Table 2 Results of comparison with a geometric-based and an algebraic-based algorithm.

From: Conic tangents based high precision extraction method of concentric circle centers and its application in camera parameters calibration

Images

Statistic

Geometric-based algorithm

Algebraic-based algorithm

Proposed

u-axis

v-axis

u-axis

v-axis

u-axis

v-axis

1

μ (pixels)

6.0989

1.2539

1.6429

1.2534

1.1051

1.1832

σ (pixels)

1.3851

0.8894

1.3102

0.4383

0.6090

0.4697

2

μ (pixels)

7.0789

0.8445

1.7555

1.1501

1.2557

1.1733

σ (pixels)

0.7615

0.5766

0.7635

0.7023

0.5278

0.6587

3

μ (pixels)

4.9383

2.1863

1.3734

0.8631

1.0590

0.7738

σ (pixels)

1.1855

1.1887

0.9512

0.7415

0.5249

0.7563

4

μ (pixels)

5.8004

2.8746

1.5443

0.5168

1.4424

0.4776

σ (pixels)

0.6357

0.6386

0.6425

0.3579

0.5823

0.3216

5

μ (pixels)

3.4344

0.8419

0.9682

1.1974

0.5872

1.1248

σ (pixels)

1.0239

0.7471

0.4610

0.8314

0.7362

0.7347

6

μ (pixels)

2.5118

2.5332

1.1287

1.2971

1.4023

1.1896

σ (pixels)

1.0418

1.0431

0.7022

0.8548

0.7423

0.7961

7

μ (pixels)

7.6339

0.8255

2.0807

0.8789

0.7046

0.8703

σ (pixels)

0.9254

0.5146

0.9294

0.6952

0.6463

0.6828

8

μ (pixels)

4.5988

2.4696

1.6673

0.7947

1.5519

0.9079

σ (pixels)

0.6437

0.6448

0.6443

0.6443

0.9314

0.6409

9

μ (pixels)

8.2009

0.3540

0.8205

0.8041

0.9520

0.8458

σ (pixels)

0.2638

0.2408

0.2624

0.2624

0.2048

0.2510

10

μ (pixels)

7.5028

0.3367

1.4126

0.4452

1.0792

0.5716

σ (pixels)

0.4152

0.2022

0.4140

0.4140

0.7361

0.4521

  1. The bold words are the minimums. Every two lines form a group. For the first line of each group, bold words indicate that the mean values of multiple results are close to the true value. For the second line of each group, bold words indicate that the multiple results are close.
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