By Herbert Freeman (Eds.)
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Additional info for Machine Vision for Inspection and Measurement
Rk and t k constitute the solution to the 3D-3D pose estimation problem. 2) Define = z * 3 , where xn = RkVn + tk. 44 Robert M. Haialick et al. 3) Define where χ = n=l n=l and A , = Σ llfc - sll 2 71=1 £* = Σ - *ll 2 44 ( ) n=l A typical convergence characteristic o f the computed depth values is shown in Figure 23. This experiment is performed in a noise free environment with Ν = 10. The depth values o f the first five points are plotted against the iteration number. 68. 4). Define by (Rkyn+tk)'Vn = V (45) V 'n n It can be shown that e £ + 1 < e\.
Here we take the median of the nonzero deviations only because, with large m , t o o many residuals can equal zero (Hogg, 1979). In robust estimation, the estimates are obtained only after an iterative process because the estimates do not have closed forms. T w o such iterative methods are presented here that can solve the minimization problem stated above (Huber, 1981). 52 Robert M. Haialick et al. Modified Residual M e t h o d In this method, the residuals are modified b y a proper ψ function before the least squares problem is solved.
Figure 28 compares the three algorithms A l , A 2 , and A 3 in the experiment set E l . Figures 29 and 30 compare the three algorithms in the experiment set E2 and E3 respectively. One more experiment is performed to compare the algorithms A 2 and A 3 . W i t h Ν = 20 and P O = 10%, algorithms A 2 and A 3 are applied for SNR from 20db to 40db in a step o f lOdb, and the algorithm A 2 is applied for Ν = 18, P O = 0% and SNR from 20db to 40db in a step o f lOdb. This compares the efficiency of the robust technique against the non-robust technique in the case where Robert M.