Wavelet hoʻololi: ka hoʻoholo 'noi Eia kekahi laʻana

Ke Hekikai o inexpensive kikohoʻe Panel i ke ano o ua nānā 'ole o ka makahiki, a me ke keka, ua lilo i ka nui loa o ka poʻe e noho lā ma ka Honua, me ka maʻa e hoʻopio i kona nāʻanuʻu, a kau lākou mau kiʻi ma lehulehu make i loko o ka nohona latike. Eia kekahi, ina o ka mua ohana Hawaii photo Archive Ua waiho ia ma ka ia album, i keia la ka mea, he mai o nā haneri o nā kiʻi. I mea e kōkua ai i nā pūnaewele a me ka EYI ma latike e noi mai ana i ka kikohoʻe kiʻi o ke kaupaona ana, no ka ho'ēmiʻana. No keia hopena, e hoʻohana 'epekema i i ka nānā' ana ma luna o nā algorithms, me he wavelet hoʻololi. He aha ka mea, e hai aku mākou 'atikala.

He aha mea he kikohoʻe kiʻi

Ke kākoʻo 'ike i loko o ke kamepiula ua poe ma ke ano o ka helu. Ma na mea hua'ōlelo, he i paʻi 'ia me ka mīkini mea, o ka papaʻaina i loko o i na keena e komo na aiee o kela a me keia o kona kiʻi kiko ano. I ka wa e hele ai i ka monochrome kiʻi, a laila ka mea i UAIAaIN ma luminance aiee, mai ka wā mawaena [0, 1], kahi 0 ua hoʻohana 'ia e hoʻohuli i iʻeleʻele, a me ka 1 - keʻokeʻo. Other kala i haawiia fractional nui, akā, me ka awkward, e hana iā lākou, no laila, ua kikooia aku ka laulā, a me ka waiwai i kohoʻia mai i ka wā mawaena waena 0 a me 255. No ke aha la i keia? Ua ka poe noonoo ole! Me keia koho ana ma ka aeaie e hoohalike ai no ka hoʻopā'ālua ka luminance o kēlā me kēia kiʻi kiko pono e like hoʻokahiʻai. Ka mea, ua maopopo i ua koi 'ia o ka hailonaʻana no iaiyoe e hoahu i he uuku kiʻi. No ka laʻana, kiʻi nui o 256 m 256 nā kiko kiʻi ai 8 Kbytes.

A mau olelo e pili ana i kiʻi mīkini'opihia ki ina hana like

No ka mea, ua ike kela kanaka keia kanaka i ka poe ilihune ma Hawaiʻi o nā kiʻi ma laila nō ei i loko o ka palapala o rectangles o ka iaʻano hoʻokahi, i ka poe i kaheaia artifacts. Ka mea, e ku ae like me ka hopena o ka ai-kapaia lossy mīkini'opihia. Ua hiki me ka nui loa emi ke kaumaha o ke kiʻi, akā naʻe, ka mea e inevitably hopena ma luna o kona mea e like ai.

No ka lossy mīkini'opihia algorithms loaʻa:

• JPEG. Kēia mea ma ka loihi kekahi o ka loa Popular algorithms. Ua Ua nānā ana ma ka hoʻohana 'ana o discrete cosine hoʻololi. Ma fairness ka mea, e ke kaulana i loaʻa nā koho no JPEG ana i nā hana lossless mīkini'opihia. Mau nā Lossless JPEG a me JPEG-ls.
• JPEG 2000. ka algorithm Ua hoʻohana ma luna oʻawa a lawe lima, a me ka nānā 'ana ma luna o ka noi o ka discrete wavelet hoʻololi.
• fractal mīkini'opihia. Ma kekahi mau hihia, ka mea e leie aku oe, e loaa i nā kiʻi o ka maikai e like ai, a hiki me ka ikaika mīkini'opihia. Eia naʻe, ma muli o ia pilikia me ka patenting o keia papa hana mau ia e mea lahaʻole.

