayiphi archiver.

kokuhlaziya

Eguqulweyo ngokubaxwa i inguqu bomfanekiso algorithm ilandelayo:

• It lengcaciso likhupha yomlando;
• kusebenza inguqu Haar ukuguqula;
• Umfanekiso decoded iguqulelwa ibe matrix.

Izinto eziluncedo xa kuthelekiswa JPEG

было сказано, что он основан на ДКП. Xa kuqwalaselwa algorithm Joint zokufota Iingcali Group waxelelwa ukuba sisekelwe phezu DCT. Le ukuguqulwa oluqhutywa iibhloko (8 x 8 pixels). Ngenxa yoko, ukuba ucinezelo olumandla umfanekiso kwanciphisa uba ubume block appreciable. Ngexesha ucinezelo usebenzisa wavelets ngxaki angekhoyo. Noko ke, ingxolo kuvela uhlobo ezahlukeneyo banayo imbonakalo eba ngeenxa ezinemiphetho. Kukholelwa ukuba nezinto ezifanayo ngomyinge lula kwe "izikwere" ezidaliweyo xa usebenzisa JPEG algorithm.

Ke kaloku, ukuba uyakwazi oko wavelets ke oko kwaye wafunyanwa ziphi ukusetyenziswa ngenxa entsimini yokujongwa ngokuveza imifanekiso digital.