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SID.m
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function [Fot, T, R, N, transformations, inv_trans] = SID(I0, transformations, canonSize, mode, inv_trans)
% ---------------------------------------------------
% \|L\|_* + lambda1*\|M\|_1 + lambda2*\|N\|_1+\lambda3*\|K\|_1 +
% \lambda4*\|Q\|_1 + \lambda5\|K@Q\|_1 + \lambda6\|Omega-K-Q\|_F^2
% s.t. Fot = T+M; M = N+R; L=T; K = DT; Q = DR; T>=0; R>=0;
% ---------------------------------------------------
if nargin < 4
mode = 1;
end
N = 0;
% parametric tranformation model
para.transformType = 'AFFINE';
% one of 'TRANSLATION', 'EUCLIDEAN', 'SIMILARITY', 'AFFINE','HOMOGRAPHY'
% main loop
para.stoppingDelta = .1; % stopping condition of main loop
if mode == 1
para.maxIter = 10; % maximum iteration number of main loops
else
para.maxIter = 1;
end
% inner loop
nbOfFrames = length(transformations);
%----------------------------------------
% Here, lambda1 to lambda6 are the coefficients can be tuned
%----------------------------------------
dv = canonSize(1);
dh = canonSize(2);
coef.lambda1 = 0;
coef.lambda2 = 0;
coef.lambda3 = 0;
coef.lambda4 = 0;
coef.lambda5 = 0;
coef.lambda6 = 0;
coef.lambda1 = 1000/sqrt(dv*dh); %/sqrt(dv*dh); %0.3
% coef.lambda2 = 5/sqrt(dv*dh); %50
coef.lambda3 = 100/sqrt(dv*dh);
% coef.lambda4 = 0/sqrt(dv*dh);
% coef.lambda5 = 0/sqrt(dv*dh);
coef.lambda6 = 0/sqrt(dv*dh);
coef.imgSize = canonSize;
%----------------------------------------
I0x = cell(1,nbOfFrames);
I0y = I0x;
for fileIndex = 1 : nbOfFrames
I0x{1,fileIndex} = imfilter( I0{1,fileIndex}, (-fspecial('sobel')') / 8 );
I0y{1,fileIndex} = imfilter( I0{1,fileIndex}, -fspecial('sobel') / 8 );
end
%% get the initial input images in canonical frame
xi_initial = cell(1,nbOfFrames) ; % initial transformation parameters
for i = 1 : nbOfFrames
if size(transformations{i},1) < 3
transformations{i} = [transformations{i} ; 0 0 1] ;
inv_trans{i} = [inv_trans{i} ; 0 0 1];
end
% inv_trans{i} = [inv_trans{i} ; 0 0 1];
xi_initial{i} = projective_matrix_to_parameters('HOMOGRAPHY',transformations{i});
end
%% start the main loop
iterNum = 0 ; % iteration number of outer loop
converged = 0 ;
prevObj = inf ; % previous objective function value
xi = cell(1,nbOfFrames) ;
while ~converged
iterNum = iterNum + 1 ;
Fot = zeros(dv*dh, nbOfFrames);
J = cell(1,nbOfFrames);
disp(['Outer Loop Iter ' num2str(iterNum)]) ;
for fileIndex = 1 : nbOfFrames
Tfm = fliptform(maketform('projective',transformations{fileIndex}'));
I = vec(imtransform(I0{1,fileIndex}, Tfm,'bicubic','XData',...
[1 canonSize(2)],'YData',[1 canonSize(1)],'Size',canonSize));
Iu = vec(imtransform(I0x{1,fileIndex},Tfm,'bicubic','XData',...
[1 canonSize(2)],'YData',[1 canonSize(1)],'Size',canonSize));
Iv = vec(imtransform(I0y{1,fileIndex},Tfm,'bicubic','XData',...
[1 canonSize(2)],'YData',[1 canonSize(1)],'Size',canonSize));
y = I; %vec(I);
Fot(:,fileIndex) = y ;
% transformation matrix to parameters
xi{fileIndex} = projective_matrix_to_parameters...
(para.transformType,transformations{fileIndex}) ;
% Compute Jacobian
J{1,fileIndex} = image_Jaco(Iu, Iv, canonSize, ...
para.transformType, xi{fileIndex});
end
% Superimposed Image Decomposition inner loop
% -----------------------------------------------------------------
% -----------------------------------------------------------------
% using QR to orthogonalize the Jacobian matrix
QR_Q = cell(1,nbOfFrames);
QR_R = QR_Q;
for fileIndex = 1 : nbOfFrames
[QR_Q{fileIndex}, QR_R{fileIndex}] = qr(J{1,fileIndex},0);
end
%[L,M,N,K,Q,T,R,delta_xi,Omega] = SID_inner(Fot,QR_Q,coef);
[L,M,N,K, T,R,delta_xi,Omega] = DeOcclusion_LMNTK(Fot,QR_Q,coef);
% [L,M,N,T,R,delta_xi, Omega] = DeOcclusion_inner(Fot, QR_Q, coef);
% [L,M,T,R,delta_xi, Omega] = DeOcclusion_LM(Fot, QR_Q, coef);
for fileIndex = 1 : nbOfFrames
delta_xi{fileIndex} = (QR_R{fileIndex})\delta_xi{fileIndex} ;
end
% step in paramters
for i = 1 : nbOfFrames
xi{i} = xi{i} + delta_xi{i};
transformations{i} = parameters_to_projective_matrix(para.transformType,xi{i});
end
% -----------------------------------------------------------------
% curObj = norm(svd(L),1) + coef.lambda1*sum(abs(M(:))) + coef.lambda2*sum(abs(N(:)))...
% + coef.lambda3*sum(abs(K{1}(:))+abs(K{2}(:))) + coef.lambda4*sum(abs(Q{1}(:))+abs(Q{2}(:)))...
% + coef.lambda5*sum(abs(K{1}(:).*Q{1}(:))+abs(K{2}(:).*Q{2}(:))) +...
% + coef.lambda6*norm(Omega{1} - K{1} - Q{1},'fro')^2+coef.lambda6*norm(Omega{2} - K{2} - Q{2},'fro')^2;
% curObj = norm(svd(L),1) + coef.lambda1*sum(abs(M(:))) + coef.lambda2*sum(abs(N(:)))...
% + coef.lambda3*sum(abs(K{1}(:))+abs(K{2}(:))) + coef.lambda4*sum(abs(Q{1}(:))+abs(Q{2}(:)))...
% + coef.lambda5*sum(abs(K{1}(:).*Q{1}(:))+abs(K{2}(:).*Q{2}(:))) +...
% + coef.lambda6*norm(Omega{1} - K{1} - Q{1},'fro')^2+coef.lambda6*norm(Omega{2} - K{2} - Q{2},'fro')^2;
curObj = norm(svd(L),1) + coef.lambda1*sum(abs(M(:)))+ coef.lambda2*sum(abs(N(:)))...
+ coef.lambda3*sum(abs(K{1}(:))+abs(K{2}(:)));
% curObj = norm(svd(L),1) + coef.lambda1*sum(abs(M(:)))+ coef.lambda2*sum(abs(N(:)));
% curObj = norm(svd(L),1) + coef.lambda1*sum(abs(M(:)));
disp(['Previous objective function: ' num2str(prevObj) ]);
disp(['Current objective function : ' num2str(curObj) ]);
if curObj>prevObj
L = L_old;
M = M_old;
N = N_old;
K = K_old;
%Q = Q_old;
T = T_old;
R = R_old;
transformations = transformations_old;
else
L_old = L;
M_old = M;
N_old = N;
K_old = K;
%Q_old = Q;
T_old = T;
R_old = R;
transformations_old = transformations;
end
if ( (prevObj - curObj < para.stoppingDelta) || iterNum >= para.maxIter )
converged = 1;
if ( prevObj - curObj >= para.stoppingDelta )
disp('Maximum iterations reached') ;
end
else
prevObj = curObj;
end
end