Rear view cameras are widely used in the automotive industry. They are used in modern car navigation systems to improve the driver’s perception of the situation behind the car. Ultra-wide-angle fisheye lenses are installed on the car for maximum coverage. But such images are not comfortable for human perception. Therefore, one of the main problems in using such cameras is fast algorithms for converting fisheye images into a set of images corresponding to wide-angle and normal virtual cameras, as well as constructing a “top view”. This work examines two image transformation algorithms, both of which provide independent transformations along Cartesian coordinate axes. The first method uses ray tracing through a lens with specified parameters to determine transformation coefficients, the second method provides an empirical selection of coefficients using visual determination of the boundaries of the required fragment interactively. The algorithms are implemented in two versions: the first one is for a regular computer (integrated into the CATIA CAD system) and the second one is built directly into the car rear view camera control processor. The option for a regular computer is used for preliminary elaboration of algorithms, as well as for complete debugging and testing of the rear view camera – both to verify the operation of geometric transformation algorithms and to validate the camera light sensitivity
1. Whitted, T. An improved illumination model for shaded display // Communication of ACM, 1980, Vol. 23, No. 6, pp. 343–349.
2. CATIA – Solution for Product Design and Experience // https://www.3ds.com/products-services/catia/ (accessed01.11.2023).
3. Jedlička, J., and Potučková, M. Correction of radial distortion in digital images // Proceedings Technical Computing Prague, 2007.
4. Pranali, D., Kutty, K., and Bangadkar, S. A generic non-linear method for fisheye correction // International Journal of Computer Applications, 2012, Vol. 51, #10, pp. 58–65.
5. Brauer-Burchardt, C. and Voss, K. A new algorithm to correct fish-eye-and strong wide-angle-lens-distortion from single images Proceedings 2001 International Conference on Image Processing (Cat. No. 01CH37205), Vol. 1. IEEE, pp. 225–228.
6. Birukov, E.D. Алгоритм коррекции изображения с широкоугольной камеры заднего вида автомобиля // Proceedings of Seminar on New Information Technologies, Keldysh Institute of Applied Math, Apr. 16, 2015, pp. 4–10.
7. Barladyan, B. Kh., Shapiro, L.Z., Valiev, I.V., Voloboy, A.G. Interactive camera distortion correction // Conference Proceedings of 22d International Conference on Computer Graphics and Vision GraphiCon‑2012, Lomonosov Moscow State University, October 01–05, pp. 12–16.
8. Feng, Mingchi, et al. Global calibration of multi-cameras based on refractive projection and ray tracing Sensors // Sensors, 2017, Vol. 17, Is. 11: 2494.
9. Ceyhan, Ufuk, et al. Measurements of aberrations of aspherical lenses using experimental ray tracing // Optical Measurement Systems for Industrial Inspection VII, Vol. 8082, SPIE, 2011, pp. 482–489.
10. Barladian, B., Birukov, E., Voloboy, A., Ershov, S., Shapiro, L. Simulation of rear camera for car navigation system // Keldysh Institute Preprints, 2016, Vol. 32, pp. 1–19, doi:10.20948/prepr-2016-32. (In Russian)
11. Valiev, I.V., Voloboy, A.G. Modelling Around View Monitor // Conference proceedings of 22d International Conference on Computer Graphics and Vision GraphiCon‑2010, Sankt Petersburg, Russia. Sep. 20–24, pp. 269–272. (In Russian)
12. Scaramuzza, D., Martinelli, A. and Siegwart, R. A flexible technique for accurate omnidirectional camera calibration and structure from motion // Fourth IEEE International Conference on Computer Vision Systems (ICVS’06), IEEE, 2006.
13. Guo, X. et al. Research on design, calibration and real-time image expansion technology of unmanned system variable-scale panoramic vision system // Sensors, 2021, Vol. 21, #14: 4708.
14. Hao, S., Wang C., Wang B. Night vision pedestrian detection using a forward-looking infrared camera / 2011 International Workshop on Multi-Platform/Multi-Sensor Remote Sensing and Mapping, 2011.
15. Ahire, A.S. Night vision system in BMW // International Review of Applied Engineering Research. – 2014, Vol. 4, # 1, pp. 1–10.

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• rear view camera
• ray tracing
• navigation
• geometrical transformations
• brightness control