% minimal representation of homography i.e., spectrally normalize uncertain homography [H,Jhr] = sugr_minimal_Homography_2D(Ha,Chh) * Ha uncertain regular homography * Chh covariance matrix of vec Ha H minimal representation: * .H homography matrix, sprectrally normalized * .Crr covariance matrix of vector of left differential factor Jrh Jacobian dr/dh, h -> r Wolfgang Förstner wfoerstn@uni-bonn.de wf 3/2011
0001 %% minimal representation of homography 0002 % i.e., spectrally normalize uncertain homography 0003 % 0004 % [H,Jhr] = sugr_minimal_Homography_2D(Ha,Chh) 0005 % 0006 % * Ha uncertain regular homography 0007 % * Chh covariance matrix of vec Ha 0008 % 0009 % H minimal representation: 0010 % * .H homography matrix, sprectrally normalized 0011 % * .Crr covariance matrix of vector of left differential factor 0012 % 0013 % Jrh Jacobian dr/dh, h -> r 0014 % 0015 % Wolfgang Förstner 0016 % wfoerstn@uni-bonn.de 0017 % 0018 % wf 3/2011 0019 0020 function [H,Jrh] = sugr_minimal_Homography_2D(Ha,Chh) 0021 0022 det_H = abs(det(Ha)); % positiv determinant 0023 factor = det_H^(-1/3); % normalizing factor 0024 H.H = Ha * factor; % normalization: det = +-1 0025 Chh = Chh * factor^2; 0026 0027 % Jhr % Jacobian J: h->r 0028 Jrh = sugr_get_Jacobian_Jrh_Homography_2D(H.H); 0029 0030 H.Crr = Jrh * Chh * Jrh'; % CovM of reduced vector 0031 H.type = 20;