From: Gehua Yang <yangg2@rp...>  20041118 18:02:02

First of all, Page 114, or Algorithm 3.7 is the Gold Standard Algorithm for estimating an AFFINE transformation, not homography. If homography is to be estimated, refer to Algorithm 3.3 on Page 98. There are two choices: Sampson error or Gold Standard error. For Sampson error, there are only 9 parameters(or one can choose other parameterization). As for Gold Standard error, there are 2n+9 variables. But there are 4n residuals: sum d(x_i, xhat_i)^2 + d(xpri_i, xhatpri_i)^2 Recall that LM takes a vector of residuals before squaring. for each d(.) function, there are two residuals. Another way to look at it is that each ideal point x hat brings in two parameters, but provides 4 constraints. Gehua  Original Message  From: Marc Anderson To: vxlusers@... Sent: Tuesday, November 16, 2004 9:58 PM Subject: [Vxlusers] Premise of vnl_levenberg_marquardt hold back Gold standard? > Hi, all vxl guys! > The class vnl_levenberg_marquardt checks if the number of parameters is > less than that of residuals before carrying out the minimization process, > otherwise it'll returns false. This requirement prevents the estimation of > homography between two images using the Gold Standard algorithm(H&Z book, > p114), in which case the number of parameters is 2n+9 while the number of > residuals is n. ( where n is the number of point correspondences ). Would > someone get the idea to figure this issue out? Thanks! 