Wavelet kuchinja: kusarudza kushanda muenzaniso

VeMubatanidzwa chipa digitaalinen makamera kwakakanganisa kuti chikamu chikuru vagere panyika, zvisinei nezera uye pabonde, awana tsika akakunda ake danho ose uye akaisa zvifananidzo zvavo pachena kuratidzwa mumagakava network. Uyezve, kana ari kwokutanga mhuri Photo Archive yakaiswa chete album, nhasi inoitwa mazana mifananidzo. Kuti zviite okuchengetera uye kupararira achiyambuka network zvinoda digital mufananidzo uremu rutapudzo. Kuti izvi zvidaro, nzira dzinoshandiswa kuti anotorerwa algorithms siyana, kusanganisira imwe wavelet rokuchinja. Chii, udza nyaya yedu.

Chii chinonzi mufananidzo-digital

mashoko Visual ari kombiyuta rinomiririrwa dziri nhamba. Zviri nyore, pikicha kubatwa digital mudziyo, ndiro tafura umo masero vakapinda tsika nerimwe raro Pixel ruvara. Kana totaura kuti monochrome mufananidzo, ipapo inotsiviwa luminance zvinokosheswa kubva penguva [0, 1], apo 0 rinoshandiswa kureva nhema, uye 1 - chena. Other Mavara vakapiwa fractional nhamba, asi navo vachinyara kuti ishande, saka siyana chinoshanda uye mutengo vakasarudzwa kubva penguva pakati 0 uye 255. Nei ichi? Hazvina nyore! With chisarudzo ichi munyika binary Representation yeEncoding ari luminance neimwe Pixel zvinoda chaizvo mumwe byte. Zviri pachena kuti zvakawanda ndangariro kunodiwa yokuchengetera kunyange mufananidzo diki. Somuenzaniso, mufananidzo kukura 256 X 256 pixels zvinoda 8 Kbytes.

A mashoko mashoma pamusoro mufananidzo compression nzira

Chokwadi munhu wose akaona kushata mifananidzo pane kukanganiswa muchimiro rectangles zvakafanana ruvara, makatumidzwa zvaishandiswa. Ivo vasimuke somugumisiro vanonzi lossy compression. Zvinogona kuderedza uremu mufananidzo Zvisinei, izvozvo vaizongoguma tinzwe pamusoro unhu wayo.

Nokuti lossy compression algorithms dzinosanganisira:

• Jpeg. Izvi nokure chimwe chezvinhu dzakakurumbira algorithms. Zvinonzi inobva kushandisa discrete cosine rokuchinja. In kururamisira zvinofanira kucherechedzwa kuti pane nzira yokuti jpeg kwokugara lossless compression. Izvi zvinosanganisira Lossless jpeg uye jpeg-Ls.
• Jpeg 2000. The algorithm rinoshandiswa musi Mobile platforms, uye kwakavakirwa kushanda kunoita discrete wavelet rokuchinja.
• Fractal compression. Mune zvimwe zviitiko, zvinoita here kuwana mifananidzo yokuisvonaka kunyange simba compression. Zvisinei, nokuda nezvinetso patenting kuti nzira iyi chichiri zvekumwe.

Lossless compression algorithms kwakaitwa:

• RLE (akashandiswa nzira chikuru mune tiff format, BMP, TGA).
• LZW (yaishandiswa GIF pamanyorerwo).
• LZ-Huffman (kushandiswa PNG urongwa).

Fourier rokuchinja

Asati atendeuka kuna wavelet, zvine musoro kuti kuongorora chokuita kushanda, ichirondedzera coefficients ari kukura kwokutanga mashoko kupinda zvokutanga zvinoriumba, kureva. E. Harmonic vibrations pamwe frequencies zvakasiyana. Nemamwe mashoko, Fourier rokuchinja - rakasiyana chishandiso unobva discrete uye kuramba nyika.

Zvinoita seizvi:

The inversion fomura zvakanyorwa sezvinotevera:

Chii chinonzi wavelet

Shure zita iri inovanza munhu akarongeka basa, izvo zvinoita kuti kuongorora akasiyana kakawanda zvinoumba Muedzo Data. girafu Its chinhu undulation vane amplitude zvinoderedza kusvika 0 kure mavambo. Vakawanda mubereko ndizvo wavelet coefficients vakatsunga chinokosha chiratidzo.

Wavelet spectrograms vakasiyana kwakajairika Fourier spectra, sezvo-siyana akabatanidza chakarondedzera anonongedzera zvavo zvenyama zvinoriumba.

