%?RegisterFourierMellin

%?This?code?is?the?result?of?my?messing?around?with?Matlab?investigating?
%?various?image?registration?techniques.??I?came?across?the?excellent?
%?（although?perhaps?a?little?messy?and?buggy）?fm_gui_v2?from?Adam?Wilmer
%?here:

%?http://www.mathworks.com/matlabcentral/fileexchange/loadFile.do?objectId=3000&objectType=file

%?Because?my?needs?are?essentially?the?algorithm?itself?in?a?neat?and?tidy
%?format?to?enable?an?easier?conversion?to?C++?I‘ve?extracted?what?I?think
%?is?the?essence?of?the?Fourier?Mellin?method?into?this?file.??Obviously
%?I?haven‘t?included?a?GUI.??In?order?to?test?it?you?need?to?set?the?first
%?two?statements?to?load?in?2?image?files?of?the?same?size?in?8?bit?grayscale.
%?I?took?lena?and?then?used?Gimp?to?rotate/shift/crop?at?various?angles.
%?It?isn‘t?sub-pixel?accurate?although?I‘m?aware?of?methods?to?achieve
%?this?by?extracting?the?peaks?around?the?peak?of?the?phase?correlation?and
%?finding?the?maxima?（least?squares?perhaps）.??

%?The?methods?towards?the?end?of?the?program?are?cribbed?directly?from
%?Adam‘s?version.??I‘m?new?to?Matlab?（been?playing?with?it?for?less?than
%?a?fortnight）?so?I?wasn‘t?able?to?get?my?head?around?his?log?polar?transform
%?or?the?final?“blending“?of?the?two?images?together.

%?I‘d?like?to?thank?Adam?for?publishing?his?version.??Without?it?I‘d?never
%?have?known?I?had?to?take?the?log?polar?transform?of?the?magnitude?of?the
%?FFT?rather?than?the?log?polar?transform?of?the?original?image!

function?RegnisterFourierMellin（）

????%?The?procedure?is?as?follows?（note?this?does?not?compute?scale）

????%?（1）???Read?in?I1?-?the?image?to?register?against
????%?（2）???Read?in?I2?-?the?image?to?register
????%?（3）???Take?the?FFT?of?I1?shifting?it?to?center?on?zero?frequency
????%?（4）???Take?the?FFT?of?I2?shifting?it?to?center?on?zero?frequency
????%?（5）???Convolve?the?magnitude?of?（3）?with?a?high?pass?filter
????%?（6）???Convolve?the?magnitude?of?（4）?with?a?high?pass?filter
????%?（7）???Transform?（5）?into?log?polar?space
????%?（8）???Transform?（6）?into?log?polar?space
????%?（9）???Take?the?FFT?of?（7）
????%?（10）??Take?the?FFT?of?（8）
????%?（11）??Compute?phase?correlation?of?（9）?and?（10）
????%?（12）??Find?the?location?（xy）?in?（11）?of?the?peak?of?the?phase?correlation
????%?（13）??Compute?angle?（360?/?Image?Y?Size）?*?y?from?（12）
????%?（14）??Rotate?the?image?from?（2）?by?-?angle?from?（13）
????%?（15）??Rotate?the?image?from?（2）?by?-?angle?+?180?from?（13）
????%?（16）??Take?the?FFT?of?（14）
????%?（17）??Take?the?FFT?of?（15）
????%?（18）??Compute?phase?correlation?of?（3）?and?（16）
????%?（19）??Compute?phase?correlation?of?（3）?and?（17）
????%?（20）??Find?the?location?（xy）?in?（18）?of?the?peak?of?the?phase?correlation
????%?（21）??Find?the?location?（xy）?in?（19）?of?the?peak?of?the?phase?correlation
????%?（22）??If?phase?peak?in?（20）?>?phase?peak?in?（21）?（yx）?from?（20）?is?the?translation
????%?（23a）?Else?（yx）?from?（21）?is?the?translation?and?also:

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件???????12590??2008-04-28?20:49??Fourier-Mellin\Register.m
?????文件???????66614??2008-04-27?20:44??Fourier-Mellin\lena.bmp
?????文件???????66614??2008-04-27?20:57??Fourier-Mellin\lena_cropped.bmp
?????文件???????66614??2008-04-27?20:57??Fourier-Mellin\lena_cropped_rotated.bmp
?????文件???????66614??2008-04-27?21:00??Fourier-Mellin\lena_cropped_rotated_shifted.bmp
?????文件???????66614??2008-04-27?20:59??Fourier-Mellin\lena_cropped_shifted.bmp
?????目錄???????????0??2010-04-26?23:06??Fourier-Mellin\