Benchmark Refactored `pixel_to_real_world`

[Kanisorn-S]

Benchmark accuracy of pixel_to_real_world in branch feat/update-real-camera-info

[Methasit-Pun]

Calibration Results

Image Point (u, v)	Predicted Position (x, y) [m]	Ground Truth (x, y) [m]	Displacement Error [cm]
(423, 286)	(0.109, 0.512)	(0.111, 0.495)	1.71
(549, 393)	(0.222, 0.413)	(0.221, 0.410)	0.32
(556, 182)	(0.230, 0.615)	(0.221, 0.622)	1.14
(427, 62)	(0.107, 0.732)	(0.105, 0.730)	0.28
(190, 213)	(-0.127, 0.580)	(-0.135, 0.590)	1.28
(62, 97)	(-0.236, 0.691)	(-0.240, 0.690)	0.41
(53, 451)	(-0.241, 0.365)	(-0.255, 0.356)	1.66
(181, 334)	(-0.137, 0.465)	(-0.156, 0.455)	2.15
(350, 480)	(0.033, 0.322)	(0.025, 0.321)	0.81
(406, 283)	(0.091, 0.516)	(0.080, 0.515)	1.10

Total Distance RMSE: 1.244 cm

X-Axis RMSE: 0.955 cm

Y-Axis RMSE: 0.797 cm

[Methasit-Pun]

12 Mar 2026
20 points for Intrinsic z = 0.55
Cam_coordinate = [-0.0386, 0.5303, 0.5238]

Image Point (u, v)	Predicted Position (x, y) [m]	Ground Truth (x, y) [m]	Displacement Error [cm]
(357,107)	(-0.006, 0.65)	(-0.04, 0.67)	3.94
(231,246)	(-0.117, 0.538)	(-0.14, 0.57)	3.94
(598,173)	(0.186, 0.596)	(0.16, 0.606)	2.79
(455,305)	(0.079, 0.487)	(0.065, 0.506)	2.36
(431,147)	(0.058, 0.624)	(0.038, 0.611)	2.39
(301,285)	(-0.055, 0.504)	(-0.056, 0.511)	0.71
(298,138)	(-0.057, 0.632)	(-0.084, 0.63)	2.71
(169,275)	(-0.169, 0.513)	(-0.176, 0.525)	1.39
(286,318)	(-0.064, 0.474)	(-0.096, 0.472)	3.21
(158,460)	(-0.174, 0.358)	(-0.186, 0.37)	1.70
(170,204)	(-0.168, 0.571)	(-0.195, 0.575)	2.73
(36,334)	(-0.269, 0.466)	(-0.295, 0.48)	2.95
(569,209)	(0.167, 0.568)	(0.153, 0.57)	1.41
(428,348)	(0.056, 0.449)	(0.059, 0.47)	2.12
(589,92)	(0.175, 0.659)	(0.161, 0.662)	1.43
(458,233)	(0.081, 0.549)	(0.068, 0.562)	1.84
(454,188)	(0.075, 0.5885)	(0.064, 0.585)	1.15
(322,324)	(-0.036, 0.469)	(-0.04, 0.485)	1.65
(320,196)	(-0.037, 0.583)	(-0.025, 0.583)	1.20
(232,332)	(-0.115, 0.463)	(-0.125, 0.48)	1.97

Total Distance RMSE: 2.35 cm

X-Axis RMSE: 1.91 cm
Y-Axis RMSE: 1.38 cm

[Methasit-Pun]

12 Mar
20 points for Intrinsic + Empirical z = 0.55 m
Cam_coordinate = [-0.0386, 0.5303, 0.5238]

Image Point (u, v)	Predicted Position (x, y) [m]	Ground Truth (x, y) [m]	Displacement Error [cm]
(357,107)	(-0.033, 0.657)	(-0.04, 0.67)	1.48
(231,246)	(-0.131, 0.547)	(-0.14, 0.57)	2.47
(598,173)	(0.179, 0.602)	(0.16, 0.606)	1.94
(455,305)	(0.066, 0.497)	(0.065, 0.506)	0.91
(431,147)	(0.034, 0.624)	(0.038, 0.611)	1.36
(301,285)	(-0.067, 0.515)	(-0.056, 0.511)	1.17
(298,138)	(-0.0813, 0.633)	(-0.084, 0.63)	0.40
(169,275)	(-0.181, 0.524)	(-0.176, 0.525)	0.51
(286,318)	(-0.078, 0.489)	(-0.096, 0.472)	2.48
(158,460)	(-0.177, 0.376)	(-0.186, 0.37)	1.08
(170,204)	(-0.186, 0.581)	(-0.195, 0.575)	1.08
(36,334)	(-0.291, 0.478)	(-0.295, 0.48)	0.45
(569,209)	(0.156, 0.573)	(0.153, 0.57)	0.42
(428,348)	(0.046, 0.464)	(0.059, 0.47)	1.43
(589,92)	(0.165, 0.667)	(0.161, 0.662)	0.64
(458,233)	(0.063, 0.555)	(0.068, 0.562)	0.86
(454,188)	(0.056, 0.591)	(0.064, 0.585)	1.00
(322,324)	(-0.046, 0.483)	(-0.04, 0.485)	0.63
(320,196)	(-0.05, 0.586)	(-0.025, 0.583)	2.52
(232,332)	(-0.123, 0.478)	(-0.125, 0.48)	0.28

