%?This?Matlab?file?demomstrates?a?level?set?method?in?the?following?paper
%????C.?Li?C.?Xu?C.?Gui?and?M.?D.?Fox?“Level?Set?Evolution?Without?Re-initialization:?A?New?Variational?Formulation“
%????in?Proc.?IEEE?Conf.?Computer?Vision?and?Pattern?Recognition?（CVPR‘05）?vol.?1?pp.?430?36?2005.
%
%?Author:?Chunming?Li?all?rights?reserved.
%?E-mail:?li_chunming@hotmail.com
%?URL:??http://vuiis.vanderbilt.edu/~licm/

clear?all;
close?all;
Img?=?imread（‘50.bmp‘）;??%?The?same?cell?image?in?the?paper?is?used?here
Img=double（Img（::1））;
sigma=1.5;????%?scale?parameter?in?Gaussian?kernel?for?smoothing.
G=fspecial（‘gaussian‘15sigma）;??%旋轉對稱高斯低通濾波器，標準方差1.5，大小15*15
Img_smooth=conv2（ImgG‘same‘）;??%?二維卷積smooth?image?by?Gaussiin?convolution
[IxIy]=gradient（Img_smooth）;??%梯度
f=Ix.^2+Iy.^2;
g=1./（1+f）;??%?邊緣指標函數edge?indicator?function.

epsilon=1.5;?%?the?papramater?in?the?definition?of?smoothed?Dirac?function

timestep=5;??%?time?step
mu=0.2/timestep;??%?coefficient?of?the?internal?（penalizing）?energy?term?P（\phi）
??????????%?Note:?the?product?timestep*mu?must?be?less?than?0.25?for?stability!

lambda=5;?%?coefficient?of?the?weighted?length?term?Lg（\phi）
alf=1.5;??%?coefficient?of?the?weighted?area?term?Ag（\phi）;
??????????%?Note:?Choose?a?positive（negative）?alf?if?the?initial?contour?is?outside（inside）?the?object.


%?define?initial?level?set?function?（LSF）?as?-c0?0?c0?at?points?outside?on
%?the?boundary?and?inside?of?a?region?R?respectively.
[nrow?ncol]=size（Img）;??
c0=4;???
initialLSF=c0*ones（nrowncol）;
w=10;
initialLSF（w+1:end-w?w+1:end-w）=0;??%?zero?level?set?is?on?the?boundary?of?R.?
?????????????????????????????????????%?Note:?this?can?be?commented?out.?The?intial?LSF?does?NOT?necessarily?need?a?zero?level?set.
?????????????????????????????????????
initialLSF（w+2:end-w-1?w+2:?end-w-1）=-c0;?%?negative?constant?-c0?inside?of?R?postive?constant?c0?outside?of?R.
u=initialLSF;
figure;imagesc（Img）;colormap（gray）;hold?on;
[ch]?=?contour（u[0?0]‘r‘）;??%輪廓????????????????????????
title（‘Initial?contour‘）;

%?start?level?set?evolution
for?n=1:500
????u=EVOLUTION（u?g?lambda?mu?alf?epsilon?timestep?1）;?????
????if?mod（n20）==0?????%20的整數倍
????????pause（0.001）;
????????imagesc（Img）;colormap（gray）;hold?on;
????????[ch]?=?contour（u[0?0]‘r‘）;?
????????iterNum=[num2str（n）?‘?iterations‘];????????
????????title（iterNum）;
????????hold?off;
????end
end
imagesc（Img）;colormap（gray）;hold?on;
[ch]?=?contour（u[0?0]‘r‘）;?
totalIterNum=[num2str（n）?‘?iterations‘];??
title（[‘Final?contour?‘?totalIterNum]）;

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2014-03-11?16:35??LevelSet_ChunmingLi_v0\
?????文件??????188470??2014-03-10?19:44??LevelSet_ChunmingLi_v0\0.001.bmp
?????文件???????66614??2014-03-11?16:14??LevelSet_ChunmingLi_v0\1.bmp
?????文件??????241470??2014-03-10?20:49??LevelSet_ChunmingLi_v0\50.bmp
?????文件??????188470??2014-03-11?16:14??LevelSet_ChunmingLi_v0\6.bmp
?????文件????????2648??2014-03-11?17:01??LevelSet_ChunmingLi_v0\Demo1.m
?????文件????????2584??2014-03-11?16:14??LevelSet_ChunmingLi_v0\Demo1_ManualBinaryInitial.m
?????文件????????2555??2014-03-11?16:14??LevelSet_ChunmingLi_v0\Demo2.m
?????文件????????2559??2014-03-11?16:14??LevelSet_ChunmingLi_v0\Demo2_ManualBinaryInitial.m
?????文件????????2229??2014-03-11?16:14??LevelSet_ChunmingLi_v0\EVOLUTION.m
?????文件??????801246??2014-03-11?16:14??LevelSet_ChunmingLi_v0\levelset_CVPR05.pdf
?????文件???????66614??2014-03-11?16:14??LevelSet_ChunmingLi_v0\peppers4-0.40.bmp
?????文件???????66614??2014-03-11?16:14??LevelSet_ChunmingLi_v0\peppers_0.5.bmp
?????文件????????8134??2014-03-11?16:14??LevelSet_ChunmingLi_v0\twoObj.bmp
?????文件???????16434??2014-03-11?16:14??LevelSet_ChunmingLi_v0\twocells.bmp
?????文件???????66614??2014-03-11?16:14??LevelSet_ChunmingLi_v0\骨架提取后1.bmp