Standardization of three-dimensional pose of cylindrical implants from intraoral radiographs: a preliminary study

Cosola, Saverio; Toti, Paolo; Peñarrocha-Diago, Miguel; Covani, Ugo; Brevi, Bruno Carlo; Peñarrocha-Oltra, David

doi:10.1186/s12903-021-01448-9

BMC Oral Health

Table 1 Measured- (radiographic) and simulated-values (simulated) of the components of vector \(\overrightarrow{\mathrm{OA}}\) and vector \(\overrightarrow{\mathrm{OR}}\) with related values of rotational angles

From: Standardization of three-dimensional pose of cylindrical implants from intraoral radiographs: a preliminary study

Radiograph		Components (mm)				Angles (°)			Optimization metric
		\({\overrightarrow{OA}}_{Y}\)	\({\overrightarrow{OA}}_{Z}\)	\({\overrightarrow{OR}}_{Y}\)	\({\overrightarrow{OR}}_{Z}\)	φ	θ	ψ	Iterations		Residual		First-order optimality		Status of equation
		Mean	Mean	Mean	Mean	Mean	Mean	Mean	Min	Max	Min	Max	Min	Max	Status of equation
1	Radiographic	0.04	9.06	12.57	− 2.75	− 15.90	31.98	1.45	6	7	0.0548	0.4935	− 2.5⋅10⁻¹⁰	− 8.6⋅10⁻¹³	Inaccuracy
	Simulated	− 0.13	9.11	12.28	− 2.36	− 13.65	34.30	2.43	5	7	0.4865	0.5778	− 4.8⋅10⁻¹¹	− 1.4⋅10⁻¹²	Inaccuracy
2	Radiographic	− 0.26	9.30	12.86	1.92	20.48	30.48	1.68	4	5	2⋅10⁻⁰⁵	0.0008	− 9.0⋅10⁻¹²	− 1.4⋅10⁻¹³	Solved
	Simulated	− 0.21	8.82	12.80	2.56	26.73	30.68	1.08	5	5	0.0029	0.0214	− 4.7⋅10⁻¹¹	− 1.2⋅10⁻¹³	Inaccuracy
3	Radiographic	3.45	9.33	12.10	− 5.64	10.80	24.58	− 22.43	6	7	3⋅10⁻⁰⁵	0.0109	− 2.7⋅10⁻¹¹	− 1.0⋅10⁻¹⁶	Inaccuracy
	Simulated	3.52	9.21	12.40	− 5.21	16.05	21.23	− 22.45	6	7	0.0014	0.0082	− 1.1⋅10⁻¹¹	− 1.1⋅10⁻¹³	Solved
4	Radiographic	− 3.61	9.20	9.20	1.61	− 27.63	46.23	31.85	5	5	0.0005	0.0185	− 5.9⋅10⁻¹¹	− 1.4⋅10⁻¹²	Inaccuracy
	Simulated	− 3.73	9.54	9.47	2.21	− 24.05	45.00	30.98	5	6	0.0280	0.0880	− 5.1⋅10⁻¹¹	− 5.9⋅10⁻¹⁴	Inaccuracy
5	Radiographic	− 3.63	8.43	4.67	5.91	− 26.33	62.40	52.30	6	6	0.0050	0.2729	− 3.7⋅10⁻¹¹	− 1.4⋅10⁻¹³	Inaccuracy
	Simulated	− 3.77	8.40	4.55	6.67	− 24.80	62.23	53.80	6	6	0.0001	0.0049	− 7.2⋅10⁻¹⁴	− 9.2⋅10⁻¹⁷	Solved
6	Radiographic	4.58	9.20	9.33	− 5.54	24.40	37.15	− 33.88	7	7	0.0501	0.1126	− 5.1⋅10⁻¹¹	− 3.8⋅10⁻¹²	Inaccuracy
	Simulated	4.27	8.04	9.13	− 4.83	31.73	36.05	− 35.93	9	9	0.6050	0.7298	− 1.9⋅10⁻¹¹	− 6.1⋅10⁻¹²	Inaccuracy
7	Radiographic	− 2.01	6.28	10.66	− 5.10	− 57.45	39.33	19.85	6	7	1.0931	1.3395	− 2.7⋅10⁻¹⁰	− 5.6⋅10⁻¹²	Unsolved
	Simulated	− 2.57	6.57	11.08	− 5.28	− 58.50	38.43	20.78	5	5	0.1128	0.1750	− 2.0⋅10⁻¹⁰	− 5.9⋅10⁻¹¹	Inaccuracy
8	Radiographic	2.77	8.35	14.04	− 3.03	33.05	9.00	− 15.35	8	8	0.0296	0.1085	− 2.6⋅10⁻¹¹	− 1.5⋅10⁻¹³	Inaccuracy
	Simulated	2.51	7.76	13.76	− 2.69	38.60	8.73	− 15.35	7	7	0.0142	0.0627	− 1.6⋅10⁻¹⁰	− 9.5⋅10⁻¹³	Inaccuracy
9	Radiographic	− 1.95	9.40	13.62	1.52	− 6.18	22.93	12.88	5	10	0.1002	0.2357	− 9.5⋅10⁻¹¹	− 2.4⋅10⁻¹²	Inaccuracy
	Simulated	− 2.23	9.38	13.41	1.91	− 6.70	24.30	14.73	6	8	0.1079	0.1540	− 8.8⋅10⁻¹¹	− 3.7⋅10⁻¹²	Inaccuracy
10	Radiographic	4.63	7.30	13.03	− 7.06	− 32.88	4.45	− 26.50	9	10	0.0451	0.1590	− 1.5⋅10⁻⁰¹	− 2.3⋅10⁻¹³	Inaccuracy