RMSE X: 0.0103 m (1.03 cm)

RMSE Y: 0.0087 m (0.87 cm)

Total RMSE: 0.0135 m (1.35 cm)

[Methasit-Pun]

Intritic High
z = 0.67m
Cam_coordinate = [-0.0361, 0.5303, 0.6458]

Image Point (u, v)	Predicted Position (x, y) [m]	Ground Truth (x, y) [m]	Displacement Error [cm]
(276,185)	(0.075, 0.595)	(0.087, 0.606)	1.63
(169,296)	(-0.197, 0.486)	(-0.191, 0.505)	1.99
(571,67)	(0.2115, 0.715)	(0.215, 0.717)	0.40
(459,184)	(0.113, 0.606)	(0.115, 0.611)	0.54
(413,197)	(0.065, 0.593)	(0.058, 0.588)	0.86
(307,308)	(-0.0496, 0.472)	(-0.041, 0.484)	1.48
(321,113)	(-0.034, 0.682)	(-0.034, 0.678)	0.40
(215,228)	(-0.149, 0.56)	(-0.135, 0.57)	1.72
(549,134)	(0.1975, 0.654)	(0.195, 0.646)	0.84
(434,247)	(0.088, 0.539)	(0.095, 0.546)	0.99
(282,312)	(-0.078, 0.467)	(-0.085, 0.468)	0.71
(177,426)	(-0.185, 0.35)	(-0.183, 0.363)	1.32
(514,311)	(0.17, 0.471)	(0.168, 0.456)	1.51
(407,427)	(0.057, 0.34)	(0.07, 0.35)	1.64
(439,178)	(0.0928, 0.613)	(0.081, 0.603)	1.55
(331,290)	(-0.023, 0.491)	(-0.022, 0.502)	1.10
(513,206)	(0.167, 0.582)	(0.157, 0.571)	1.49
(402,321)	(0.055, 0.458)	(0.058, 0.472)	1.43
(345,100)	(-0.0087, 0.695)	(-0.0125, 0.696)	0.39
(240,214)	(-0.1222, 0.575)	(-0.114, 0.59)	1.71

RMSE X: 0.0075 m (0.75 cm)

RMSE Y: 0.0104 m (1.04 cm)

Total RMSE: 0.0128 m (1.28 cm)

[Methasit-Pun]

Int + Emp
z = 0.67m
Cam_coordinate = [-0.0361, 0.5303, 0.6458]

Image Point (u, v)	Predicted Position (x, y) [m]	Ground Truth (x, y) [m]	Displacement Error [cm]
(276,185)	(0.06, 0.611)	(0.087, 0.606)	2.75
(169,296)	(-0.167, 0.502)	(-0.191, 0.505)	2.42
(571,67)	(0.225, 0.716)	(0.215, 0.717)	1.00
(459,184)	(0.113, 0.601)	(0.115, 0.611)	1.02
(413,197)	(0.068, 0.59)	(0.058, 0.588)	1.02
(307,308)	(-0.038, 0.481)	(-0.041, 0.484)	0.42
(321,113)	(-0.014, 0.684)	(-0.034, 0.678)	2.09
(215,228)	(-0.121, 0.57)	(-0.135, 0.57)	1.40
(549,134)	(0.201, 0.647)	(0.195, 0.646)	0.61
(434,247)	(0.086, 0.537)	(0.095, 0.546)	1.27
(282,312)	(-0.0614, 0.478)	(-0.085, 0.468)	2.56
(177,426)	(-0.167, 0.366)	(-0.183, 0.363)	1.63
(514,311)	(0.158, 0.465)	(0.168, 0.456)	1.35
(407,427)	(0.05, 0.35)	(0.07, 0.35)	2.00
(439,178)	(0.094, 0.608)	(0.081, 0.603)	1.39
(331,290)	(-0.013, 0.498)	(-0.022, 0.502)	0.98
(513,206)	(0.163, 0.575)	(0.157, 0.571)	0.72
(402,321)	(0.052, 0.462)	(0.058, 0.472)	1.17
(345,100)	(-0.009, 0.696)	(-0.0125, 0.696)	0.35
(240,214)	(-0.096, 0.583)	(-0.114, 0.59)	1.93

RMSE X: 0.0145 m (1.45 cm)

RMSE Y: 0.0058 m (0.58 cm)

Total RMSE: 0.0156 m (1.56 cm)

[Methasit-Pun]

Intrinsic Equation (Pinhole Camera)

$$X_c = \frac{(u - c_x) \cdot Z_c}{f_x}$$$$Y_c = \frac{(v - c_y) \cdot Z_c}{f_y}$$

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Empirical Calibration

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The test compares pure intrinsic parameters versus intrinsic + empirical calibration models at two different Z-axis standoffs to isolate systematic vs. quantization errors.

Camera Height (H)	Intrinsic Only (RMSE)	Intrinsic + Empirical (RMSE)	Observation
0.67 m	1.28 cm	1.56 cm	Pure intrinsic performs best; empirical model overfits/adds noise.
0.55 m	2.35 cm	1.35 cm	Empirical correction successfully mitigates systematic distortion.

The error increase at 0.55 m using only intrinsics confirms that systematic error