ECE181B Proj02 Report

7/26/2019 ECE181B Proj02 Report

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08-Feb-10

ECE/CS 181B

COMPUTER VISION

SIFT

Date: 8 Feb 2010


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08-Feb-10

Introdut!on:

Sa"e#In$ar!ant Feature Tran%&or' (SIFT) !% an a"*or!t+' to detet andde%r!be "oa" &eature% !n !'a*e% t+at !% !nde,endent o& t+e !'a*e %a"e-no!%e- !""u'!nat!on and "oa" *eo'etr! d!%tort!on. T+e SIFT a"*or!t+' a%

r%t ,ub"!%+ed b Da$!d oe !n 1333- and !% de%r!bed !n deta!" !n +!% ,a,er4D!%t!nt!$e !'a*e &eature% &ro' %a"e#!n$ar!ant 5e,o!nt%6 &ro' 2007. Oneo& t+e 'a!n u%e% o& t+e SIFT a"*or!t+' !% 4For an obet !n an !'a*e- t+ereare 'an 9&eature%9 +!+ are !ntere%t!n* ,o!nt% on t+e obet- t+at an beetrated to ,ro$!de a ;&eature; de%r!,t!on o& t+e obet. T+!% de%r!,t!onetrated &ro' a tra!n!n* !'a*e an t+en be u%ed to !dent!& t+e obet+en atte',t!n* to "oate t+e obet !n a te%t !'a*e onta!n!n* 'an ot+erobet%.6

T+e erent %a"e%- and t+en t+e d!>erene o& %ue%%!$e =au%%!an#b"urred!'a*e% are ta5en. ?e,o!nt% are t+en ta5en a% 'a!'a/'!n!'a o&t+e D!>erene o& =au%%!an%(Do=) t+at our at 'u"t!,"e %a"e%. T+e net%te, !% to "ter out unanted ,o!nt%- t+!% !% done b re'o$!n* ,o!nt% !t+"o ontra%t or are ,oor" "oa"!@ed a"on* an ed*e (done b "oo5!n* at,r!n!,a" ur$ature%). T+en a"" 5e,o!nt% are a%%!*ned an or!entat!on and a'a*n!tude. F!na"" a de%r!,tor !% a"u"ated &or ea+ ,o!nt ba%ed on t+e!'a*e "o%e%t !n %a"e to t+e 5e,o!nt9% %a"e.

Met+od:

1. Sa"e#%,ae etre'a detet!on:

T+e %tart!n* ,o!nt o& t+e a"*or!t+' !% to !dent!& a %et o& &eature% t+at are!n$ar!ant to %a"!n* tran%&or'% b +oo%!n* 95e ,o!nt%9 !n re*!on% o& !ntere%t!n t+e !'a*e. T+e%e &eature% are ea+ de%r!bed b a 'u"t!d!'en%!ona"

&eature de%r!,tor $etor t+at !"" be de%r!bed "ater. To a+!e$e !n$ar!aneat d!>erent !'a*e %a"e%- t+e *!$en !'a*e !% re,eated" %'oot+ed u%!n*=au%%!an "o,a%% "ter% o& $ar!n* $a"ue% o& $ar!ane.

Ae +oo%e a %et o& !'a*e% %'oot+ed b $ar!ane $a"ue% &ro' to 2!n an Ota$e and e$a"uate t+e d!>erene o& =au%%!an %'oot+ed !'a*e%(Do=) a% &o""o%:
http://en.wikipedia.org/wiki/Difference_of_Gaussianshttp://en.wikipedia.org/wiki/Difference_of_Gaussians


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08-Feb-10

A+ere and are to re&erene 5erne"% o&d!>erent $ar!ane% and I(-) !% t+e or!*!na" !'a*e under on%!derat!on.

Ae etend t+!% !dea to &urt+er ota$e% ran*!n* &ro' 2 to 7- et andon%trut %et% o& D!>erene o& =au%%!an !'a*e% to e$a"uate "oa" etre'a.

oa" Etre'a:

Ae %ee5 %u+ ,!e"% !n ea+ %et +!+ are e!t+er t+e "oa" 'a!'u' or'!n!'u' ,o!nt% aro%% t+e!r 2 ne!*+bour% !n t+e %a'e ,"ane and t+e

,"ane% abo$e and be"o t+e !'a*e under on%!derat!on- a% %+on:

T+e%e are t+e !n!t!a" %et o& 5e,o!nt% o& !ntere%t !n t+e %et o& %'oot+ed!'a*e% !n ea+ ota$e.


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2. ?e,o!nt oa"!@at!on and F!"ter!n*:

One a %et o& 5e,o!nt% are !dent!ed !n ea+ ota$e- e need to "ter out!non%!%tent ,!e"% and reta!n on" t+o%e +!+ are tru" %!*n!ant &ordetet!on and re'a!n !n$ar!ant to %a"e %,ae tran%&or'at!on%. T+e *oa" !%to "ter out "o ontra%t 5e,o!nt% a% e"" a% 5e,o!nt% ob%er$ed neared*e%- a% t+e are not %tab"e !n &ut+er %te,% o& ,roe%%!n*. To a+!e$e t+!%-t+e ,roedure ado,ted !% t+e &o""o!n*:

o ontra%t 5e,o!nt e"!'!nat!on:

T+e %a"e %,ae &unt!on D(x,y,)!% %+!&ted on ea+ %a',"e ,o!nt and t+e

"oat!on o& t+e etre'a ,o!nt !% obta!ned u%!n* t+e re"at!on:

A+ere ea+ o& t+e ,art!a" der!$at!$e% %+on are a,,"!ed at t+e "oat!on o&t+e %a',"e ,o!nt% . T+e $a"ue o& t+!% &unt!on e$a"uated at t+e o>%et ,o!nt%an be u%ed to "ter out 5e,o!nt% !t+ "o ontra%t %u+ a% 0.0 (a%

%u**e%ted !n oe% ,a,er).

