%%
function?[?imf_matrix?]?=?bemd（?input_image?）

%?BEMD?This?program?calculates?the?Bidimensional?EMD?of?a?2-d?signal?using
%?the?process?of?sifting.?It?is?dependent?on?the?function?SIFT.

tic

%?Make?a?‘double‘?copy?of?the?image

input_image_d?=?cast（input_image‘double‘）;

%?Assigning?the?initial?values?of?‘h‘?（data?for?sifting）?and?‘k‘?（imf?index）

h_func?=?input_image_d;
k=1;

%?The?process?of?Sifting

while（k<4）
????[imf_temp?residue_temp]?=?sift（h_func）;?
????imf_matrix（::k）?=?imf_temp;?%#ok
????k?=?k+1;
????h_func?=?residue_temp;
end

%?Assigning?the?final?residue?to?the?last?IMF?index

imf_matrix（::k）?=?residue_temp;

%?End?of?BEMD?Computation

toc

end

%%

function?[?h_imf?residue?]?=?sift（?input_image?）

%?This?function?sifts?for?a?single?IMF?of?the?given?2D?signal?input

%?Pre-processing

[len?bre]?=?size（input_image）;
x?=?1:len;
y?=?1:bre;
input_image_temp?=?input_image;

while（1）
????
????%?Finding?the?extrema?in?the?2D?signal
????
????[zmax?imax?zmin?imin]?=?extrema2（input_image_temp）;
????[xmax?ymax]?=?ind2sub（size（input_image_temp）imax）;
????[xmin?ymin]?=?ind2sub（size（input_image_temp）imin）;

????%?Interpolating?the?extrema?to?get?the?extrema?suraces

????[zmaxgrid??tmpx?tmpx]?=?gridfit（ymaxxmaxzmaxyx）;
????[zmingrid?tmpx?tmpx]?=?gridfit（yminxminzminyx）;
????
????%?Averaging?the?extrema?to?get?the?Zavg?surface
????
????zavggrid?=?（zmaxgrid?+?zmingrid）/2;
????
????%?Computation?of?the?h_imf?（IMF?for?the?‘h‘?input）
????
????h_imf?=?input_image_temp?-?zavggrid;

????%?Computing?IMF?cost
????
????eps?=?0.00000001;
????num?=?sum（sum（（h_imf-input_image_temp）.^2））;
????den?=?sum（sum（（input_image_temp）.^2））?+?eps;
????cost?=?num/den;

????%?Checking?the?IMF?accuracy
????
????if?cost<0.2
????????break;
????else
????????input_image_temp?=?h_imf;
????end
????
end

%?Computation?of?the?Residue?after?IMF?computation
residue?=?input_image?-?h_imf;

end

%%

function?[xmaximaxxminimin]?=?extrema（x）
%EXTREMA???Gets?the?global?extrema?points?from?a?time?series.
%???[XMAXIMAXXMINIMIN]?=?EXTREMA（X）?returns?the?global?minima?and?maxima?
%???points?of?the?vector?X?ignoring?NaN‘s?where
%????XMAX?-?maxima?points?in?descending?order
%????IMAX?-?indexes?of?the?XMAX
%????XMIN?-?minima?points?in?descending?order
%????IMIN?-?indexes?of?the?XMIN
%
%???DEFINITION?（from?http://en.wikipedia.org/wiki/Maxima_and_minima）:
%???In?mathematics?maxima?and?minima?also?known?as?extrema?are?points?in
%???the?domain?of?a?function?at?which?the?function?takes?a?largest?value
%???（maximum）?or?smallest?value?（minimum）?either?within?a?given
%???neighbourhood?（local?extrema）?or?on?the?function?domain?in?its?entirety
%???（global?extrema）.
%
%???Example:
%??????x?=?2*pi*linspace（-11）;
%??????y?=?cos（x）?-?0.5?+?0.5*rand（size（x））;?y（40:45）?=?1.85;?y（50:53）=NaN;
%??????[ymaximaxyminimin]?=?extrema（y）;
%??????plot（xyx（imax）ymax‘g.‘x（imin）ymin‘r.‘）
%
%???See?also?EXTREMA2?MAX?MIN

%???Written?by
%???Lic.?on?Physics?Carlos?Adri醤?Vargas?

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????文件???????45840??2011-05-02?21:03??bemd.m
?????文件????????1343??2014-02-12?13:28??license.txt