Wavelet kushandurwa

nzira iyi chiratidzo kutendeuka (Mabasa) inoita kushandura kubva nguva nenguva-Frequency kumiririrwa.

To wavelet Kushandurwa zvaiita, nokuti unoenderana wavelet basa, zvinotevera ezvinhu anofanira akasangana:

• Kana kuti vamwe mashandiro ψ (T) -Fourier rokuchinja rine chimiro

ichocho anofanira kugutsikana:

Mukuwedzera:

• Wavelet anofanira kuva finite simba;
• izvozvo zvinofanira kuva integrable kuramba uye chiine nerutsigiro;
• wavelet inofanira vemunyika vose kakawanda uye nguva (nzvimbo).

mhando

A kuramba wavelet rokuchinja rinoshandiswa kuti nhengo anonongedzera. Zvikuru zviri zvayo discrete analogue. Pashure pezvose, rinogona kushandiswa mashoko kubudiswa mu makombiyuta. Zvisinei, dambudziko iri kuti nzira kuti discrete fiberboard hazvigoni yaunganidzwa nyore yakakodzera discretization Masvomhu DNP.

The Dambudziko wakawanikwa Daubechies, uyo aikwanisa kusarudza nzira yokuvaka akatevedzana orthogonal wavelets, chimwe nechimwe kunorondedzerwa neboka finite nhamba coefficients. Gare gare kutsanya algorithms dzakasikwa, dzakadai algorithm Malla. In kushandisirwa anoora kana kudzorera inodiwa kuti kuvhiya CN, apo N - mharidzo urefu, uye pamwe - nhamba coefficients.

Vayvlet Haar

To tsonyera chifananidzo, zvinokosha kuwana imwe nguva dzose pakati mashoko ayo, uye kunyange nani kana ichava refu namaketani zeros. Izvi ndipo zvinogona kubatsira kuti wavelet rokuchinja algorithm. Zvisinei, tinofanira kuramba kudzokorora kushanda nzira kuitira.

Chokutanga zvakafanira kuyeuka kuti mifananidzo nokupenya pedyo pixels kazhinji dzinoratidzwa shoma. Kunyange kana pane mifananidzo chaiyo nzvimbo unopinza, achisiyanisa kusiyana kubwinya, anogara bedzi chikamu chiduku chacho. Somuenzaniso, tora pamusoro anozivikanwa bvunzo Lenna grayscale mufananidzo. Kana isu kutora chizvaro pakati luminance pakati pixels zvayo, ipapo chikamu chokutanga mutsetse achaonekwa ari kutevedzana kwezviitiko nhamba 154, 155, 156, 157, 157, 157, 158, 156.

unogona kushandisa vanonzi Delta nzira kuti zeros kwairi. Kuti aite izvi, chengeta chete nhamba yokutanga, uye nokuda vamwe chete kusiyana nerimwe yapfuura mumwe chete chiratidzo "+" kana "-".

Zvinoguma kutevedzana 154,1,1,1,0,0,1, -2.

A zvakaipira Delta-yeEncoding ndiro yayo non-nzvimbo. Mune mamwe manzwi, hazvibviri kutora chete bande pakati kutevedzana uye kuziva chii kupenya kwakanyorwa encoded, decoded, kana kwete vose tsika pamberi pake.

Kukunda chinetso ichi, nhamba rakakamurwa vaviri vaviri uye mumwe vari hafu mubatanidzwa (v. A) uye hafu musiyano (v. D), m. F. For (154,155) (156,157) (157,157) (158,156) vane (154.5, 0,5) (156.5,0.5) (157,0.0), (157, -1.0). Muchiitiko chino, zvinokwanisika nguva dzose kuwana kukosha nhamba mbiri ari peya.

Kazhinji, ari discrete wavelet rokuchinja pamusoro chiratidzo S, tine:

Nzira iyi anotevera kubva discrete nyaya kuramba wavelet rokuchinja, Haar uye zvinowanzoshandiswa minda date kubudiswa uye compression siyana.

compression

Sezvambotaurwa, mumwe kushanda kunoita wavelet rokuchinja algorithm ndiye jpeg 2000 compression nzira uchishandisa Haar kubva pashanduro Vector pakati pixels vaviri X uye Y Vector (X + Y) / 2 uye (X - Y) / 2. Zvakakwana vawande kwokutanga Vector iri chizvaro pazasi.

