boundaries

function[B,L,N,A]=bwboundaries(varargin)

%BWBOUNDARIESTraceregionboundariesinabinaryimage.

%B=BWBOUNDARIES(BW)tracestheexteriorboundaryofobjects,

%descends

%intotheoutermostobjects(parents)andtracestheirchildren(objects

%completelyenclodbytheparents).BWmustbeabinaryimagewhere

%nonzeropixelsbelongtoanobjectand0-pixelsconstitutethe

%-by-1cellarray,wherePisthenumberofobjects

%llcontainsaQ-by-2matrix,whereQisthenumber

%wofthe

%Q-by-2matricescontainstherowandcolumncoordinatesofaboundary

%pixel.

%

%B=BWBOUNDARIES(BW,CONN)specifiestheconnectivitytouwhentracing

%ault

%valueforCONNis8.

%

%B=BWBOUNDARIES(BW,CONN,OPTIONS)providesanoptionalstring

%'noholes'speedsuptheoperationofthealgorithmby

%havingitarchonlyforobject(parentandchild)boundaries.

%Bydefault,orwhen'holes'stringisspecified,thealgorithmarches

%forbothobjectandholeboundaries.

%

%[B,L]=BWBOUNDARIES(...)returnsthelabelmatrix,L,asthecond

%

%two-dimensionalarrayofnonnegativeintegersthatreprent

%-thregionincludesallelementsinLthathave

%berofobjectsandholesreprentedbyLis

%equaltomax(L(:)).Thezero-valuedelementsofLmakeupthebackground.

%

%[B,L,N,A]=BWBOUNDARIES(...)returnsthenumberofobjectsfound(N)

%stNcellsinBareobjectboundaries.

%uare,spar,

%logicalmatrixwithsideoflengthmax(L(:)),whorowsandcolums

%correspondtothepositionofboundariesstoredinB.

%TheboundarienclodbyaB{m}aswellastheboundaryenclosing

%B{m}canbothbefoundusingAasfollows:

%

%enclosing_boundary=find(A(m,:));

%enclod_boundaries=find(A(:,m));

%

%ClassSupport

%-------------

%BWcanbelogicalornumericanditmustbereal,2-D,andnonspar.

%L,rlogical.

%

%Example1

%---------

%ythelabeled

%objectsusingthejetcolormap,onagraybackground,withregion

%boundariesoutlinedinwhite.

%

%I=imread('');

%BW=im2bw(I,graythresh(I));

%[B,L]=bwboundaries(BW,'noholes');

%imshow(label2rgb(L,@jet,[.5.5.5]))

%holdon

%fork=1:length(B)

%boundary=B{k};

%plot(boundary(:,2),boundary(:,1),'w','LineWidth',2)

%end

%

%Example2

%---------

%ytheregion

%ytextshowingtheregionnumber

%(badonthelabelmatrix),onally,

%displaytheadjacencymatrixusingSPY.

%

%HINT:Aftertheimageisdisplayed,uthezoomtoolinordertoread

%individuallabels.

%

%BW=imread('');

%[B,L,N,A]=bwboundaries(BW);

%imshow(BW);holdon;

%colors=['b''g''r''c''m''y'];

%fork=1:length(B),

%boundary=B{k};

%cidx=mod(k,length(colors))+1;

%plot(boundary(:,2),boundary(:,1),colors(cidx),'LineWidth',2);

%%randomizetextpositionforbettervisibility

%rndRow=ceil(length(boundary)/(mod(rand*k,7)+1));

%col=boundary(rndRow,2);row=boundary(rndRow,1);

%h=text(col+1,row-1,num2str(L(row,col)));

%t(h,'Color',colors(cidx),'FontSize',14,'FontWeight','bold');

%end

%figure;spy(A);

%

%Example3

%---------

%Displayobjectboundariesinredandholeboundariesingreen.

%

%BW=imread('');

%[B,L,N]=bwboundaries(BW);

%imshow(BW);holdon;

%fork=1:length(B),

%boundary=B{k};

%if(k>N)

%plot(boundary(:,2),boundary(:,1),'g','LineWidth',2);

%el

%plot(boundary(:,2),boundary(:,1),'r','LineWidth',2);

%end

%end

%

%Example4

%---------

%Displayparentboundariesinred(anyemptyrowofadjacency

%matrixbelongstoaparent)andtheirholesingreen.

%

%BW=imread('');

%[B,L,N,A]=bwboundaries(BW);

%imshow(BW);holdon;

%fork=1:length(B),

%if(~sum(A(k,:)))

%boundary=B{k};

%plot(boundary(:,2),boundary(:,1),'r','LineWidth',2);

%forl=find(A(:,k))'

%boundary=B{l};

%plot(boundary(:,2),boundary(:,1),'g','LineWidth',2);

%end

%end

%end

%

%SeealsoBWTRACEBOUNDARY,BWLABEL,BWLABELN.

%Copyright1993-2003TheMathWorks,Inc.