Ed*e Re%,on%e E"!'!nat!on:

Ed*e% +a$e a "ar*e ,r!n!,a" ur$ature !n one d!ret!on but "o ur$ature !nt+e ,er,end!u"ar d!ret!on. T+ere&ore- to e$a"uate t+e%e ,ara'eter% and"ter out %u+ 5e,o!nt% re%!dent on ed*e%- e on%!der a 22 Ge%%!an'atr! o& t+e &or' be"o:

A+ere D!- are t+e re%,et!$e ,art!a" der!$at!$e% 'ent!oned ear"!er. To%!',"!& our de!%!on on ed*e re%,on%e% a"on* D- Dand D d!ret!on%- eu%e %o'e "!near a"*ebra to obta!n t+e &o""o!n* ob%er$at!onH


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A+ere r !% t+e t+re%+o"d. erene%:


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and t+en an ot+er "oa" ,ea5 t+at !% !t+!n 80J o& t+e +!*+e%t ,ea5 !% u%edto a"%o reate a 5e,o!nt !t+ t+at or!entat!on.

7. ?e,o!nt de%r!,tor: a re,re%entat!on o& t+e "oa" re*!on around t+edeteted 5e,o!nt% ba%ed on +!%to*ra' o& or!ented ed*e%.

T!"" no e +a$e *ot t+e "oat!on o& t+e 5e,o!nt%- t+e!r 'a*n!tude andor!entat!on. T+e net %te, !% to o',ute a de%r!,tor &or t+e "oa" !'a*ere*!on t+at !% +!*+" d!%t!nt!$e et !% a% !n$ar!ant a% ,o%%!b"e to re'a!n!n*$ar!at!on%- %u+ a% +an*e !n !""u'!nat!on or D $!e,o!nt.

F!r%t t+e !'a*e *rad!ent 'a*n!tude% and or!entat!on% are %a',"ed aroundt+e 5e,o!nt "oat!on- u%!n* t+e %a"e o& t+e 5e,o!nt to %e"et t+e "e$e" o&

=au%%!an b"ur &or t+e !'a*e. In order to a+!e$e or!entat!on !n$ar!ane- t+eoord!nate% o& t+e de%r!,tor and t+e *rad!ent or!entat!on% are rotatedre"at!$e to t+e 5e,o!nt or!entat!on. < =au%%!an e!*+t!n* &unt!on !t+eKua" to one +a"& t+e !dt+ o& t+e de%r!,tor !ndo !% u%ed to a%%!*n ae!*+t to t+e 'a*n!tude o& ea+ %a',"e ,o!nt. T+e 5e,o!nt de%r!,tor !%%+on on t+e r!*+t %!de o& t+e abo$e *ure. It a""o% &or %!*n!ant %+!&t !n*rad!ent ,o%!t!on% b reat!n* or!entat!on +!%to*ra'% o$er 77 %a',"e


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re*!on%. T+e *ure %+o% e!*+t d!ret!on% &or ea+ or!entat!on +!%to*ra'-!t+ t+e "en*t+ o& ea+ arro orre%,ond!n* to t+e 'a*n!tude o& t+at+!%to*ra' entr. < *rad!ent %a',"e on t+e "e&t an %+!&t u, to 7 %a',"e,o%!t!on% +!"e %t!"" ontr!but!n* to t+e %a'e +!%to*ra' on t+e r!*+t- t+ereba+!e$!n* t+e obet!$e o& a""o!n* &or "ar*er "oa" ,o%!t!ona" %+!&t%. T+e

de%r!,tor !% &or'ed &ro' a $etor onta!n!n* t+e $a"ue% o& a"" t+eor!entat!on +!%to*ra' entr!e%- orre%,ond!n* to t+e "en*t+% o& t+e arro% ont+e r!*+t %!de o& t+e F!*ure. < 778 L 128 e"e'ent &eature $etor &or ea+5e,o!nt !% o',uted.F!na""- t+e &eature $etor !% 'od!ed to redue t+ee>et% o& !""u'!nat!on +an*e. F!r%t- t+e $etor !% nor'a"!@ed to un!t "en*t+.< +an*e !n !'a*e ontra%t !n +!+ ea+ ,!e" $a"ue !% 'u"t!,"!ed b aon%tant !"" 'u"t!," *rad!ent% b t+e %a'e on%tant- %o t+!% ontra%t+an*e !"" be ane"ed b $etor nor'a"!@at!on. < br!*+tne%% +an*e !n+!+ a on%tant !% added to ea+ !'a*e ,!e" !"" not a>et t+e *rad!ent$a"ue%- a% t+e are o',uted &ro' ,!e" d!>erene%.

Re%u"t%:SIFT a% !',"e'ented u%!n* M


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08-Feb-10

Lena image with arrows pointing the dominant angle


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Arrows showing dominant angle in a noisy Lena image


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at!hing o" #eypoints o" Lena image with rotated Lena image

at!hing o" #eypoints o" Lena image with noisy Lena image


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at!hing o" #eypoints o" Lena image with s$b sampled Lena image

at!hing o" #eypoints o" Lena image with %a$ssian smoothed Lena image


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Re&erene%:

1 +tt,://en.!5!,ed!a.or*/!5!/Sa"e#!n$ar!ant&eaturetran%&or'

2 +tt,://,eo,"e.%.ub.a/"oe/5e,o!nt%/

Te%t I'a*e%:

+tt,://.ee.u%b.edu/'an/ee1Q8/"ena.*!&

Documents

ECE181B Proj02 Report