%?This?code?demonstrates?the?level?set?evolution?（LSE）?and?bias?field?estimation
%?proposed?in?the?following?paper:
%??????C.?Li?R.?Huang?Z.?Ding?C.?Gatenby?D.?N.?metaxas?and?J.?C.?Gore?
%??????“A?Level?Set?Method?for?Image?Segmentation?in?the?Presence?of?Intensity
%??????Inhomogeneities?with?Application?to?MRI“?IEEE?Trans.?Image?Processing?2011
%

%?Note:?
%????This?code?implements?the?two-phase?formulation?of?the?model?in?the?above?paper.
%????The?two-phase?formulation?uses?the?signs?of?a?level?set?function?to?represent
%????two?disjoint?regions?and?therefore?can?be?used?to?segment?an?image?into?two?regions
%????which?are?represented?by?（u>0）?and?（u<0）?where?u?is?the?level?set?function.
%
%????All?rights?researved?by?Chunming?Li?who?formulated?the?model?designed?and?
%????implemented?the?algorithm?in?the?above?paper.
%
%?E-mail:?lchunming@gmail.com
%?URL:?http://www.engr.uconn.edu/~cmli/
%?Copyright?（c）?by?Chunming?Li
%?Author:?Chunming?Li

close?all;
clear?all;
%Img=imread（‘heart_ct.bmp‘）;
Img=imread（‘myBrain_axial.bmp‘）;
Img=double（Img（::1））;
A=255;
Img=A*normalize01（Img）;?%?rescale?the?image?intensities
nu=0.001*A^2;?%?coefficient?of?arc?length?term

sigma?=?4;?%?scale?parameter?that?specifies?the?size?of?the?neighborhood
iter_outer=50;?
iter_inner=10;???%?inner?iteration?for?level?set?evolution

timestep=.1;
mu=1;??%?coefficient?for?distance?regularization?term?（regularize?the?level?set?function）

c0=1;
figure（1）;
imagesc（Img[0?255]）;?colormap（gray）;?axis?off;?axis?equal

%?initialize?level?set?function
initialLSF?=?c0*ones（size（Img））;
initialLSF（30:9050:90）?=?-c0;
u=initialLSF;

hold?on;
contour（u[0?0]‘r‘）;
title（‘Initial?contour‘）;

figure（2）;
imagesc（Img[0?255]）;?colormap（gray）;?axis?off;?axis?equal
hold?on;
contour（u[0?0]‘r‘）;
title（‘Initial?contour‘）;

epsilon=1;
b=ones（size（Img））;??%%%?initialize?bias?field

K=fspecial（‘gaussian‘round（2*sigma）*2+1sigma）;?%?Gaussian?kernel
KI=conv2（ImgK‘same‘）;
KONE=conv2（ones（size（Img））K‘same‘）;

[rowcol]=size（Img）;
N=row*col;

for?n=1:iter_outer
????[u?b?C]=?lse_bfe（uImg?b?KKONE?nutimestepmuepsilon?iter_inner）;

????if?mod（n2）==0
????????pause（0.001）;
????????imagesc（Img[0?255]）;?colormap（gray）;?axis?off;?axis?equal;
????????hold?on;
????????contour（u[0?0]‘r‘）;
????????iterNum=[num2str（n）?‘?iterations‘];
????????title（iterNum）;
????????hold?off;
????end
???
end
Mask?=（Img>10）;
Img_corrected=normalize01（Mask.*Img./（b+（b==0）））*255;

figure（3）;?imagesc（b）;??colormap（gray）;?axis?off;?axis?equal;
title（‘Bias?field‘）;

figure（4）;
imagesc（Img_corrected）;?colormap（gray）;?axis?off;?axis?equal;
title（‘Bias?corrected?image‘）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2013-11-06?08:23??11-levelset_segmentation_biasCorrection_v1\
?????文件????????2751??2013-08-27?20:01??11-levelset_segmentation_biasCorrection_v1\Demo.m
?????文件????????4087??2013-08-27?19:53??11-levelset_segmentation_biasCorrection_v1\Demo_MultiPhase.asv
?????文件????????4239??2013-11-02?09:19??11-levelset_segmentation_biasCorrection_v1\Demo_MultiPhase.m
?????文件???????18177??2013-07-25?09:12??11-levelset_segmentation_biasCorrection_v1\head000001.png
?????文件???????20534??2009-04-16?18:56??11-levelset_segmentation_biasCorrection_v1\heart_ct.bmp
?????文件??????????73??2012-11-29?23:06??11-levelset_segmentation_biasCorrection_v1\Heaviside.m
?????文件??????263222??2013-04-23?07:59??11-levelset_segmentation_biasCorrection_v1\I870_0001.BMP
?????文件?????2103949??2013-07-25?21:17??11-levelset_segmentation_biasCorrection_v1\levelset_segmentation_biasCorrection.pdf
?????文件????????3246??2012-11-29?22:56??11-levelset_segmentation_biasCorrection_v1\lse_bfe.m
?????文件????????3621??2013-08-27?17:26??11-levelset_segmentation_biasCorrection_v1\lse_bfe_3Phase.asv
?????文件????????3621??2013-08-27?17:29??11-levelset_segmentation_biasCorrection_v1\lse_bfe_3Phase.m
?????文件???????36682??2007-10-31?16:21??11-levelset_segmentation_biasCorrection_v1\myBrain_axial.bmp
?????文件?????????164??2012-11-06?10:18??11-levelset_segmentation_biasCorrection_v1\normalize01.m
?????文件???????25102??2013-10-09?13:14??11-levelset_segmentation_biasCorrection_v1\XXI870_0001.bmp