Kana pfungwa zvakawanda, tora zvakawanda chizvaro, izvo vakaronga pamusoro diagonal chizvaro H. Naizvozvo, kutanga Vector vakazvimirira pakureba kwaro chinogadzirwa vari vaviri vaviri.

filters

The zvichiguma "hafu-Verengai" - ndiwo avhareji luminance netsika pixels vari vaviri vaviri. Ndiyo ukoshi kana kuchinjwa kuti mufananidzo Umupe kopi, akaderedza muna 2 nguva. In ichi hafu-Muchidimbu neavhareji kupenya, t. E. "yakasvinwa" anongoitika watsemuka tsika dzavo uye chiito sezvo maitikiro filters.

Zvino ngatitarise kubata avo anoratidza musiyano. Vari "voga" interpixel "watsemuka", achibvisa kugara zvinoriumba, kureva. E. "yakasvinwa" tsika yakaderera frequencies.

Kunyange kubva pamusoro Haar wavelet rokuchinja "dummies" zvinova pachena kuti peya filters kuti agovane chiratidzo muruoko zvinoriumba maviri: yakakwirira kakawanda uye vakaderera maitikiro. Zvinongoreva kuzodzosera kubatanidza zvinhu izvi kuti vawane chepakutanga chiratidzo.

muenzaniso

Ngatitii tinoda dzvinya mufananidzo (bvunzo mufananidzo Lenna). Funga nezvomuenzaniso wavelet rokuchinja chizvaro pakati Pixel brightnesses. Rokuti mukuru-kakawanda mufananidzo ndiwo mutoro kuratidza yakaisvonaka akadzama uye anotsanangura ruzha. Kana low-kakawanda, rine mashoko pamusoro pezvakaita kumeso uye anotsvedzerera gradients kokubwinya.

Features mapikicha Maonero evanhu vakadaro kuti ekupedzisira unokosha zvikuru zvinoriumba. Izvi zvinoreva kuti kana compressed mumwe rutivi mukuru-kakawanda Data anogona kuraswa. The zvakawanda nokuti rinokosha shoma uye iri encoded zvikuru yakabatana isiri.

Kuwedzera mwero compression ingashandiswa kakawanda Haar shanduko yakaderera maitikiro Data.

Kushandiswa maviri-dimensional arrays

Sezvambotaurwa, mufananidzo digitaalinen iri kombiyuta vari muchimiro chizvaro pakati intensities tsika pixels ayo. Saka, tinofanira kuva kufarira mbiri-dimensional Haar wavelet rokuchinja. To dzika zvakafanira kungoti kuita ayo ndeiya yakaita kutendeutsa mumwe musara uye mumwe shongwe chizvaro pakati intensities ose pixels mumufananidzo.

Tsika pedyo zero, anogona kuraswa pasina chinokosha kuvadza decoded mufananidzo. Izvi zvinozivikanwa se quantization. Uye panguva ino mashoko akarasika. Nenzira, nhamba nullable zvikonzero angachinja nokudaro nokugadzirisa mwero compression.

Matanho ose aya kuchaguma kuti chizvaro inotengwa ine yakawanda 0. Zvinofanira kunyorwa mutsetse norwonzi ari rugwaro faira dzvinya chero Archiver.

decoding

The Ivan Kuchin kwokushanduka chifananidzo inotevera algorithm:

• It unpacks ane arşive;
• rinoshanda Ivan Kuchin Haar rokuchinja;
• The mufananidzo decoded iri kuchinjwa kuva chizvaro.

Advantages zvichienzaniswa jpeg

было сказано, что он основан на ДКП. Kana kufunga algorithm Joint Photographic Nyanzvi Group akaudzwa kuti kunobva DCT. kutendeuka uku kuitwa kutigumbura (8 X 8 pixels). Somugumisiro, kana compression simba pamusoro shoma mufananidzo anova kuti munhu misa mamiriro. Panguva compression achishandisa wavelets dambudziko rakadaro vasipo. Zvisinei, ruzha zvingaita yakasiyana mhando vane chimiro ripples kumativi kumicheto. Zvinofungidzirwa kuti zvakafanana zvinoratidza avhareji chisanyanya kuoneka pane "dzinoungana" izvo zvinosikwa paaishandisa jpeg algorithm.

Zvino kuti munoziva wavelets vari zvavari uye chii zvinobatsira navo chakawanikwa mumunda kubudiswa uye compressing digitaalinen mifananidzo.