Benchmark `pixel_to_real_world` for Different Camera Height

[Kanisorn-S]

Benchmark pixel_to_real_world accuracy for different camera height

• Try adjusting the camera to be closer to the working surface and see if error decreases
• If the error decreases -> Use multi-resolution to solve
• If the error increases or remain constant -> Different issue. Cannot be solved using multi-resolution

[Methasit-Pun]

Change height from 67.11 cm (29 inch from ref) to 54.41cm (24 inch from ref)

(u, v) [px]	Current (x, y) [m]	Correct (x, y) [m]	Error X [m]	Error Y [m]	Distance Error [m]
(75, 299)	(-0.185, 0.511)	(-0.207, 0.495)	0.022	0.016	0.027
(263, 462)	(-0.041, 0.380)	(0.003, 0.394)	-0.044	-0.014	0.046
(426, 279)	(0.090, 0.550)	(0.068, 0.510)	0.022	0.040	0.046
(573, 440)	(0.189, 0.410)	(0.170, 0.405)	0.019	0.005	0.020
(81, 245)	(-0.180, 0.552)	(-0.194, 0.563)	0.014	-0.011	0.018
(266, 83)	(-0.039, 0.679)	(-0.081, 0.660)	0.042	0.019	0.046
(640, 65)	(0.225, 0.676)	(0.210, 0.680)	0.015	-0.004	0.016
(344, 311)	(0.020, 0.490)	(-0.010, 0.490)	0.030	0.000	0.030
(506, 389)	(0.149, 0.439)	(0.131, 0.520)	0.018	-0.081	0.083
(271, 287)	(-0.037, 0.518)	(-0.076, 0.520)	0.039	-0.002	0.039
RMSE			0.029	0.030	0.042

Formulas Used:

• Error X: $\text{Current } x - \text{Correct } x$

• Error Y: $\text{Current } y - \text{Correct } y$

• Distance Error: $\sqrt{(\text{Error X})^2 + (\text{Error Y})^2}$

• RMSE: $\sqrt{\frac{\sum (\text{Error})^2}{n}}$ (calculated independently for X, Y, and the combined distance).

[Methasit-Pun]

H_b = Height from base

Metric	H_b = 54.41cm	H_b = 67.11 cm	Difference
X-Axis RMSE	2.914 cm (0.029 m)	0.955 cm	-1.959 cm
Y-Axis RMSE	2.981 cm (0.030 m)	0.797 cm	-2.184 cm
Total Distance RMSE	4.170 cm (0.042 m)	1.244 cm	-2.926 cm

RMSE pixel_to_real error increase when reduce height (no calibration on height change)
Therefore, the root cause of your original error is systematic (calibration-based), not a multi-resolution (quantization) issue.

[Methasit-Pun]

@Kanisorn-S