Lossless mīkini'opihia algorithms hanaʻia e:

• RLE (hoʻohana 'ia e like me ka iniiaiie iaoia i loko o ka TIFF waihona, BMP, TGA).
• LZW (hoʻohana 'ia i loko o GIF waihona).
• LZ-Huffman (hoʻohana no ka PNG waihona).

Fourier hoʻololi

Ma mua o haliu ae la ia i ka wavelet, ka mea i ano e makaikai i ka nā mana, hōʻike no nā coefficients o ke anoe ana o ka loiloi mua 'ike i loko o kula haʻahaʻaa eiiiiiaiou, oa. E. Harmonic kuekueni me kekahi nä alapine. Ma nā hua'ōlelo, ka Fourier hoʻololi - he hanana paahana ai pili aku discrete a me ke ana lani.

Ua nana e like keia:

Ua palapala ia ka hahana haʻilula like penei:

He aha mea he wavelet

Ma hope o kēia inoa hūnā iā he makemakika papa, a e leie aku oe e kālailai i kaʻokoʻa alapine (frequency) eiiiiiaiou o ka hoʻokolohua aeaiiuo. Ka pakuhi mea he undulation kona ikaika hawewe emi i 0 aku, mai ke kumu. I mau hoihoi i ka wavelet coefficients hoʻoholo integral maika i.

Wavelet spectrograms i okoa maiʻike mau Fourier spectra, mai nā hiʻona pili pae mau lepa a me kā lākou mau kino ke keʻena.

Wavelet hou '

Kēia hana o ka neaiaea huli (oihana) e leie aku ka mea, e unuhi mai i ka manawa i loko o ka manawa-alapine (frequency) e hoohalike ai.

E wavelet hou 'ua hiki, no ka mea e like wavelet papa, me ka ana ma lalo pono e halawai:

• Inā no kekahi papa ψ (Halau) -Fourier hoʻololi i ka palapala

mea ano pono e māʻona:

Eia hou:

• Wavelet pono i ka finite ikehu;
• ka mea, e ia integrable ana, a i kana olelo hoopomaikai kākoʻo;
• wavelet pono e IIeEeAIEUIeXAIIUE nā ma ka alapine (frequency), a me ka manawa (makahiki).

ano

A ana wavelet hoʻololi ua hoʻohana 'ia no ka mau no lepa. Nui hou hoihoi 'o kona discrete mea like. Ma hope o nā mea a pau, ka mea hiki ke hoʻohana no ka 'ike i loko o aaioee kamepiula' ē aʻe. Eia naʻe, he pilikia aicieeaao i ole e i ka haʻilula no ka discrete fiberboard ke loaa ma ka mea kūpono discretization nā papakuhikuhi DNP.

Ke kākoʻo pāʻoihana a hiki i keia pilikia i loaʻa ma Daubechies, ka mea i hiki ke koho i kekahi papa hana, e kūkulu i ka moʻo o orthogonal wavelets, kela mea keia mea o ka i ho'ākāka 'ia ma kekahi finite helu o coefficients. Hope i hana hookeai algorithms, e like me ka algorithm Malla. Ma kona palapala noi, e decompose paha ke koi 'ia mea, e hana ana CN, ma N e hoʻihoʻi - hāpana lōʻihi, a me - i ka helu o coefficients.

Vayvlet Haar

E oOeEIAOO i kiʻi, ia mea pono e imi i kekahi regularity i waena o konaʻikepili, a hiki maikaʻi ina mea e e kaula hao lōʻihi o nā 'Aʻohe hualoaʻa. Kēia mea ma ka mea hiki e pono i ka wavelet hoʻololi algorithm. Eia naʻe, ua hoʻomau i ka nānā i ka hana epekema ma ka mea.