	Simulated	4.59	7.37	13.78	− 6.85	− 32.90	4.95	− 24.58	9	12	0.7022	0.9830	− 7.8⋅10⁻¹¹	− 4.7⋅10⁻¹²	Inaccuracy
11	Radiographic	− 5.05	− 8.36	− 9.45	3.96	9.88	− 10.38	148.23	15	17	0.1892	0.2592	− 1.2⋅10⁻¹¹	− 7.8⋅10⁻¹²	Inaccuracy
	Simulated	− 5.60	− 8.53	− 9.98	4.00	0.00	0.00	147.13	16	42	0.7688	0.8621	− 0.2570	1.2⋅10⁻⁰⁸	Inaccuracy
12	Radiographic	− 1.87	− 8.66	− 10.43	1.80	26.53	− 14.15	166.73	12	14	1.0170	1.1464	− 2.9⋅10⁻¹¹	− 5.1⋅10⁻¹²	Unsolved
	Simulated	− 2.17	− 8.67	− 9.86	1.22	24.85	− 12.13	166.78	8	9	0.0224	0.0686	− 4.6⋅10⁻¹²	− 7.5⋅10⁻¹³	Inaccuracy
13	Radiographic	− 0.16	− 9.93	− 8.66	− 0.96	− 13.13	27.08	180.55	9	10	0.0213	0.0963	− 4.1⋅10⁻¹¹	− 4.2⋅10⁻¹³	Inaccuracy
	Simulated	0.13	− 9.62	− 8.66	− 1.05	− 12.00	26.63	179.58	9	10	0.0252	0.0549	− 1.9⋅10⁻¹¹	− 2.5⋅10⁻¹²	Inaccuracy
14	Radiographic	0.51	− 8.64	− 6.16	1.81	− 34.68	49.80	184.43	7	7	0.0002	0.0098	− 1.1⋅10⁻¹²	− 3.9⋅10⁻¹⁵	Solved
	Simulated	0.39	− 8.53	− 6.47	1.87	− 34.05	47.53	183.20	6	7	8⋅10⁻⁰⁶	0.0163	− 6.5⋅10⁻¹¹	− 4.1⋅10⁻¹⁴	Inaccuracy
15	Radiographic	− 3.31	− 9.67	− 8.69	0.14	17.08	27.63	159.08	8	9	0.0296	0.1491	− 4.6⋅10⁻¹¹	− 9.4⋅10⁻¹³	Inaccuracy
	Simulated	− 3.33	− 9.25	− 9.26	0.35	19.33	19.20	159.55	6	8	4⋅10⁻⁰⁵	0.0222	− 1.8⋅10⁻¹¹	− 2.9⋅10⁻¹²	Inaccuracy
16	Radiographic	− 3.74	− 9.16	− 7.08	3.11	1.40	41.20	150.30	8	9	0.1664	0.2373	− 9.7⋅10⁻¹¹	− 1.6⋅10⁻¹²	Inaccuracy
	Simulated	− 3.77	− 8.60	− 7.38	3.16	− 2.35	38.99	151.10	7	8	1⋅10⁻⁰⁶	0.0083	− 1.7⋅10⁻¹²	− 7.9⋅10⁻¹⁵	Solved
17	Radiographic	− 3.44	− 9.42	− 9.75	0.79	− 13.88	− 10.80	160.45	8	12	0.0374	0.0944	− 5.0⋅10⁻¹²	− 7.3⋅10⁻¹³	Inaccuracy
	Simulated	− 3.42	− 9.44	− 10.07	0.92	− 10.93	− 5.08	161.15	13	21	0.1083	0.1725	− 2.2⋅10⁻¹¹	− 2.2⋅10⁻¹²	Inaccuracy
18	Radiographic	1.44	− 9.85	− 10.23	− 1.59	18.78	− 10.00	184.40	16	18	1.4629	1.6826	− 8.4⋅10⁻¹²	− 7.4⋅10⁻¹³	Unsolved
	Simulated	0.96	− 9.44	− 9.87	− 2.12	20.25	− 5.60	184.30	12	14	0.1740	0.2635	− 2.9⋅10⁻¹¹	− 4.2⋅10⁻¹²	Inaccuracy
19	Radiographic	− 1.98	− 8.48	− 7.86	3.39	23.10	− 38.70	164.18	8	8	0.2027	0.2352	− 6.7⋅10⁻¹³	− 9.2⋅10⁻¹⁴	Inaccuracy
	Simulated	− 2.15	− 8.40	− 8.28	3.51	24.23	− 35.25	163.35	7	8	0.2834	0.3826	− 3.7⋅10⁻¹¹	− 2.4⋅10⁻¹²	Inaccuracy
20	Radiographic	2.77	− 9.16	− 9.04	− 1.84	30.15	− 18.55	193.43	10	12	0.7990	0.9605	− 9.6⋅10⁻¹¹	− 1.5⋅10⁻¹²	Inaccuracy
	Simulated	2.58	− 9.09	− 9.48	− 2.40	27.65	− 11.80	192.18	11	11	0.7052	0.8434	− 3.0⋅10⁻¹¹	− 3.4⋅10⁻¹²	Inaccuracy

Results of the fitting (status of the fitting) with the optimization metric, that is, the output of the variables those the machine by using “Levenberg–Marquardt algorithm” tried to minimize so that you end up with the best performing machine models: system of equations solved if residuals ≤ 10^–2; possible inaccuracy in solution if 10^–2 < residuals ≤ 1; system of equations unsolved if residuals > 1

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ISSN: 1472-6831

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