Global Optimization of Redescending Robust Estimators

Table 3

Circles and corresponding parameters: for each circle (circle no.), x_c and y_c are the coordinates of the center, r the radius, No. Points the number of points generated for the circle, and P₁, P₂, P₃ the circle parameters explained below.

Circle no.	xc	yc	r	No. points	P1	P2	P3
1	10.0	10.0	5.0	136	−20.0	−20.0	175
2	20.0	10.0	8.0	219	−40.0	−20.0	436
3	20.0	20.0	5.0	136	−40.0	−40.0	775
4	20.0	32.0	5.0	136	−40.0	−64.0	1399
5	55.0	28.0	5.0	136	−110.0	−56.0	3784
6	45.0	28.0	3.0	82	−90.0	−56.0	2800
7	40.0	18.0	7.5	205	−80.0	−36.0	1868

All points (x_i, y_i) belonging to a circumference of center (x_c, y_c) and radius r satisfy the following equation: