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multi_chanvese.m
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multi_chanvese.m
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%%%%% multi-chanvese %%%%%%
function [seg,phi,its] = multi_chanvese(I,init_mask,kai,sz,max_its,alpha,thresh,display)
%-- default value for parameter alpha is .1
if(~exist('alpha','var'))
alpha = .2;
end
%-- default value for parameter thresh is 0
if(~exist('thresh','var'))
thresh = 0;
end
%-- default behavior is to display intermediate outputs
if(~exist('display','var'))
display = true;
end
color='r';
%-- ensures image is 2D double matrix
I = im2graydouble(I);
%-- Create a signed distance map (SDF) from mask
phi = mask2phi(init_mask);
%--main loop
its = 0; stop = 0;
prev_mask = init_mask; c = 0;
nbr=[1,1;1,0;1,-1;0,1;0,-1;-1,1;-1,0;-1,-1];
NB_width=1.2; %%%% increment by 0.2
increa = 0.2;
epsilon_merge = 0.001;
[dimx,dimy]=size(kai);
phi_temp=zeros(dimx,dimy);
numObj = uint16(max(kai(:)));
se2= strel('disk',2);
while ((its < max_its) && ~stop)
idx = find(phi < NB_width & phi > -NB_width); % get the curve's narrow band
num_idx = numel(idx);
if ~isempty(idx)
%-- intermediate output
if (display>0)
showCurveAndPhi(phi,I,color);
title([num2str(its),' iteration']);
drawnow
% if ( mod(its,5)==1 )
% keyboard
% end
end
%-- find interior and exterior mean
%upts = find(phi<=0); % interior points
vpts = find(phi>0); % exterior points
%u = sum(I(upts))/(length(upts)+eps); % interior mean
v = sum(I(vpts))/(length(vpts)+eps); % exterior mean
%F = (I(idx)-u).^2-(I(idx)-v).^2; % force from image information
curvature = get_curvature(phi,idx); % force from curvature penalty
%dphidt = F./max(abs(F)) + alpha*curvature; % gradient descent to minimize energy
if(its==20)
keyboard
end
dphidt=zeros(1,num_idx);
%F=zeros(1,num_idx);
%regularTerm=zeros(1,num_idx);
for obj_iter = 1:1:numObj
upts = (kai==obj_iter);
tmp_sz = nnz(upts);
u=sum(I(upts))/(tmp_sz+eps);
imgk = imdilate(upts,se2);
tmp = find(imgk(idx)>0);
F=(I(idx(tmp))-u).^2 - (I(idx(tmp))-v).^2;
regularTerm=zeros(numel(tmp),1);
if(tmp_sz<sz(obj_iter)*0.75)
regularTerm(:,1)=alpha*curvature(tmp)-0.1/(1+exp(10*tmp_sz/sz(obj_iter)-8.5));
elseif(tmp_sz>sz(obj_iter)*1.25)
regularTerm(:,1)=alpha*curvature(tmp)+0.1/(1+exp(-10*tmp_sz/sz(obj_iter)+11.5));
end
try
dphidt(tmp)=F./max(abs(F))+regularTerm;
catch
keyboard
end
end
%-- maintain the CFL condition
dt = .45/(max(abs(dphidt))+eps);
%-- evolve the curve
%phi(idx) = phi(idx) + dt.*dphidt;
phi_temp(idx) = dt.*dphidt;
%%%% extract narrow band points iteratively%%%%
for bd_iter = increa:increa:NB_width
nb = find((phi<bd_iter & phi>=bd_iter-increa) | (phi>-bd_iter & phi<=-bd_iter+increa));
num_nb = numel(nb);
if(num_nb==0)
continue;
end
[nbx,nby]=ind2sub([dimx,dimy],nb);
for i=1:1:num_nb
tx=nbx(i);ty=nby(i);
if(phi(tx,ty)>0 && phi_temp(tx,ty)<=0)
a=kai(max(tx-1,1):1:min(tx+1,dimx),max(ty-1,1):1:min(ty+1,dimy));
a(2,2)=0;
tmp_obj=unique(nonzeros(a));
On=numel(tmp_obj);
if(On==1)
kai(tx,ty)=tmp_obj;
phi(tx,ty)=phi_temp(tx,ty);
continue;
end
if(On==0)
phi(tx,ty)=epsilon_merge;
continue;
%disp('expanding to an isolated point');
%keyboard
end
a(2,2)=1;
b=(a==0);
cc=bwconncomp(b,8);
if(cc.NumObjects~=1)
phi(tx,ty)=epsilon_merge;
continue;
end
a(2,2)=0;
b=(a>0);
cc=bwconncomp(b,4);
if(cc.NumObjects~=1) %%% not simple
phi(tx,ty)=epsilon_merge;
continue;
end
kai(tx,ty)=tmp_obj(1);
phi(tx,ty)=phi_temp(tx,ty);
elseif(phi(tx,ty)<=0 && phi_temp(tx,ty)>0)
a=kai(max(tx-1,1):1:min(tx+1,dimx),max(ty-1,1):1:min(ty+1,dimy));
a(2,2)=0;
tmp_obj=unique(nonzeros(a));
if(numel(tmp_obj)>1)
disp('unexpected touching');
keyboard;
elseif(numel(tmp_obj)==0)
disp('isolated point');
keyboard
end
b=(a>0);
cc=bwconncomp(b,4);
if(cc.NumObjects~=1) %%% not simple
phi(tx,ty)=-epsilon_merge;
continue;
end
a(2,2)=1;
b=(a==0);
cc=bwconncomp(b,8);
if(cc.NumObjects~=1)
phi(tx,ty)=-epsilon_merge;
continue;
end
phi(tx,ty)=phi_temp(tx,ty);
