function?vertex?=?AC_deform（vertexalphabetatauFextITERtype）
%?AC_DEFORM?????Deform?an?active?contour?（AC）?also?known?as?snake.
%?????vertex1?=?AC_DEFORM（vertex0alphabetatauFextiter）
%?????vertex1?=?AC_DEFORM（vertex0alphabetatauFextitertype）
%???
%?????Inputs
%?????vertex0?????position?of?the?vertices?n-by-2?matrix?each?row?of?
%?????????????????which?is?[x?y].?n?is?the?number?of?vertices.
%?????alpha???????AC?elasticity?（1st?order）?parameter?ranges?from?0?to?1.
%?????beta????????AC?rigidity?（2nd?order）?parameter?ranges?from?0?to?1.
%?????tau?????????time?step?of?each?iteration.
%?????Fext????????the?external?force?fieldd1-by-d2-by-2?matrix?
%?????????????????the?force?at?（xy）?is?[Fext（yx1）?Fext（yx2）].
%?????iter????????number?of?iterations?usually?ranges?from?1?to?5.
%?????type????????‘close‘?-?close?contour?（default）?the?last?vertex?and
%???????????????????????????first?vertex?are?connected?
%?????????????????‘open‘??-?open?contour??the?last?vertex?and?first?vertex
%???????????????????????????are?not?connected?
%???????????????
%?????Outputs
%?????vertex1?????position?of?the?vertices?after?deformation?n-by-2?matrix
%?????
%?????Note?that?if?the?vertices?are?outside?the?valid?range?i.e.?y>d1?||
%?????y<1?||?x>d2?||?x<1?they?will?be?pulled?inside?the?valid?range.?
%?
%?????Example
%?????????See?EXAMPLE_VFC?EXAMPLE_PIG.
%
%?????See?also?AMT?AM_VFC?AM_VFK?AM_PIG?AC_INITIAL?AC_REMESH
%?????AC_DISPLAY?AM_GVF?EXAMPLE_VFC?EXAMPLE_PIG.?
%?
%?????Reference
%?????[1]?Bing?Li?and?Scott?T.?Acton?“Active?contour?external?force?using
%?????vector?field?convolution?for?image?segmentation“?Image?Processing
%?????IEEE?Trans.?on?vol.?16?pp.?2096-2106?2007.??
%?????[2]?Bing?Li?and?Scott?T.?Acton?“Automatic?Active?Model
%?????Initialization?via?Poisson?Inverse?Gradient“?Image?Processing
%?????IEEE?Trans.?on?vol.?17?pp.?1406-1420?2008.???
%?
%?（c）?Copyright?Bing?Li?2005?-?2009.

%?Revision?Log
%???11-30-2005??original?
%???01-30-2006??external?force?interpolation?outside?the?image?
%???02-18-2006??add?open?contour?codes
%???01-30-2009??minor?bug?fix

%%?inputs?check
if?~ismember（nargin?6:7）?||?ndims（Fext）?~=?3?||?size（Fext3）?~=?2
????error（‘Invalid?inputs?to?AC_DEFORM!‘）????
end
if?nargin?==?6
????type?=?‘close‘;
end

N?=?size（vertex1）;
if?size（vertex2）?~=?2
????error（‘Invalid?vertex?matrix!‘）
end

if?N?????return
end

%%?compute?T?=?（I?+?tao*A）?of?equation?（9）?in?reference?[1]
Lap?=?sparse（1:N?1:N?-2）?+?sparse（1:N?[N?1:N-1]?1）?+?sparse（1:N?[2:N?1]?1）;

if?strcmp（type‘open‘）?%?offset?tau?for?boundary?vertices????
????tau?=?sparse（1:N?1:N?tau）;
????tau（1）?=?0;
????tau（end）?=?0;
????offset?=?sparse（1:N?1:N?1）;
????offset（11）=0;??????offset（NN）?=?0;
????offset（12）=1;??????offset（NN-1）?=?1;
????Lap?=?offset*Lap;
end

T?=sparse（1:N1:N1）+?tau*（beta*Lap*Lap-alpha*Lap）;

%%?Another?way?to?compute?T?for?close?AC
%?a