Fundamentals to Computer Vision by Shah M.

By Shah M.

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IÊ >ÃÈ}˜Ê >Ê Vœ˜`ˆÌˆœ˜>Ê «ÀœL>LˆˆÌÞÊ “>ÌÀˆÝ Q*­ É®RÊ̜Ê̅iÊ`ˆÀiVÌi`Ê>ÀVÊvÀœ“ʘœ`iÊÊÌœÊ °ÊÊ/…iÊii“i˜ÌÊ>ÌÊ̅iʍ̅ÊÀœÜ >˜`ʈ̅ VœÕ“˜ÊœvÊ*­ É®]Ê`i˜œÌi`ÊLÞÊ*­  Ɉ®]ÊÀi«ÀiÃi˜ÌÃÊ̅iÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʜv Ê>ÃÃՓˆ˜}Ê̅iÊ«ÀˆœÀʜVVÕÀÀi˜ViʜvÊʈ°Ê/…ˆÃʈÃÊ`iÃVÀˆLi`ʈ˜Êˆ}°£°£ä° œ“«ÕÌ>̈œ˜>Ê˜Ìiˆ}i˜Vi\Ê*Àˆ˜Vˆ«iÃ]Ê/iV…˜ˆµÕiÃÊ>˜`Ê««ˆV>̈œ˜Ã Ó£ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ  *Ê­ ÊÉÊ® Êʈ}°Ê£°£ä\ÊÃÈ}˜ˆ˜}Ê>ÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʓ>ÌÀˆÝʈ˜Ê̅iÊ`ˆÀiVÌi`Ê>ÀV ÊÊVœ˜˜iVÌi`ÊvÀœ“ÊÊÊÌœÊ ° ˆÛi˜Ê̅iÊ«ÀœL>LˆˆÌÞÊ`ˆÃÌÀˆLṎœ˜ÊœvÊ] `i˜œÌi` LÞÊQ*­£®Ê*­Ӯʰ°o*­˜®R ]ÊÜi V>˜Ê Vœ“«ÕÌiÊ Ì…iÊ «ÀœL>LˆˆÌÞÊ `ˆÃÌÀˆLṎœ˜ œvÊ iÛi˜ÌÊ Ê LÞ ÕȘ} ̅iÊ vœœÜˆ˜} iÝ«ÀiÃȜ˜\ *­ ®ÊrÊQ*­ £®Ê*­ Ó®Êo°*­ “®RÊ£Êzʓ ÊrÊÊQ*­£®Ê*­Ó®Êo°*­˜®RÊ£ÊzÊÊʘ Ê°ÊQ*­ ÊÉ®R ˜ ÊrÊÊÊQ*­®RÊÊ£Êz ˜Ê°ÊQ*­ ÊÉ®Rʘ zÊʓ ÊÊÊÊÊÊÊÊÊ­£°£® zÊʓ 7iʘœÜʈÕÃÌÀ>ÌiÊ̅iÊVœ“«ÕÌ>̈œ˜ÊœvÊ*­ ®Ê܈̅Ê>˜ÊiÝ>“«i° Ý>“«iÊ£°Ó\Ê œ˜Ãˆ`iÀÊ>Ê >ÞiÈ>˜ÊLiˆivÊÌÀiiÊ`iÃVÀˆLˆ˜}Ê̅iÊ«œÃÈLiÊV>ÕÃiÃʜv >Ê`iviV̈ÛiÊV>À° >ÀÊ `œià ˜œÌÊÃÌ>ÀÌ  >ÌÌiÀÞ `iviV̈Ûi Ê >ÌÌiÀÞ œœÃi ÕiÊ ÃÞÃÌi“ `iviV̈Ûi Ê >ÌÌiÀÞ i݅>ÕÃÌi` ÊÊ Õi ݅>ÕÃÌi` Ê -܈ÌV…ià `iviV̈Ûi }˜ˆÌˆœ˜ Ã܈ÌV… `iviV̈Ûi Ê ˆ}°Ê£°££\ÊÊ`ˆ>}˜œÃ̈VÊÌÀiiÊvœÀÊ>ÊV>À° *œÜiÀ‡œ˜ Ài>Þ `iviV̈Ûi  ˜Ê˜ÌÀœ`ÕV̈œ˜ÊÌœÊ œ“«ÕÌ>̈œ˜> ˜Ìiˆ}i˜Vi ÓÓ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ iÀi]Ê i>V…Ê iÛi˜ÌÊ ˆ˜Ê ̅iÊ ÌÀiiÊ ­ˆ}°Ê £°££®Ê V>˜Ê …>ÛiÊ ÌÜœÊ «œÃÈLiÊ Û>ÕiÃ\Ê ÌÀÕiÊ œÀ v>Ãi°Ê/…ÕÃÊ̅iʓ>ÌÀˆViÃÊ>ÃÜVˆ>Ìi`Ê܈̅Ê̅iÊ>ÀVÃÊ܈Ê…>ÛiÊ`ˆ“i˜Ãˆœ˜ÃÊ ­ÓÊÝÊÓ®° œÜ]Ê}ˆÛi˜Ê*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­Ê rÊv>Ãi®R/]Ê ÜiÊ V>˜Ê i>ȏÞÊ Vœ“«ÕÌiÊ*­ ®] *­ ®]Ê*­ ®]Ê*­
®]Êo]*­®Ê«ÀœÛˆ`i`ÊÜiʎ˜œÜÊ̅iÊÌÀ>˜ÃˆÌˆœ˜Ê«ÀœL>LˆˆÌÞÊ “>ÌÀˆVià Vœ˜˜iVÌi`Ê ÜˆÌ…Ê Ì…iÊ ˆ˜ŽÃ°Ê ÃÊ >˜Ê ˆÕÃÌÀ>̈ÛiÊ iÝ>“«i]Ê ÜiÊ Vœ“«ÕÌiÊ *­ ®Ê ܈̅ *­ É®Ê>˜`Ê*­®° iÌÊ*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­ÊrÊv>Ãi®R/ ÊrÊQÊÊä°ÇÊ Êä°ÎÊR ÊÊÊÊÊÊÊÊÊÊÊÊÊÊ .

IÀiÊÊ«Ê>˜`ʵÊ>ÀiÊLˆ˜>ÀÞÊ«Àœ«œÃˆÌˆœ˜ÃÊ­ˆ°i°Êv>VÌÃÊ܈̅ÊLˆ˜>ÀÞÊÌÀÕ̅ÊÛ>ÕiîÊ>˜`Ê . ]Ê ÜiÊ >ÃÈ}˜Ê >Ê Vœ˜`ˆÌˆœ˜>Ê «ÀœL>LˆˆÌÞÊ “>ÌÀˆÝ Q*­ É®RÊ̜Ê̅iÊ`ˆÀiVÌi`Ê>ÀVÊvÀœ“ʘœ`iÊÊÌœÊ °ÊÊ/…iÊii“i˜ÌÊ>ÌÊ̅iʍ̅ÊÀœÜ >˜`ʈ̅ VœÕ“˜ÊœvÊ*­ É®]Ê`i˜œÌi`ÊLÞÊ*­  Ɉ®]ÊÀi«ÀiÃi˜ÌÃÊ̅iÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʜv Ê>ÃÃՓˆ˜}Ê̅iÊ«ÀˆœÀʜVVÕÀÀi˜ViʜvÊʈ°Ê/…ˆÃʈÃÊ`iÃVÀˆLi`ʈ˜Êˆ}°£°£ä° œ“«ÕÌ>̈œ˜>Ê˜Ìiˆ}i˜Vi\Ê*Àˆ˜Vˆ«iÃ]Ê/iV…˜ˆµÕiÃÊ>˜`Ê««ˆV>̈œ˜Ã Ó£ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ  *Ê­ ÊÉÊ® Êʈ}°Ê£°£ä\ÊÃÈ}˜ˆ˜}Ê>ÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʓ>ÌÀˆÝʈ˜Ê̅iÊ`ˆÀiVÌi`Ê>ÀV ÊÊVœ˜˜iVÌi`ÊvÀœ“ÊÊÊÌœÊ ° ˆÛi˜Ê̅iÊ«ÀœL>LˆˆÌÞÊ`ˆÃÌÀˆLṎœ˜ÊœvÊ] `i˜œÌi` LÞÊQ*­£®Ê*­Ӯʰ°o*­˜®R ]ÊÜi V>˜Ê Vœ“«ÕÌiÊ Ì…iÊ «ÀœL>LˆˆÌÞÊ `ˆÃÌÀˆLṎœ˜ œvÊ iÛi˜ÌÊ Ê LÞ ÕȘ} ̅iÊ vœœÜˆ˜} iÝ«ÀiÃȜ˜\ *­ ®ÊrÊQ*­ £®Ê*­ Ó®Êo°*­ “®RÊ£Êzʓ ÊrÊÊQ*­£®Ê*­Ó®Êo°*­˜®RÊ£ÊzÊÊʘ Ê°ÊQ*­ ÊÉ®R ˜ ÊrÊÊÊQ*­®RÊÊ£Êz ˜Ê°ÊQ*­ ÊÉ®Rʘ zÊʓ ÊÊÊÊÊÊÊÊÊ­£°£® zÊʓ 7iʘœÜʈÕÃÌÀ>ÌiÊ̅iÊVœ“«ÕÌ>̈œ˜ÊœvÊ*­ ®Ê܈̅Ê>˜ÊiÝ>“«i° Ý>“«iÊ£°Ó\Ê œ˜Ãˆ`iÀÊ>Ê >ÞiÈ>˜ÊLiˆivÊÌÀiiÊ`iÃVÀˆLˆ˜}Ê̅iÊ«œÃÈLiÊV>ÕÃiÃʜv >Ê`iviV̈ÛiÊV>À° >ÀÊ `œià ˜œÌÊÃÌ>ÀÌ  >ÌÌiÀÞ `iviV̈Ûi Ê >ÌÌiÀÞ œœÃi ÕiÊ ÃÞÃÌi“ `iviV̈Ûi Ê >ÌÌiÀÞ i݅>ÕÃÌi` ÊÊ Õi ݅>ÕÃÌi` Ê -܈ÌV…ià `iviV̈Ûi }˜ˆÌˆœ˜ Ã܈ÌV… `iviV̈Ûi Ê ˆ}°Ê£°££\ÊÊ`ˆ>}˜œÃ̈VÊÌÀiiÊvœÀÊ>ÊV>À° *œÜiÀ‡œ˜ Ài>Þ `iviV̈Ûi  ˜Ê˜ÌÀœ`ÕV̈œ˜ÊÌœÊ œ“«ÕÌ>̈œ˜> ˜Ìiˆ}i˜Vi ÓÓ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ iÀi]Ê i>V…Ê iÛi˜ÌÊ ˆ˜Ê ̅iÊ ÌÀiiÊ ­ˆ}°Ê £°££®Ê V>˜Ê …>ÛiÊ ÌÜœÊ «œÃÈLiÊ Û>ÕiÃ\Ê ÌÀÕiÊ œÀ v>Ãi°Ê/…ÕÃÊ̅iʓ>ÌÀˆViÃÊ>ÃÜVˆ>Ìi`Ê܈̅Ê̅iÊ>ÀVÃÊ܈Ê…>ÛiÊ`ˆ“i˜Ãˆœ˜ÃÊ ­ÓÊÝÊÓ®° œÜ]Ê}ˆÛi˜Ê*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­Ê rÊv>Ãi®R/]Ê ÜiÊ V>˜Ê i>ȏÞÊ Vœ“«ÕÌiÊ*­ ®] *­ ®]Ê*­ ®]Ê*­
®]Êo]*­®Ê«ÀœÛˆ`i`ÊÜiʎ˜œÜÊ̅iÊÌÀ>˜ÃˆÌˆœ˜Ê«ÀœL>LˆˆÌÞÊ “>ÌÀˆVià Vœ˜˜iVÌi`Ê ÜˆÌ…Ê Ì…iÊ ˆ˜ŽÃ°Ê ÃÊ >˜Ê ˆÕÃÌÀ>̈ÛiÊ iÝ>“«i]Ê ÜiÊ Vœ“«ÕÌiÊ *­ ®Ê ܈̅ *­ É®Ê>˜`Ê*­®° iÌÊ*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­ÊrÊv>Ãi®R/ ÊrÊQÊÊä°ÇÊ Êä°ÎÊR ÊÊÊÊÊÊÊÊÊÊÊÊÊÊ .

IÊ >ÃÈ}˜Ê >Ê Vœ˜`ˆÌˆœ˜>Ê «ÀœL>LˆˆÌÞÊ “>ÌÀˆÝ Q*­ É®RÊ̜Ê̅iÊ`ˆÀiVÌi`Ê>ÀVÊvÀœ“ʘœ`iÊÊÌœÊ °ÊÊ/…iÊii“i˜ÌÊ>ÌÊ̅iʍ̅ÊÀœÜ >˜`ʈ̅ VœÕ“˜ÊœvÊ*­ É®]Ê`i˜œÌi`ÊLÞÊ*­  Ɉ®]ÊÀi«ÀiÃi˜ÌÃÊ̅iÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʜv Ê>ÃÃՓˆ˜}Ê̅iÊ«ÀˆœÀʜVVÕÀÀi˜ViʜvÊʈ°Ê/…ˆÃʈÃÊ`iÃVÀˆLi`ʈ˜Êˆ}°£°£ä° œ“«ÕÌ>̈œ˜>Ê˜Ìiˆ}i˜Vi\Ê*Àˆ˜Vˆ«iÃ]Ê/iV…˜ˆµÕiÃÊ>˜`Ê««ˆV>̈œ˜Ã Ó£ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ  *Ê­ ÊÉÊ® Êʈ}°Ê£°£ä\ÊÃÈ}˜ˆ˜}Ê>ÊVœ˜`ˆÌˆœ˜>Ê«ÀœL>LˆˆÌÞʓ>ÌÀˆÝʈ˜Ê̅iÊ`ˆÀiVÌi`Ê>ÀV ÊÊVœ˜˜iVÌi`ÊvÀœ“ÊÊÊÌœÊ ° ˆÛi˜Ê̅iÊ«ÀœL>LˆˆÌÞÊ`ˆÃÌÀˆLṎœ˜ÊœvÊ] `i˜œÌi` LÞÊQ*­£®Ê*­Ӯʰ°o*­˜®R ]ÊÜi V>˜Ê Vœ“«ÕÌiÊ Ì…iÊ «ÀœL>LˆˆÌÞÊ `ˆÃÌÀˆLṎœ˜ œvÊ iÛi˜ÌÊ Ê LÞ ÕȘ} ̅iÊ vœœÜˆ˜} iÝ«ÀiÃȜ˜\ *­ ®ÊrÊQ*­ £®Ê*­ Ó®Êo°*­ “®RÊ£Êzʓ ÊrÊÊQ*­£®Ê*­Ó®Êo°*­˜®RÊ£ÊzÊÊʘ Ê°ÊQ*­ ÊÉ®R ˜ ÊrÊÊÊQ*­®RÊÊ£Êz ˜Ê°ÊQ*­ ÊÉ®Rʘ zÊʓ ÊÊÊÊÊÊÊÊÊ­£°£® zÊʓ 7iʘœÜʈÕÃÌÀ>ÌiÊ̅iÊVœ“«ÕÌ>̈œ˜ÊœvÊ*­ ®Ê܈̅Ê>˜ÊiÝ>“«i° Ý>“«iÊ£°Ó\Ê œ˜Ãˆ`iÀÊ>Ê >ÞiÈ>˜ÊLiˆivÊÌÀiiÊ`iÃVÀˆLˆ˜}Ê̅iÊ«œÃÈLiÊV>ÕÃiÃʜv >Ê`iviV̈ÛiÊV>À° >ÀÊ `œià ˜œÌÊÃÌ>ÀÌ  >ÌÌiÀÞ `iviV̈Ûi Ê >ÌÌiÀÞ œœÃi ÕiÊ ÃÞÃÌi“ `iviV̈Ûi Ê >ÌÌiÀÞ i݅>ÕÃÌi` ÊÊ Õi ݅>ÕÃÌi` Ê -܈ÌV…ià `iviV̈Ûi }˜ˆÌˆœ˜ Ã܈ÌV… `iviV̈Ûi Ê ˆ}°Ê£°££\ÊÊ`ˆ>}˜œÃ̈VÊÌÀiiÊvœÀÊ>ÊV>À° *œÜiÀ‡œ˜ Ài>Þ `iviV̈Ûi  ˜Ê˜ÌÀœ`ÕV̈œ˜ÊÌœÊ œ“«ÕÌ>̈œ˜> ˜Ìiˆ}i˜Vi ÓÓ ÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚÚ iÀi]Ê i>V…Ê iÛi˜ÌÊ ˆ˜Ê ̅iÊ ÌÀiiÊ ­ˆ}°Ê £°££®Ê V>˜Ê …>ÛiÊ ÌÜœÊ «œÃÈLiÊ Û>ÕiÃ\Ê ÌÀÕiÊ œÀ v>Ãi°Ê/…ÕÃÊ̅iʓ>ÌÀˆViÃÊ>ÃÜVˆ>Ìi`Ê܈̅Ê̅iÊ>ÀVÃÊ܈Ê…>ÛiÊ`ˆ“i˜Ãˆœ˜ÃÊ ­ÓÊÝÊÓ®° œÜ]Ê}ˆÛi˜Ê*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­Ê rÊv>Ãi®R/]Ê ÜiÊ V>˜Ê i>ȏÞÊ Vœ“«ÕÌiÊ*­ ®] *­ ®]Ê*­ ®]Ê*­
®]Êo]*­®Ê«ÀœÛˆ`i`ÊÜiʎ˜œÜÊ̅iÊÌÀ>˜ÃˆÌˆœ˜Ê«ÀœL>LˆˆÌÞÊ “>ÌÀˆVià Vœ˜˜iVÌi`Ê ÜˆÌ…Ê Ì…iÊ ˆ˜ŽÃ°Ê ÃÊ >˜Ê ˆÕÃÌÀ>̈ÛiÊ iÝ>“«i]Ê ÜiÊ Vœ“«ÕÌiÊ *­ ®Ê ܈̅ *­ É®Ê>˜`Ê*­®° iÌÊ*­®ÊrÊQ*­ÊrÊÌÀÕi®ÊÊ*­ÊrÊv>Ãi®R/ ÊrÊQÊÊä°ÇÊ Êä°ÎÊR ÊÊÊÊÊÊÊÊÊÊÊÊÊÊ .

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