Journal of Optimization

Research Article

PRO: A Novel Approach to Precision and Reliability Optimization Based Dominant Point Detection

Table 3

Performance of various methods for all the datasets for Experiment 3.

(a) Maximum precision measure per line segment (MPLS)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.19	0.19	0.20	0.20	0.20	0.20	0.20	0.20	0.20	0.20	0.20
PRO0.6	0.59	0.59	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60	0.60
PRO1.0	0.97	0.97	0.99	1.00	0.99	0.99	1.00	1.00	1.00	1.00	0.99

RDP1	0.77	0.75	0.84	0.90	0.83	0.82	0.87	0.87	0.87	0.87	0.84
RDP2	1.32	1.33	1.44	1.54	1.43	1.43	1.51	1.51	1.51	1.50	1.45
RDP3	1.89	1.95	2.06	2.19	2.06	2.08	2.14	2.14	2.15	2.13	2.08

Masood [14]	1.25	1.16	1.63	1.78	1.47	1.51	1.72	1.71	1.73	1.72	1.57
Carmona-Poyatoet al. [16, 19]	1.19	2.44	1.58	2.07	1.90	2.35	2.17	2.18	2.15	2.19	2.02

(b) Maximum reliability measure per line segment (MRLS)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15	0.15
PRO0.6	0.51	0.51	0.56	0.58	0.55	0.55	0.57	0.57	0.57	0.57	0.55
PRO1.0	0.90	0.89	0.96	0.99	0.96	0.96	0.98	0.98	0.98	0.98	0.96

RDP1	0.72	0.69	0.82	0.88	0.79	0.78	0.85	0.85	0.85	0.84	0.81
RDP2	1.49	1.40	1.74	1.98	1.68	1.66	1.86	1.84	1.86	1.83	1.73
RDP3	2.53	2.32	3.11	4.02	3.08	3.06	3.53	3.52	3.52	3.51	3.22

Masood [14]	1.23	1.10	1.73	1.93	1.51	1.52	1.79	1.79	1.80	1.80	1.62
Carmona-Poyatoet al. [16, 19]	1.12	2.16	1.47	1.99	1.74	2.13	2.03	2.02	2.00	2.05	1.87

(c) Maximum precision measure per digital curve (MPDC)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.01	0.01	0.00	0.00	0.01	0.01	0.01	0.01	0.01	0.01	0.01
PRO0.6	0.30	0.28	0.11	0.31	0.28	0.28	0.28	0.28	0.27	0.27	0.27
PRO1.0	0.44	0.43	0.21	0.49	0.43	0.44	0.43	0.42	0.41	0.42	0.41

RDP1	0.29	0.28	0.11	0.32	0.28	0.28	0.28	0.27	0.27	0.26	0.26
RDP2	0.51	0.53	0.26	0.54	0.52	0.48	0.50	0.48	0.48	0.49	0.48
RDP3	0.73	0.78	0.32	0.69	0.63	0.67	0.64	0.63	0.63	0.61	0.63

Masood [14]	0.89	0.83	1.17	1.34	1.11	1.13	1.30	1.29	1.29	1.29	1.16
Carmona-Poyatoet al. [16, 19]	0.87	1.18	1.19	1.49	1.27	1.41	1.49	1.48	1.48	1.49	1.34

(d) Maximum reliability measure per digital curve (MRDC)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.01	0.01	0.00	0.01	0.01	0.01	0.01	0.01	0.01	0.01	0.01
PRO0.6	0.26	0.23	0.09	0.27	0.23	0.23	0.24	0.23	0.23	0.23	0.22
PRO1.0	0.37	0.37	0.17	0.41	0.37	0.36	0.36	0.35	0.35	0.35	0.34

RDP1	0.25	0.23	0.09	0.27	0.24	0.24	0.24	0.23	0.23	0.23	0.23
RDP2	0.44	0.46	0.22	0.47	0.46	0.40	0.44	0.42	0.42	0.43	0.42
RDP3	0.69	0.71	0.31	0.63	0.59	0.61	0.59	0.58	0.60	0.56	0.59

Masood [14]	0.86	0.76	1.26	1.42	1.12	1.12	1.32	1.33	1.32	1.32	1.18
Carmona-Poyatoet al. [16, 19]	0.84	1.23	1.13	1.58	1.23	1.44	1.50	1.52	1.50	1.53	1.35

(e) Average dimensionality reduction (ADR)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.40	0.39	0.47	0.45	0.48	0.47	0.38	0.40	0.38	0.39	0.42
PRO0.6	0.16	0.13	0.21	0.20	0.18	0.17	0.11	0.11	0.11	0.11	0.15
PRO1.0	0.13	0.10	0.17	0.16	0.14	0.13	0.09	0.09	0.08	0.09	0.12

