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Bundlecost.m
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Bundlecost.m
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%
% Bundlecost.m
% SfSM: High Quality Structure from Small Motion for Rolling Shutter Cameras
%
%
% Created by Sunghoon Im on 2017. 1. 25..
% Copyright @ 2017 Sunghoon Im. All rights reserved.
%
function [F,J]=Bundlecost(p, params)
fx=params.K(1,1); a=params.K(1,2); cx=params.K(1,3);
fy=params.K(2,2); cy=params.K(2,3);
scale_t=1;
scale_X=1;
n=size(params.feats,1)/2;
ni = n-1;
[Rvec,Tvec,X_world] = deserialize(p,n);
rol=params.rol;
h = params.h';
t = h*rol;
nf=size(params.feats,2);
F=zeros(n*nf*2,1);
X_1=[X_world; ones(1,size(X_world,2))];
X=X_world(1,:); Y=X_world(2,:); Z=X_world(3,:);
r0=zeros(6*nf, 1);
c0=zeros(6*nf, 1);
v0=zeros(6*nf, 1);
r=zeros(30*nf, ni-1);
c=zeros(30*nf, ni-1);
v=zeros(30*nf, ni-1);
rn=zeros(18*nf, 1);
cn=zeros(18*nf, 1);
vn=zeros(18*nf, 1);
for i=1:n
uv_feat=params.feats(i*2-1:i*2,:);
Rvec_i=Rvec(:,i);
r10=Rvec_i(1); r20=Rvec_i(2); r30=Rvec_i(3);
Tvec_i=Tvec(:,i);
t10=Tvec_i(1); t20=Tvec_i(2); t30=Tvec_i(3);
tt = t(:,i)';
if( i ~= n)
Rvec_i1=Rvec(:,i+1);
r11=Rvec_i1(1); r21=Rvec_i1(2); r31=Rvec_i1(3);
Tvec_i1=Tvec(:,i+1);
t11=Tvec_i1(1); t21=Tvec_i1(2); t31=Tvec_i1(3);
r1 = (1-tt)*r10 + tt*r11;
r2 = (1-tt)*r20 + tt*r21;
r3 = (1-tt)*r30 + tt*r31;
t1 = (1-tt)*t10 + tt*t11;
t2 = (1-tt)*t20 + tt*t21;
t3 = (1-tt)*t30 + tt*t31;
else
r1 = r10*ones(1,nf);
r2 = r20*ones(1,nf);
r3 = r30*ones(1,nf);
t1 = t10*ones(1,nf);
t2 = t20*ones(1,nf);
t3 = t30*ones(1,nf);
end
xy_i = zeros(3, nf);
xy_i(1,:) = sum([ones(1,nf); -r3; r2; t1].*X_1);
xy_i(2,:) = sum([r3; ones(1,nf); -r1; t2].*X_1);
xy_i(3,:) = sum([-r2; r1; ones(1,nf); t3].*X_1);
nxy_i = xy_i./repmat(xy_i(3,:),[3,1]);
uv_proj=params.K*nxy_i;
uv_proj=uv_proj(1:2,:);
F((i-1)*nf*2+1:i*nf*2)= uv_feat(:) - uv_proj(:);
% ºÐ¸ð ¹ÌºÐ + ºÐÀÚ ¹ÌºÐ
X_i=xy_i(1,:); Y_i=xy_i(2,:); Z_i=xy_i(3,:);
Z_i_2=Z_i.^(-2);
X_i_Z_i_2=X_i.*Z_i_2;
Y_i_Z_i_2=Y_i.*Z_i_2;
dZi_dr10 = (1-tt).*Y; %
dx_dr10 = -dZi_dr10.*X_i_Z_i_2;
dy_dr10 = -(1-tt).*Z./Z_i -dZi_dr10.*Y_i_Z_i_2;
