Two Simulated Annealing Optimization Schemas for Rational Bézier Curve Fitting in the Presence of Noise

Table 1

Experimental results on the three examples in our benchmark for the simulated annealing schemas discussed in this paper.

Model			Statistical results
Dataset	Type	Schema		BIC (best)	BIC (avg)
logo	NR		10010	−691.913	−691.830	13	0.0005	0.0001	N.A.
logo	R	AIO	4208	−661.908	−658.804	13	0.0002	0.0003	N.A.
logo	R	SEQ	13031	−770.212	−701.338	13	0.0001	0.0001	N.A.
shoe	NR		16624	2915.200	3020.101	24	0.0191	0.0152	0.0076
shoe	R	AIO	6648	2098.859	2470.634	24	0.0012	0.0061	0.0053
shoe	R	SEQ	20202	1996.226	2289.712	24	0.0024	0.0061	0.0052
torus	NR		18546	−2204.821	−2301.567	20
torus	R	AIO	1529	−6067.465	−6001.324	21
torus	R	SEQ	5286	−7798.643	−7796.846	20
torus10	NR		13276	4307.409	4390.492	17	0.0311	0.0342	0.0458
torus10	R	AIO	3768	4354.618	4414.523	19	0.0300	0.0304	0.0401
torus10	R	SEQ	23119	4341.604	4381.367	17	0.0312	0.0323	0.0402
torus20	NR		12027	3887.839	4991.823	20	0.0222	0.0201	0.0364
torus20	R	AIO	3778	3474.463	3479.345	20	0.0130	0.0137	0.0181
torus20	R	SEQ	45775	3446.804	3465.673	20	0.0128	0.0139	0.0182
torus30	NR		16174	3033.538	3561.901	20	0.0109	0.0094	0.0172
torus30	R	AIO	5546	3060.624	3066.298	20	0.0097	0.0089	0.0151
torus30	R	SEQ	48511	3021.939	3035.634	20	0.0098	0.0089	0.0148
torus40	NR		11015	6662.487	6700.738	40	0.0183	0.0144	0.0346
torus40	R	AIO	5111	2740.208	2788.422	20	0.0074	0.0073	0.0094
torus40	R	SEQ	53640	2708.680	2729.980	20	0.0074	0.0072	0.0096
torus50	NR		14101	2386.160	2501.900	25	0.0057	0.0059	0.0076
torus50	R	AIO	4205	2357.285	2408.811	21	0.0054	0.0053	0.0076
torus50	R	SEQ	45206	2344.050	2378.280	20	0.0055	0.0052	0.0076
torus60	NR		12052	3574.142	4713.190	20	0.0179	0.0121	0.0340
torus60	R	AIO	4012	2116.800	2145.321	20	0.0041	0.0045	0.0620
torus60	R	SEQ	45191	2051.304	2080.235	20	0.0031	0.0033	0.0038
torus70	NR		8860	3574.142	3866.889	21	0.0058	0.0057	0.0116
torus70	R	AIO	4205	2210.012	2284.590	21	0.0039	0.0040	0.0054
torus70	R	SEQ	45797	1963.317	1995.759	20	0.0038	0.0039	0.0056
torus80	NR		14100	3574.142	3934.296	25	0.0038	0.0044	0.0052
torus80	R	AIO	4002	1814.950	2008.400	21	0.0032	0.0036	0.0044
torus80	R	SEQ	13366	1803.356	1931.721	20	0.0032	0.0036	0.0043
torus90	NR		14100	1828.028	1981.534	25	0.0031	0.0041	0.0048
torus90	R	AIO	4204	1671.145	1799.627	21	0.0030	0.0030	0.0042
torus90	R	SEQ	13350	1654.944	1786.873	20	0.0030	0.0031	0.0044