Mua ia mea pono e hoole i nā kiʻi i ka olinolino o ka pili nā kiko kiʻi ua ana wehewehe aku ma ka uuku dala. Oia hoi, ina he mau kiʻi ma luna maoli kahua me ka lena, contrasting oko o ka'ōlinolino, ka mea noho wale o ka hapa uuku o ke kiʻi. E like me ke kumu, lawe ma luna o ka ike ho'āʻo Lenna grayscale kiʻi. Inā mākou e lawe i ka'ōpū mai o ka luminance o kona nā kiko kiʻi, a laila, e hōʻike i ka hapa o ka mua laina like me ka kaʻina o nā helu 154, 155, 156, 157, 157, 157, 158, 156.

oe ke pili i ka ai-kapaia aaeuoa papa hana e kiʻi 'Aʻohe hualoaʻa no ia. E hana i kēia, e mālama wale nō i ka helu mua, a no na mea e ae lawe wale i ka oko o kela a me keia o ka mua kekahi me ka hoailona "+" a "-".

I ka hopena o ke kaʻina, 154,1,1,1,0,0,1, -2.

A keakea o aaeuoa-hoʻopā'ālua o kona 'ole-Wahiiki. Ma na olelo e ae, he mea hiki ole ke lawe wale i kekahi māhele o ke kaʻina, a loaʻa mai mea nani ia ua encoded, decoded, ina ole a pau o na aiee ma ke alo o ka ona.

E lanakila keia keakea, ua puunaueia i ka helu i hui a me kēlā mea me ka hapalua o ka huina o (v. A) a me ka hapalua o ke koena unuhi (v. D), m. F. No ka (154,155) (156,157) (157,157) (158,156) i (154.5, 0,5) (156.5,0.5) (157,0.0), (157, -1.0). Ma keia hihia, e mea mau mea hiki, e imi i ka waiwai o ka mea helu elua i loko o kekahi mau.

I mau, ka discrete wavelet hoʻololi i ka neaiaea S, ua loaʻa:

Kēia papa hana penei, mai ka discrete hihia o ana wavelet hoʻololi, Haar a hoʻomano hoʻohana 'ia ma kekahi mau kihapai o kaʻikepili aaioee a me ka mīkini'opihia.

mīkini'opihia

E like me ua oleloia, kekahi o na palapala noi o wavelet hoʻololi algorithm o ka JPEG 2000 mīkini'opihia iaoia me ka hoʻohana 'Haar ma muli o ka unuhi maʻi lele ana o nā kiko kiʻiʻelua i loko o ka X a me Y maʻi lele (X + Y) / 2 a (X - Y) / 2. He lawa e hoonui i ka loiloi mua maʻi lele i loko o ka'ōpū mai ma lalo nei.

Inā na kumu nui, lawe nui mua, a i hoonohonoho ia ma ka diagonal mua H. No laila, i ka loiloi mua maʻi lele kū kaʻawale o kona lōʻihi ua hoʻokō 'ia ma ka hui.

kānana

Ke kūpono "hapa-huina" - o ka awelika luminance aiee o nā kiko kiʻi i loko o hui. Ia mea i ka waiwai, i ka wa hoohuliia ai i ke kiʻi, e haawi lakou ia ia i kope, hoemi i ka 2 manawa. Ma keia hapa-dalaʻawelike o ka'ōlinolino, 'ole. E. "i wae'" huikau ka poha o ko lākou mau loina a me ka hana e like me ka alapine (frequency) kānana.

Ano, e ka hana a me ka poe e hōʻike i ka likeʻole. Ka mea, i "kaʻawale" interpixel "o poha", wehe i ka ikaika ke keʻena, oa. E. "i wae '" aiee ma haʻahaʻa nä alapine.

A hiki mai ka luna Haar wavelet hoʻololi no ka "dummies" ka mea i maopopo ia ia mea he paʻa o nā kānana, e mahele i ka hōʻailona i loko o nā eiiiiiaiou: ka alapine kiʻekiʻe a me ka haahaa alapine (frequency). ʻEli hou wale-hui i kēia mau kumu, e loaa i ka palapala neaiaea.