dZi_dr20 = -(1-tt).*X; %
dx_dr20 = (1-tt).*Z./Z_i -dZi_dr20.*X_i_Z_i_2;
dy_dr20 = -dZi_dr20.*Y_i_Z_i_2;
dx_dr30 = -(1-tt).*Y./Z_i; %
dy_dr30 = (1-tt).*X./Z_i;
dZi_dr11 = tt.*Y; %
dx_dr11 = -dZi_dr11.*X_i_Z_i_2;
dy_dr11 = -tt.*Z./Z_i -dZi_dr11.*Y_i_Z_i_2;
dZi_dr21 = -tt.*X; %
dx_dr21 = tt.*Z./Z_i -dZi_dr21.*X_i_Z_i_2;
dy_dr21 = -dZi_dr21.*Y_i_Z_i_2;
dx_dr31 = -tt.*Y./Z_i; %
dy_dr31 = tt.*X./Z_i;
dx_dt10 = (1-tt).*scale_t./Z_i; %
dy_dt10 = zeros(1,nf);
dx_dt20 = zeros(1,nf); %
dy_dt20 = (1-tt).*scale_t./Z_i;
dx_dt30 = -(1-tt).*scale_t.*X_i_Z_i_2; %
dy_dt30 = -(1-tt).*scale_t.*Y_i_Z_i_2;
dx_dt11 = tt.*scale_t./Z_i; %
dy_dt11 = zeros(1,nf);
dx_dt21 = zeros(1,nf); %
dy_dt21 = tt.*scale_t./Z_i;
dx_dt31 = -tt.*scale_t.*X_i_Z_i_2; %
dy_dt31 = -tt.*scale_t.*Y_i_Z_i_2;
dZi_dX = -scale_X*r2; %
dx_dX = scale_X./Z_i - dZi_dX.*X_i_Z_i_2;
dy_dX = scale_X*r3./Z_i - dZi_dX.*Y_i_Z_i_2;
dZi_dY = scale_X*r1; %
dx_dY = scale_X*(-r3)./Z_i - dZi_dY.*X_i_Z_i_2;
dy_dY = scale_X./Z_i - dZi_dY.*Y_i_Z_i_2;
dZi_dZ = scale_X; %
dx_dZ = scale_X*(r2)./Z_i - dZi_dZ.*X_i_Z_i_2;
dy_dZ = scale_X*(-r1)./Z_i - dZi_dZ.*Y_i_Z_i_2;
du_dr10 = fx*dx_dr10+a*dy_dr10;
dv_dr10 = fy*dy_dr10;
du_dr20 = fx*dx_dr20+a*dy_dr20;
dv_dr20 = fy*dy_dr20;
du_dr30 = fx*dx_dr30+a*dy_dr30;
dv_dr30 = fy*dy_dr30;
du_dt10 = fx*dx_dt10+a*dy_dt10;
dv_dt10 = fy*dy_dt10;
du_dt20 = fx*dx_dt20+a*dy_dt20;
dv_dt20 = fy*dy_dt20;
du_dt30 = fx*dx_dt30+a*dy_dt30;
dv_dt30 = fy*dy_dt30;
du_dr11 = fx*dx_dr11+a*dy_dr11;
dv_dr11 = fy*dy_dr11;
du_dr21 = fx*dx_dr21+a*dy_dr21;
dv_dr21 = fy*dy_dr21;
du_dr31 = fx*dx_dr31+a*dy_dr31;
dv_dr31 = fy*dy_dr31;
du_dt11 = fx*dx_dt11+a*dy_dt11;
dv_dt11 = fy*dy_dt11;
du_dt21 = fx*dx_dt21+a*dy_dt21;
dv_dt21 = fy*dy_dt21;
du_dt31 = fx*dx_dt31+a*dy_dt31;
dv_dt31 = fy*dy_dt31;
du_dX = fx*dx_dX+a*dy_dX;
dv_dX = fy*dy_dX;
du_dY = fx*dx_dY+a*dy_dY;
dv_dY = fy*dy_dY;
du_dZ = fx*dx_dZ+a*dy_dZ;
dv_dZ = fy*dy_dZ;
ui=(((i-1)*nf*2+1):2:(i*nf*2))';
vi=(((i-1)*nf*2+2):2:(i*nf*2))';
Xi=(1:nf)';
if i==1
r0(:) = [ ui; vi;
ui; vi;
ui; vi; ];
c0(:) = [ 6*(ni)+3*Xi-2; 6*(ni)+3*Xi-2;
6*(ni)+3*Xi-1; 6*(ni)+3*Xi-1;
6*(ni)+3*Xi; 6*(ni)+3*Xi; ];
v0(:) = [ -du_dX'; -dv_dX';
