Road marking BRDF model applicable for a wide range of incident illumination conditions

Rik Marco Spieringhs; Rik Marco Spieringhs; Jan Audenaert; Kevin Smet; Ingrid Heynderickx; Peter Hanselaer

doi:10.1364/JOSAA.470968

Journal of the Optical Society of America A
Vol. 40,
Issue 3,
pp. 590-601
(2023)
•https://doi.org/10.1364/JOSAA.470968

Road marking BRDF model applicable for a wide range of incident illumination conditions

Rik Marco Spieringhs, Jan Audenaert, Kevin Smet, Ingrid Heynderickx, and Peter Hanselaer

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Rik Marco Spieringhs, Jan Audenaert, Kevin Smet, Ingrid Heynderickx, and Peter Hanselaer, "Road marking BRDF model applicable for a wide range of incident illumination conditions," J. Opt. Soc. Am. A 40, 590-601 (2023)

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Table of Contents Category
- Instrumentation, Measurement, and Metrology
Optics & Photonics Topics
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The topics in this list come from the Optics and Photonics Topics applied to this article.

About this Article
History
- Original Manuscript: July 19, 2022
- Revised Manuscript: December 20, 2022
- Manuscript Accepted: January 26, 2023
- Published: February 24, 2023

Abstract

To drive safely and comfortably, an adequate contrast between the road surface and road markings is needed. This contrast can be improved by using optimized road illumination designs and luminaires with dedicated luminous intensity distributions, taking advantage of the (retro)reflective characteristics of the road surface and road markings. Since little is known about road markings’ (retro)reflective characteristics for the incident and viewing angles relevant for street luminaires, bidirectional reflectance distribution function (BRDF)-values of some retroreflective materials are measured for a wide range of illumination and viewing angles using a luminance camera in a commercial near-field goniophotometer setup. The experimental data are fitted to a new and optimized “RetroPhong” model, which shows good agreement with the data [root mean squared error $({\rm{RMSE}}) \lt {0.13}$, normalized root mean squared error $({\rm{NRMSE}}) \lt {0.04}$, and the normalized cross correlation ratio $({\rm{NCC}}) \gt {0.8}$]. The RetroPhong model is benchmarked with other relevant (retro)reflective BRDF models, and the results suggest that the RetroPhong model is most suitable for the current set of samples and measurement conditions.

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Data availability

Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.

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Incident Angles
$φ_{i}$	$θ_{i}$
0	0, 10, 20, 30, 40, 50, 60, 70, 80, 85
23	70, 80, 85
45	70, 80, 85

Viewing Angles
$φ_{o}$	$θ_{o}$
25.7	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
51.4	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
77.1	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
102.9	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
128.6	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
154.3	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
180	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
205.7	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
231.4	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
257.1	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
282.9	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
308.6	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
334.3	3.3, 10.7, 21.3, 34.8, 50.8, 69.3
360	3.3, 10.7, 21.3, 34.8, 50.8, 69.3

RetroPhong
RM	RMSE	NRMSE	NCC	$k_{d}$	$n$	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$
1	0.102	0.0370	0.879	0.620	24.0	0.158	0.0415	0.00133	5.47
2	0.106	0.0201	0.861	0.594	24.0	0.0696	0.0733	6.58e-05	8.74
3	0.280	0.0216	0.814	0.701	68.0	0.184	1.53e-12	0.00570	3.40

RetroPhong
RM	RMSE	NRMSE	NCC	$k_{d}$	$n$	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$
2	0.121	0.0251	0.837	0.620	24.0	0.158	0.0415	0.00133	5.47
3	0.361	0.0247	0.757	0.620	24.0	0.158	0.0415	0.00133	5.47

RetroPhong
RM	RMSE	NRMSE	NCC	$k_{d}$	$n$	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$
1	0.102	0.0370	0.879	0.620	24.0	0.158	0.0415	0.00133	5.47
RetroPhong without specular component
RM	RMSE	NRMSE	NCC	$k_{d}$	$n$	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$
1	0.172	0.0308	0.614	0.620	24.0	0.158	0.0415	–	–

Oren–Nayar	$α_{m}$	$ρ$
Road marking 1	0.865	0.268
Road marking 2	0.705	0.275
Road marking 3	1.26	0.470
Beckmann-Retro	$k_{d}$	$α$	$R_{0}$
Road marking 1	0.796	8.20	0.995
Road marking 2	0.822	9.36	0.993
Road marking 3	0.996	1.61e3	1.00
Blinn-Retro	$k_{d}$	$α_{b}$	$α_{r}$
Road marking 1	0.919	2.77e3	7.91e3
Road marking 2	0.881	2.50e3	7.10e3
Road marking 3	0.993	6.72e3	1.65e4
ABC-Retro	$k_{d}$	$R_{0}$	$A_{b}$	$B_{b}$	$C_{b}$	$A_{r}$	$B_{r}$	$C_{r}$
Road marking 1	0.534	0.0472	1.82	13.5	1.51	1.02	0.0775	6.97
Road marking 2	0.0303	0.140	1.59	32.6	1.08	1.19	0.00779	0.0179
Road marking 3	0.747	0.00466	6.66	37.8	0.710	3.58	22.9	0.729
RetroPhong	$k_{d}$	$n$	$k_{1}$	$k_{2}$	$k_{3}$	$k_{4}$
Road marking 1	0.620	24.0	0.158	0.0415	0.00133	5.47
Road marking 2	0.594	24.0	0.0696	0.0733	6.58e−05	8.74
Road marking 3	0.701	68.0	0.184	1.53e−12	0.00570	3.40

Road Marking 1	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.102	0.0370	0.879	6
Oren–Nayar	0.203	0.0515	0.310	2
Beckmann-Retro	0.160	0.0676	0.615	3
Blinn-Retro	0.194	0.0871	0.285	3
ABC-Retro	0.116	0.0477	0.819	8
Road marking 2	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.106	0.0201	0.861	6
Oren–Nayar	0.203	0.0820	0.399	2
Beckmann-Retro	0.171	0.0475	0.582	3
Blinn-Retro	0.197	0.0547	0.316	3
ABC-Retro	0.125	0.0305	0.804	8
Road marking 3	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.280	0.0216	0.814	6
Oren–Nayar	0.415	0.0428	0.508	2
Beckmann-Retro	0.490	0.0396	0.581	3
Blinn-Retro	0.487	0.0393	0.219	3
ABC-Retro	0.224	0.0181	0.886	8

Road Marking 1	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.102	0.0370	0.879	6
Oren–Nayar	0.203	0.0515	0.310	2
Beckmann-Retro	0.160	0.0676	0.615	3
Blinn-Retro	0.194	0.0871	0.285	3
ABC-Retro	0.116	0.0477	0.819	8
Road marking 2	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.106	0.0201	0.861	6
Oren–Nayar	0.203	0.0820	0.399	2
Beckmann-Retro	0.171	0.0475	0.582	3
Blinn-Retro	0.197	0.0547	0.316	3
ABC-Retro	0.125	0.0305	0.804	8
Road marking 3	RMSE	NRMSE	NCC	Number of Coefficients
RetroPhong	0.280	0.0216	0.814	6
Oren–Nayar	0.415	0.0428	0.508	2
Beckmann-Retro	0.490	0.0396	0.581	3
Blinn-Retro	0.487	0.0393	0.219	3
ABC-Retro	0.224	0.0181	0.886	8

Abstract

Data availability

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Figures (9)

Tables (7)

Equations (20)

Journal of the Optical Society of America A