Direct Least Absolute Deviation Fitting of Ellipses

Table 2

Mean and standard deviation of the relative error and estimated ellipse parameters on simulated Gaussian noise data with tested methods.

Methods	Noise level	Relative error
DLS	0.5	0.23%/0.18	72.00/0.04	64.01/0.05	70.01/0.05	50.00/0.05	30.00/0.14
	5	2.43%/0.78	71.96/0.46	64.00/0.44	69.85/0.57	50.85/0.53	30.24/1.33
	10	6.53%/1.61	71.92/0.88	64.01/1.00	70.05/0.98	52.94/0.99	29.40/2.86
	15	12.61%/2.23	72.15/1.46	63.84/1.68	71.43/1.59	55.80/1.49	29.23/4.37
	20	19.61%/2.93	72.11/1.92	64.26/1.97	73.35/1.85	59.33/2.11	30.50/6.26
	25	27.02%/3.38	72.26/2.90	64.29/2.74	76.51/2.23	62.75/2.44	31.04/8.88
HyperLS	0.5	0.21%/0.16	72.00/0.04	64.01/0.05	70.01/0.05	49.99/0.05	30.00/0.14
	5	2.03%/0.65	71.96/0.46	64.00/0.45	69.96/0.61	50.05/0.54	30.25/1.38
	10	4.28%/1.38	71.91/0.92	64.00/1.04	70.14/1.30	50.11/1.16	29.27/3.24
	15	7.49%/2.53	72.17/1.58	63.81/1.85	71.35/2.69	50.11/1.93	29.02/5.68
	20	11.56%/3.49	72.12/2.25	64.29/2.36	73.18/4.22	50.73/3.30	30.64/9.65
	25	17.69%/5.82	72.23/4.05	64.31/3.46	78.44/6.89	50.48/3.84	30.50/14.51
SampsonLS	0.5	0.23%/0.16	71.99/0.04	64.01/0.05	70.01/0.05	49.99/0.05	29.99/0.14
	5	2.40%/0.78	71.96/0.46	63.99/0.45	69.71/0.55	49.37/0.56	30.27/1.28
	10	7.98%/2.40	71.89/0.98	64.09/1.09	69.12/1.31	47.03/1.53	29.67/3.02
	15	20.51%/5.62	71.94/2.29	64.02/2.12	69.76/3.06	40.79/3.50	30.22/6.54
	20	49.30%/12.95	73.19/6.58	64.12/4.53	79.35/10.19	26.23/10.93	29.27/10.09
	25	69.01%/11.07	72.21/27.81	53.12/96.88	106.86/100.53	23.59/33.39	30.32/14.70
ElliFit	0.5	0.23%/0.14	72.00/0.04	64.01/0.05	70.02/0.05	49.99/0.05	29.97/0.14
	5	3.36%/0.80	71.96/0.47	64.00/0.44	71.33/0.61	49.84/0.52	27.10/1.25
	10	11.56%/1.77	71.91/1.01	64.00/0.96	76.42/1.41	49.25/1.06	20.30/2.18
	15	22.31%/2.57	72.28/1.83	63.90/1.63	86.60/2.96	48.76/1.35	15.35/2.88
	20	32.76%/3.60	72.40/3.40	64.17/2.02	100.37/6.03	49.30/1.94	12.50/3.27
	25	44.58%/4.89	72.30/6.97	64.18/2.71	121.54/11.85	50.32/2.31	10.65/3.53
RANSAC	0.5	1.22%/0.38	71.99/0.27	63.99/0.27	69.97/0.36	49.96/0.34	30.08/0.73
	5	6.68%/2.35	72.18/1.55	64.32/1.45	70.68/2.21	50.21/1.82	30.39/4.96
	10	14.49%/4.77	72.04/3.58	64.23/3.64	73.12/4.84	50.10/4.28	29.10/11.67
	15	25.43%/11.05	71.89/7.02	64.29/8.06	77.11/11.53	49.59/12.49	30.50/17.60
	20	35.94%/15.77	73.63/22.75	66.36/11.86	86.19/29.44	51.30/17.03	30.57/21.58
	25	51.86%/20.75	58.89/97.75	50.42/129.44	95.55/73.27	88.45/176.15	33.40/22.94
Proposed ()	0.5	0.26%/0.15	72.00/0.05	64.01/0.06	70.01/0.07	50.00/0.06	29.99/0.17
	5	2.96%/1.31	72.09/0.66	64.18/0.58	69.56/0.83	50.77/0.75	29.95/2.24
	10	6.63%/1.97	72.18/1.37	64.21/1.02	69.37/1.54	52.24/1.45	28.29/4.34
	15	10.77%/3.00	72.27/1.512	63.95/1.65	70.72/1.69	54.85/1.83	29.03/4.52
	20	16.82%/3.79	72.31/1.94	64.35/1.98	72.26/2.00	58.00/2.33	30.27/5.89
	25	23.89%/3.97	72.32/2.76	64.33/2.48	75.06/2.26	61.31/2.52	30.39/8.10
Proposed ()	0.5	0.39%/0.25	72.01/0.09	64.01/0.09	70.00/0.13	50.00/0.12	30.02/0.28
	5	2.34%/0.95	72.05/0.55	64.09/0.50	69.81/0.67	49.89/0.65	30.05/1.79
	10	4.84%/1.77	72.14/1.19	64.15/1.06	69.94/1.43	49.65/1.25	28.74/3.72
	15	7.78%/2.59	72.27/1.59	63.98/1.96	71.15/2.62	49.62/2.21	28.93/5.65
	20	11.75%/3.80	72.32/2.45	64.47/2.28	72.94/4.35	49.95/3.68	30.47/9.43
	25	17.87%/6.39	72.63/3.61	64.61/3.27	78.39/7.08	48.95/4.53	30.40/14.06