%?FRANKOTCHELLAPPA??-?Generates?integrable?surface?from?gradients
%
%?An?implementation?of?Frankot?and?Chellappa‘a?algorithm?for?constructing
%?an?integrable?surface?from?gradient?information.
%
%?Usage:??????z?=?frankotchellappa（dzdxdzdy）
%
%?Arguments:??dzdx??-?2D?matrices?specifying?a?grid?of?gradients?of?z
%?????????????dzdy?????with?respect?to?x?and?y.
%
%?Returns:????z??????-?Inferred?surface?heights.

%?Reference:
%
%?Robert?T.?Frankot?and?Rama?Chellappa
%?A?Method?for?Enforcing?Integrability?in?Shape?from?Shading
%?IEEE?PAMI?Vol?10?No?4?July?1988.?pp?439-451
%
%?Note?this?code?just?implements?the?surface?integration?component?of?the
%?paper?（Equation?21?in?the?paper）.??It?does?not?implement?their?shape?from
%?shading?algorithm.

%?Copyright?（c）?2004?Peter?Kovesi
%?School?of?Computer?Science?&?Software?Engineering
%?The?University?of?Western?Australia
%?http://www.csse.uwa.edu.au/
%?
%?Permission?is?hereby?granted?free?of?charge?to?any?person?obtaining?a?copy
%?of?this?software?and?associated?documentation?files?（the?“Software“）?to?deal
%?in?the?Software?without?restriction?subject?to?the?following?conditions:
%?
%?The?above?copyright?notice?and?this?permission?notice?shall?be?included?in?
%?all?copies?or?substantial?portions?of?the?Software.
%
%?The?Software?is?provided?“as?is“?without?warranty?of?any?kind.

%?October?2004

function?z?=?frankotchellappa（dzdxdzdy）
????
????if?~all（size（dzdx）?==?size（dzdy））
??????error（‘Gradient?matrices?must?match‘）;
????end

????[rowscols]?=?size（dzdx）;
????
????%?The?following?sets?up?matrices?specifying?frequencies?in?the?x?and?y
????%?directions?corresponding?to?the?Fourier?transforms?of?the?gradient
????%?data.??They?range?from?-0.5?cycles/pixel?to?+?0.5?cycles/pixel.?The
????%?fiddly?bits?in?the?line?below?give?the?appropriate?result?depending?on
????%?whether?there?are?an?even?or?odd?number?of?rows?and?columns
????
????[wx?wy]?=?meshgrid（（[1:cols]-（fix（cols/2）+1））/（cols-mod（cols2））?...
			（[1:rows]-（fix（rows/2）+1））/（rows-mod（rows2）））;
????
????%?Quadrant?shift?to?put?zero?frequency?at?the?appropriate?edge
????wx?=?ifftshift（wx）;?wy?=?ifftshift（wy）;

????DZDX?=?fft2（dzdx）;???%?Fourier?transforms?of?gradients
????DZDY?=?fft2（dzdy）;

????%?Integrate?in?the?frequency?domain?by?phase?shifting?by?pi/2?and
????%?weighting?the?Fourier?coefficients?by?their?frequencies?in?x?and?y?and
????%?then?dividing?by?the?squared?frequency.??eps?is?added?to?the
????%?denominator?to?avoid?division?by?0.
????
????Z?=?（-j*wx.*DZDX?-j*wy.*DZDY）./（wx.^2?+?wy.^2?+?eps）;??%?Equation?21
????
????z?=?real（ifft2（Z））;??%?Reconstruction

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2016-10-20?22:48??frankotchellappa\
?????文件??????316158??2011-08-31?16:12??frankotchellappa\Depth?Recovery?from?Noisy?Gradient?Vector?Fields?Using?Regularization-可使用.pdf
?????文件???????55985??2016-04-04?22:30??frankotchellappa\DepthFromGradient.pdf
?????目錄???????????0??2016-10-20?22:57??frankotchellappa\frankotchellappa_MatlabCode\
?????文件????????2612??2015-12-05?18:04??frankotchellappa\frankotchellappa_MatlabCode\frankotchellappa.m
?????文件????????6881??2016-04-13?20:29??frankotchellappa\frankotchellappa_MatlabCode\g2sTestSurf.m
?????文件????????1608??2016-10-20?22:46??frankotchellappa\frankotchellappa_MatlabCode\TestFrankotchellappa.m
?????文件?????????521??2016-10-20?22:57??frankotchellappa\frankotchellappa_MatlabCode\說明：運行TestFrankotchellappa.m簡短說明.txt