-du_dY'; -dv_dY';
-du_dZ'; -dv_dZ'; ];
elseif i == n
rn(:) = [ ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi; ];
cn(:) = [ (i*3-2-3)*ones(nf,1); (i*3-2-3)*ones(nf,1);
(i*3-1-3)*ones(nf,1); (i*3-1-3)*ones(nf,1);
(i*3-3)*ones(nf,1); (i*3-3)*ones(nf,1);
3*(ni)+(i*3-2-3)*ones(nf,1); 3*(ni)+(i*3-2-3)*ones(nf,1);
3*(ni)+(i*3-1-3)*ones(nf,1); 3*(ni)+(i*3-1-3)*ones(nf,1);
3*(ni)+(i*3-3)*ones(nf,1); 3*(ni)+(i*3-3)*ones(nf,1);
6*(ni)+3*Xi-2; 6*(ni)+3*Xi-2;
6*(ni)+3*Xi-1; 6*(ni)+3*Xi-1;
6*(ni)+3*Xi; 6*(ni)+3*Xi; ];
vn(:) = [ -du_dr10'; -dv_dr10';
-du_dr20'; -dv_dr20';
-du_dr30'; -dv_dr30';
-du_dt10'; -dv_dt10';
-du_dt20'; -dv_dt20';
-du_dt30'; -dv_dt30';
-du_dX'; -dv_dX';
-du_dY'; -dv_dY';
-du_dZ'; -dv_dZ'; ];
else
r(:,i-1) = [ ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi;
ui; vi; ];
c(:,i-1) = [ (i*3-2-3)*ones(nf,1); (i*3-2-3)*ones(nf,1);
(i*3-1-3)*ones(nf,1); (i*3-1-3)*ones(nf,1);
(i*3-3)*ones(nf,1); (i*3-3)*ones(nf,1);
3*(ni)+(i*3-2-3)*ones(nf,1); 3*(ni)+(i*3-2-3)*ones(nf,1);
3*(ni)+(i*3-1-3)*ones(nf,1); 3*(ni)+(i*3-1-3)*ones(nf,1);
3*(ni)+(i*3-3)*ones(nf,1); 3*(ni)+(i*3-3)*ones(nf,1);
(i*3-2-3)*ones(nf,1)+3; (i*3-2-3)*ones(nf,1)+3;
(i*3-1-3)*ones(nf,1)+3; (i*3-1-3)*ones(nf,1)+3;
(i*3-3)*ones(nf,1)+3; (i*3-3)*ones(nf,1)+3;
3*(ni)+(i*3-2-3)*ones(nf,1)+3; 3*(ni)+(i*3-2-3)*ones(nf,1)+3;
3*(ni)+(i*3-1-3)*ones(nf,1)+3; 3*(ni)+(i*3-1-3)*ones(nf,1)+3;
3*(ni)+(i*3-3)*ones(nf,1)+3; 3*(ni)+(i*3-3)*ones(nf,1)+3;
6*(ni)+3*Xi-2; 6*(ni)+3*Xi-2;
6*(ni)+3*Xi-1; 6*(ni)+3*Xi-1;
6*(ni)+3*Xi; 6*(ni)+3*Xi; ];
v(:,i-1) = [ -du_dr10'; -dv_dr10';
-du_dr20'; -dv_dr20';
-du_dr30'; -dv_dr30';
-du_dt10'; -dv_dt10';
-du_dt20'; -dv_dt20';
-du_dt30'; -dv_dt30';
-du_dr11'; -dv_dr11';
-du_dr21'; -dv_dr21';
-du_dr31'; -dv_dr31';
-du_dt11'; -dv_dt11';
-du_dt21'; -dv_dt21';
-du_dt31'; -dv_dt31';
-du_dX'; -dv_dX';
-du_dY'; -dv_dY';
-du_dZ'; -dv_dZ'; ];
end
end
J=sparse([r0(:);r(:);rn(:)],[c0(:);c(:);cn(:)],[v0(:);v(:);vn(:)],n*nf*2,length(p));
end
function [r,t,X]=deserialize(p, n)
r=[[0;0;0],reshape(p(1:3*(n-1)),3,[])];
t=[[0;0;0],reshape(p(3*(n-1)+1:6*(n-1)),3,[])];
p=p(6*(n-1)+1:end);
X=reshape(p,3,[]);
end