Computer Vision Pattern Recognition

# Machine Vision for Inspection and Measurement by Herbert Freeman (Eds.)

By Herbert Freeman (Eds.)

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Extra resources for Machine Vision for Inspection and Measurement

Example text

5 for Huber's and 6 for Tukey's. The nonlinear regression problem can be formulated as follows. m Let f{ : E —» 2£, i = 1 , . . , η be functions that map m-dimensional m space into a real line. Let θ = (#i,02I · ·-,0M)' £ E be the Tridimensional unknown vector to be estimated. ,n (63) which minimizes (64) can be found in several different ways. T o create a scale invariant version of the M-estimator, the robust estimate of scale such as the following is introduced. 6745 is one half of the interquantile range of the Gaussian normal distribution i V ( 0 , 1 ) .

Robert M. Haialick et al. 5 18% 28% 38% 48% 58% Outlier Outlier Outlier Outlier Outlier 8 SIGNAL TO NOISE RATIO Figure 14: Mean absolute rotational and translational distance errors of the least squares method as a function of SNR for the 2D-2D pose estimation problem. The outliers are removed and the least squares method is applied. The number o f corresponding point pairs is 20. The percentage of the outliers is changed from 10% to 50% with a scale o f 20 % . yN b e Ν points in Euclidean 3-space.

Corresponding point data set sizes vary between 10 and 200 pairs. Each point on the graph represents 1,000 trials. Pose Estimation from Corresponding Point Data 37 TRANSLATION VECTOR ERROR (Deg) BO 70 H —- 10 DATA P T S 2 5 DATA P T S - X - 0 10 20 30 40 100 DATA P T S 200 DATA P T S 50 60 SIGNAL TO NOISE RATIO (db) Figure 18: Mean translation vector error versus signal to noise ratio with uniform noise. Corresponding point data set sizes vary between 10 and 200 paris. Each point on the graph represents 1,000 trials.