Eia kekahi laʻana

Ina ua makemake e oOeEIAOO i ke kiʻi (ho'āʻo kiʻi Lenna). E noonoo i ke kumu hoohalike o ke wavelet hoʻololi i ka'ōpū mai o ke kiʻi kiko brightnesses. Ke kiʻekiʻe-alapine (frequency) ke keʻena o ke kiʻi, ua kuleana no ka hōʻike nani au mamuli, a wehewehe i ka leo. Like no me ka haʻahaʻa-alapine (frequency), ka mea, he 'ike e pili ana i ke kinona o ka maka, a me ka laumania gradients o ka olinolino.

Hiʻona kiʻi o kanaka pokole, ua like ia i ka la mahope mea oi nui ke keʻena. Kēia 'o ia hoʻi i ka wā'opihia i kekahi hapa o ka mea kiʻekiʻe-alapineʻikepili hiki ke kāpaeʻia. Ka hou no laila, no ka mea, ua emi ka waiwai a me ka ua encoded hou compactly.

E hoomahuahua i ka degere o ka mīkini'opihia hiki ke hoopili mau manawa Haar hou 'ana i ka haʻahaʻa-alapine (frequency) aeaiiuo.

Ka hoʻohanaʻana i nā-dimensional huihui ikehu lā

E like me ua oleloia, o ka mīkini kiʻi i loko o ke kamepiula i loko o ka palapala o ka'ōpū mai o intensities aiee o kona nā kiko kiʻi. Penei, mākou e e hoihoi i loko o ka mau-dimensional Haar wavelet hoʻololi. E hoʻokō i ia mea e pono ai wale no ka hana kona dimensional huli ana no kēlā me kēia lālani a me kēlā me kēia kolamu o ka'ōpū mai o na intensities o nā kiko kiʻi i loko o ke kiʻi.

Nā Loina Hawaiʻi kokoke loa i ka 'Aʻohe, hiki ke kāpaeʻia me ka nui poino i ka decoded kiʻi. Kēia kaʻina ua ike like quantization. A ma keia kahua o ka 'ike ua nalowale. Ma ke ala, i ka helu ana o nullable aʻe e hoʻololi, i laila ka hōʻoiaʻana i ka degere o ka mīkini'opihia.

A pau kēia mauʻanuʻu palapala i loko i ka'ōpū mai ua loaa iloko ona i kakauia nui dala o 0. Ua e ke palapala laina ma ka laina ma ke kikokikona waihona, a oOeEIAOO kekahi archiver.

ho omńkalakala i

Ke inverse hou 'ia ma ke kiʻi ma luna o nā kēia algorithm:

• Ua unpacks he Archive;
• pili inverse Haar hoʻololi;
• Ke decoded kiʻi ua hoohuliia i loko o ka'ōpū mai.

Pono e hoʻohālike au iā JPEG

было сказано, что он основан на ДКП. I ka noonoo pono i ka algorithm Olelo kiʻi poe akamai i Group i hai aku i ka mea, ua nānā 'ana ma luna o DCT. Ua huli ana ua lawe mai i loko o ālai '(8 m 8 nā kiko kiʻi). E like me ka hopena, ina he ikaika mīkini'opihia ma ka hoemi kiʻi i appreciable aeie 'ole. Ma mīkini'opihia hoʻohana wavelets e like me ka pilikia i kahi e. Eia naʻe, halulu e ikea kekahiʻano a i keʻano o nā ripples a puni penei. Ua Ua manaoio e like artifacts ma awelika emi mai kekahi 'o "kihikihiʻo" ka wā hoʻohana' ana i JPEG algorithm a i hana.

Ano, ia oe i ka wavelets mea mea mea mau a me ka mea hiki ana no ia i loaʻa i loko o ke kahua o ka aaioee a compressing kikohoʻe kiʻi.