%$Revision:1.1.6.3$$Date:2003/05/0317:50:06$

[BW,conn,findholes]=parInputs(varargin{:});

[objs,L]=FindObjectBoundaries(BW,conn);

if(findholes)

[holes,LabeledHoles]=FindHoleBoundaries(BW,conn);

%Generatecombinedholes+objectslabelmatrix

L=L+(LabeledHoles~=0)*length(objs)+LabeledHoles;

el

holes={};

end

%Createtheoutputmatrix

B=[objs;holes];

%Returnnumberofobjectboundaries

N=length(objs);

if(nargout>3)

%Produceanadjacencymatrixshowingparent-hole-childrelationships

A=CreateAdjMatrix(B,N);

end

%-----------------------------------------------------------------------------

function[BW,conn,findholes]=parInputs(varargin)

checknargin(1,4,nargin,mfilename);

BW=varargin{1};

checkinput(BW,{'numeric','logical'},{'real','2d','nonspar'},...

mfilename,'BW',1);

if~islogical(BW)

BW=BW~=0;

end

firstStringToProcess=0;

ifnargin<2

conn=8;

el

ifischar(varargin{2})

firstStringToProcess=2;

conn=8;

el

ifnargin>2,

firstStringToProcess=3;

end

conn=varargin{2};

checkinput(conn,{'double'},{},mfilename,'CONN',2);

if(conn~=4&conn~=8)

eid=sprintf('Images:%s:badScalarConn',mfilename);

msg='AscalarconnectivityspecifierCONNmusteitherbe4or8';

error(eid,msg);

end

end

end

findholes=true;

iffirstStringToProcess

validStrings={'noholes','holes'};

fork=firstStringToProcess:nargin

%checkforoptions

string=checkstrs(varargin{k},validStrings,mfilename,'OPTION',k);

switchstring

ca'noholes'

findholes=fal;

ca'holes'

findholes=true;

otherwi

error('Images:bwboundaries:unexpectedError','%s',...

'Unexpectedlogicerror.')

end

end

end

%-----------------------------------------------------------------------------

function[A]=CreateAdjMatrix(B,numObjs)

A=spar(fal(length(B)));

levelCellArray=GroupBoundariesByTreeLevel(B,numObjs);

%scanthroughallthelevelpairs

fork=1:length(levelCellArray)-1,

parentsIdx=levelCellArray{k};%outsideboundaries

childrenIdx=levelCellArray{k+1};%insideboundaries

parents=B(parentsIdx);

children=B(childrenIdx);

sampChildren=GetSamplePointsFromBoundaries(children);

form=1:length(parents),

parent=parents{m};

inside=inpolygon(sampChildren(:,2),sampChildren(:,1),...

parent(:,2),parent(:,1));

%castingtologicalisnecessarybecauofthebug,eGECK#137394

inside=logical(inside);

A(childrenIdx(inside),parentsIdx(m))=true;

end

end

%-----------------------------------------------------------------------------

functionpoints=GetSamplePointsFromBoundaries(B)

points=zeros(length(B),2);

form=1:length(B),

boundary=B{m};

points(m,:)=boundary(1,:);

end

%-----------------------------------------------------------------------------

%

%firstelementoftheoutputcellarrayholdsadoublearrayofindices

%ofboundarieswhicharetheoutermost(firstlayerofanonion),the

%condholdsthecondlayer,andsoon.

functionidxGroupedByLevel=GroupBoundariesByTreeLevel(B,numObjs)

processHoles=~(length(B)==numObjs);

%partheinput

objIdx=1:numObjs;

objs=B(objIdx);

ifprocessHoles

holeIdx=numObjs+1:length(B);

holes=B(holeIdx);

el

holes={};

end

%initializeoutputandloopcontrolvariables

idxGroupedByLevel={};

done=fal;

findHole=fal;%startwithanobjectboundary

while~done

if(findHole)

I=FindOutermostBoundaries(holes);

holes=holes(~I);%removeprocesdboundaries

idxGroupedByLevel=[idxGroupedByLevel,{holeIdx(I)}];

holeIdx=holeIdx(~I);%removeindicesofprocesdboundaries

el

I=FindOutermostBoundaries(objs);

objs=objs(~I);

idxGroupedByLevel=[idxGroupedByLevel,{objIdx(I)}];

objIdx=objIdx(~I);

end

if(processHoles)

findHole=~findHole;

end

if(impty(holes)&&impty(objs))

done=true;

end

end

%-----------------------------------------------------------------------------

%Returnsalogicalvectorshowingthelocationsofoutermostboundaries

%intheinputvector(ie1fortheboundariesthatareoutermostand

%0forallotherboundaries)

functionI=FindOutermostBoundaries(B)

%Lookforparentboundaries

I=fal(1,length(B));

form=1:length(B),

boundary=B{m};

x=boundary(1,2);%grabasamplepointfortesting

y=boundary(1,1);

surrounded=fal;

forn=[1:(m-1),(m+1):length(B)],%excludeboundaryundertest

boundary=B{n};

if(inpolygon(x,y,boundary(:,2),boundary(:,1))),

surrounded=true;

break;

end

end

I(m)=~surrounded;

end

%-----------------------------------------------------------------------------

function[B,L]=FindObjectBoundaries(BW,conn)

L=bwlabel(BW,conn);

B=bwboundariesmex(L,conn);

%-----------------------------------------------------------------------------

function[B,L]=FindHoleBoundaries(BW,conn)

%ctsare8connected,thenholes

%mustbe4connectedandviceversa.

if(conn==4)

backgroundConn=8;

el

backgroundConn=4;

end

%Turnholesintoobjects

BWcomplement=imcomplement(BW);

%clearunwanted"hole"objectsfromtheborder

BWholes=imclearborder(BWcomplement,backgroundConn);

%gettheholes!

L=bwlabel(BWholes,backgroundConn);

B=bwboundariesmex(L,backgroundConn);