kai(tx,ty)=0;
else
phi(tx,ty)=phi_temp(tx,ty);
end
end
end
%-- Keep SDF smooth
phi = sussman(phi, .5);
new_mask = phi<=0;
c = convergence(prev_mask,new_mask,thresh,c);
if c <= 5
its = its + 1;
prev_mask = new_mask;
else stop = 1;
end
else
break;
end
end
%-- final output
showCurveAndPhi(phi,I,color);
title([num2str(its),' iteration']);
drawnow
%-- make mask from SDF
seg = phi<=0; %-- Get mask from levelset
%---------------------------------------------------------------------
%-- AUXILIARY FUNCTIONS ----------------------------------------------
%---------------------------------------------------------------------
%-- Displays the image with curve superimposed
function showCurveAndPhi(phi,I,cl)
figure(2);
imagesc(I,[0, 255]); axis off; axis equal; colormap(gray);
hold on; contour(phi,[0 0],cl,'Linewidth',1); hold off;
% delete(h);
% test = isequal(size(c,2),0);
% while (test==false)
% s = c(2,1);
% if ( s == (size(c,2)-1) )
% t = c;
% figure(1)
% hold on; plot(t(1,2:end)',t(2,2:end)',cl,'Linewidth',3);
% test = true;
% else
% t = c(:,2:s+1);
% figure(1)
% hold on; plot(t(1,1:end)',t(2,1:end)',cl,'Linewidth',3);
% c = c(:,s+2:end);
% end
% end
%-- converts a mask to a SDF
function phi = mask2phi(init_a)
phi=bwdist(init_a)-bwdist(1-init_a)+im2double(init_a)-.5;
%-- compute curvature along SDF
function curvature = get_curvature(phi,idx)
[dimy, dimx] = size(phi);
[y x] = ind2sub([dimy,dimx],idx); % get subscripts
%-- get subscripts of neighbors
ym1 = y-1; xm1 = x-1; yp1 = y+1; xp1 = x+1;
%-- bounds checking
ym1(ym1<1) = 1; xm1(xm1<1) = 1;
yp1(yp1>dimy)=dimy; xp1(xp1>dimx) = dimx;
%-- get indexes for 8 neighbors
idup = sub2ind(size(phi),yp1,x);
iddn = sub2ind(size(phi),ym1,x);
idlt = sub2ind(size(phi),y,xm1);
idrt = sub2ind(size(phi),y,xp1);
idul = sub2ind(size(phi),yp1,xm1);
idur = sub2ind(size(phi),yp1,xp1);
iddl = sub2ind(size(phi),ym1,xm1);
iddr = sub2ind(size(phi),ym1,xp1);
%-- get central derivatives of SDF at x,y
phi_x = -phi(idlt)+phi(idrt);
phi_y = -phi(iddn)+phi(idup);
phi_xx = phi(idlt)-2*phi(idx)+phi(idrt);
phi_yy = phi(iddn)-2*phi(idx)+phi(idup);
phi_xy = -0.25*phi(iddl)-0.25*phi(idur)...
+0.25*phi(iddr)+0.25*phi(idul);
phi_x2 = phi_x.^2;
phi_y2 = phi_y.^2;
%-- compute curvature (Kappa)
curvature = ((phi_x2.*phi_yy + phi_y2.*phi_xx - 2*phi_x.*phi_y.*phi_xy)./...
(phi_x2 + phi_y2 +eps).^(3/2)).*(phi_x2 + phi_y2).^(1/2);
%-- Converts image to one channel (grayscale) double
function img = im2graydouble(img)
[dimy, dimx, c] = size(img);
if(isfloat(img)) % image is a double
if(c==3)
img = rgb2gray(uint8(img));
end
else % image is a int
if(c==3)
img = rgb2gray(img);
end
img = double(img);
end
%-- level set re-initialization by the sussman method
function D = sussman(D, dt)
% forward/backward differences
a = D - shiftR(D); % backward
b = shiftL(D) - D; % forward
c = D - shiftD(D); % backward
d = shiftU(D) - D; % forward
a_p = a; a_n = a; % a+ and a-
b_p = b; b_n = b;
c_p = c; c_n = c;
d_p = d; d_n = d;
a_p(a < 0) = 0;
a_n(a > 0) = 0;
b_p(b < 0) = 0;
b_n(b > 0) = 0;
c_p(c < 0) = 0;
c_n(c > 0) = 0;
d_p(d < 0) = 0;
d_n(d > 0) = 0;
dD = zeros(size(D));
D_neg_ind = find(D < 0);
D_pos_ind = find(D > 0);
dD(D_pos_ind) = sqrt(max(a_p(D_pos_ind).^2, b_n(D_pos_ind).^2) ...
+ max(c_p(D_pos_ind).^2, d_n(D_pos_ind).^2)) - 1;
dD(D_neg_ind) = sqrt(max(a_n(D_neg_ind).^2, b_p(D_neg_ind).^2) ...
+ max(c_n(D_neg_ind).^2, d_p(D_neg_ind).^2)) - 1;
D = D - dt .* sussman_sign(D) .* dD;
%-- whole matrix derivatives
function shift = shiftD(M)
shift = shiftR(M')';
function shift = shiftL(M)
shift = [ M(:,2:size(M,2)) M(:,size(M,2)) ];
function shift = shiftR(M)
shift = [ M(:,1) M(:,1:size(M,2)-1) ];
function shift = shiftU(M)
shift = shiftL(M')';
function S = sussman_sign(D)
S = D ./ sqrt(D.^2 + 1);
% Convergence Test
function c = convergence(p_mask,n_mask,thresh,c)
diff = p_mask - n_mask;
n_diff = sum(abs(diff(:)));
if n_diff < thresh
c = c + 1;
else
c = 0;
end