Home > General-Functions > SUGR > Homography_2D > sugr_get_Jacobian_Jhr_Homography_2D.m

sugr_get_Jacobian_Jhr_Homography_2D

PURPOSE ^

% Get Jacobian Jhr dh/dr (h = vec H) for estimating 2D Homography

SYNOPSIS ^

function [Jhr,Jkr,Jhk] = sugr_get_Jacobian_Jhr_Homography_2D(H)

DESCRIPTION ^

% Get Jacobian Jhr dh/dr (h = vec H) for estimating 2D Homography  
 
 [Jhr,Jkr,Jhk] = sugr_get_Jacobian_Jhr_Homography_2D(H)
 
 H   = 3x3-matrix, spectrally normalized Homography

 Jhr = 9x8-matrix Jacobian dh/dr,r -> h
 Jkr = 9x9-matrix Jacobian dk/dr,r -> k
 Jhk = 9x9-matrix Jacobian dh/dk,k -> h

 Wolfgang Förstner
 wfoerstn@uni-bonn.de

 wf 2/2011

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 %% Get Jacobian Jhr dh/dr (h = vec H) for estimating 2D Homography
0002 %
0003 % [Jhr,Jkr,Jhk] = sugr_get_Jacobian_Jhr_Homography_2D(H)
0004 %
0005 % H   = 3x3-matrix, spectrally normalized Homography
0006 %
0007 % Jhr = 9x8-matrix Jacobian dh/dr,r -> h
0008 % Jkr = 9x9-matrix Jacobian dk/dr,r -> k
0009 % Jhk = 9x9-matrix Jacobian dh/dk,k -> h
0010 %
0011 % Wolfgang Förstner
0012 % wfoerstn@uni-bonn.de
0013 %
0014 % wf 2/2011
0015 
0016 function [Jhr,Jkr,Jhk] = sugr_get_Jacobian_Jhr_Homography_2D(H)
0017 
0018 Ht  = H';      
0019 Jkr = [eye(8); [-1,0,0,0,-1,0,0,0]];    % 9x8-Jacobian dk/dr,r  -> k
0020 Jhk = kron(Ht,eye(3));                  % 9x9-Jacobian dh/dk,k  -> h
0021 Jhr = Jhk * Jkr;                        % 9x8-Jacobian dh/dr,r  -> h

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