RDP1	0.16	0.14	0.21	0.20	0.19	0.17	0.12	0.12	0.12	0.12	0.16
RDP2	0.12	0.10	0.16	0.15	0.14	0.13	0.08	0.08	0.08	0.08	0.11
RDP3	0.10	0.08	0.13	0.12	0.11	0.10	0.07	0.07	0.07	0.07	0.09

Masood [14]	0.16	0.13	0.19	0.19	0.18	0.16	0.17	0.17	0.17	0.18	0.17
Carmona-Poyatoet al. [16, 19]	0.22	0.13	0.24	0.24	0.21	0.19	0.21	0.21	0.21	0.21	0.21

(f) Maximum deviation ()


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.35	0.38	0.44	0.74	0.43	0.47	0.59	0.58	0.58	0.56	0.51
PRO0.6	1.33	1.33	1.46	1.69	1.49	1.50	1.64	1.63	1.64	1.63	1.53
PRO1.0	2.06	2.10	2.31	2.65	2.32	2.34	2.53	2.54	2.55	2.54	2.39

RDP1	1.00	0.99	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00	1.00
RDP2	1.97	1.96	2.00	2.00	2.00	1.99	2.00	2.00	2.00	2.00	1.99
RDP3	2.90	2.92	2.99	3.00	2.99	2.99	3.00	3.00	2.99	3.00	2.98

Masood [14]	2.22	2.05	0.94	2.32	2.62	2.75	3.08	3.06	3.11	3.08	2.52
Carmona-Poyatoet al. [16, 19]	2.05	3.91	2.63	3.49	3.17	3.83	3.59	3.63	3.57	3.63	3.35

(g) Integral square error (ISE)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	0.57	2.02	0.91	1.77	1.33	1.63	1.50	1.53	1.62	1.52	1.44
PRO0.6	26.81	104.08	33.95	79.63	58.44	69.66	64.36	64.15	66.35	61.50	62.89
PRO1.0	59.15	223.97	72.15	180.79	128.52	155.97	146.07	145.18	146.00	139.92	139.77

RDP1	27.03	95.15	32.90	69.67	53.39	62.14	57.64	59.48	60.48	54.44	57.23
RDP2	72.44	301.13	96.81	212.56	161.30	192.01	178.20	183.98	181.87	166.89	174.72
RDP3	154.28	739.04	200.78	480.41	356.05	470.48	398.36	406.30	442.71	387.20	403.56

Masood [14]	39.77	64.52	72.68	81.58	54.97	64.17	83.32	82.04	86.37	77.45	70.69
Carmona-Poyatoet al. [16, 19]	71.73	5171.01	149.44	754.50	417.71	1690.91	639.90	617.49	600.87	728.07	1084.16

(h) Figure of merit (FOM)


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	∞	∞	3.65	1.94	2.50	2.18	2.12	2.13	2.03	2.14	2.33 (excluding ∞)
PRO0.6	0.32	0.24	0.20	0.09	0.14	0.14	0.12	0.12	0.12	0.13	0.16
PRO1.0	0.19	0.13	0.11	0.05	0.08	0.07	0.07	0.07	0.07	0.07	0.09

RDP1	0.32	0.24	0.20	0.09	0.16	0.15	0.13	0.13	0.13	0.14	0.17
RDP2	0.17	0.10	0.09	0.04	0.07	0.06	0.06	0.06	0.06	0.06	0.08
RDP3	0.09	0.05	0.05	0.02	0.04	0.03	0.03	0.03	0.03	0.03	0.04

Masood [14]	0.28	0.24	0.13	0.10	0.15	0.15	0.11	0.11	0.11	0.11	0.15
Carmona-Poyatoet al. [16, 19]	0.15	0.07	0.05	0.02	0.03	0.02	0.02	0.02	0.02	0.02	0.04

(i) Average time taken per image


	Afreight	Google	Berkley	Cars_INRIA	Caltech 101	Caltech 256	PASCAL 2007	PASCAL 2008	PASCAL 2009	PASCAL 2010	Mean

PRO0.2	1.75	7.94	2.89	4.29	7.59	15.38	15.67	15.62	16.35	15.84	10.33
PRO0.6	0.35	0.79	0.61	0.83	1.56	2.66	3.16	3.14	3.29	3.21	1.96
PRO1.0	0.23	0.55	0.50	0.62	1.01	1.74	2.05	2.04	2.13	2.08	1.29

RDP1	0.38	0.89	2.71	1.13	1.72	2.93	3.45	3.44	3.59	3.51	2.37
RDP2	0.20	0.50	0.89	0.57	0.91	1.56	1.84	1.83	1.91	1.86	1.21
RDP3	0.16	0.40	0.60	0.37	0.66	0.94	1.36	1.39	1.45	1.44	0.88

Masood [14]	1.97	1065.14	3.03	21.38	26.69	113.75	27.24	25.88	28.93	25.64	133.96
Carmona-Poyatoet al. [16, 19]	0.31	6.49	0.50	2.06	1.48	2.75	2.92	2.89	3.01	2.70	2.51