zhang_constraint_eq.m

% return a vector of values that should be zero if the proposed parameter
% solution x satisfies the constraints. this corresponds to the ceq
% function in fmincon. so if you want to enforce a constraint that the
% first two parameters should sum to 8 and the 3rd and 4th parameters
% should sum to 9, then you would return y = [ x(1)+x(2)-8; x(3)+x(4)-9 ];
% note that this function is entirely dependent on the particular
% calibration setup: if you know that the second last and last photos are
% exactly 10mm apart (because you used a translation stage to capture them)
% then you could enforce that constraint on the T parameter.
%
% For the GlassScan project, we take Nfree images of the LCD monitor being
% manually moved around, then Ntstage images of it being translated from its
% current position, away from the camera 10mm each step, and then Nrstage images
% of the grid on the rotation stage. deltaT is the distance between successive
% nTStage grids (in mm) and deltaR is the rotation angle between successive
% nRStage grids (in degrees)
function [c,ceq] = zhang_constraint_eq( calib, x )

Calibration = zhang_load( calib );
c = [];

% EXAMPLE:
%
% This function currently assumes that the final 3 images are taken with a
% translation stage exactly 1in apart. Hence the R parameters for all three
% images should be equal. Als, image A and B are 1in apart,
% and B and C are 1in apart, and A and C are 2in apart. This final
% transitive constraint implicitly constrains the 3 grids to undergo pure
% translation along a 1D line.
%
% Calibration = zhang_unpackparamvector( Calibration, x );
% active = [Calibration.Images.Active];
% Images = Calibration.Images(active);
% T3 = Images(end).T;
% R3 = Images(end).Rv;
% T2 = Images(end-1).T;
% R2 = Images(end-1).Rv;
% T1 = Images(end-2).T;
% R1 = Images(end-2).Rv;
% 
% enforcedDistance = 25.4;
% ceq = [R1-R2; R2-R3; norm(T1-T2)-enforcedDistance];
%
% END OF EXAMPLE