Automatic Linearization and Calibration of Distortions in Optical Systems

Calibration of optical systems is one of the major issues in the computer vision community. Many applications in computer vision use low or medium quality cameras.

Abstract
Calibration of optical systems is one of the major issues in the computer vision community. Many applications in computer vision use low or medium quality cameras, which usually introduce some amount of geometric distortions. This work deals with the calibration of a certain optical system to be used in future applications. In order to improve the system’s performance, a few distortion models have been thoroughly examined and analyzed. Additional analysis in the optical domain has yielded an enhanced understanding regarding the cause of the distortion. Finally, an optical solution was obtained and implemented. The revised optical system has been tested and shown excellent results.

The problem
A certain optical system meant to be used as a building block in future applications has shown poor results in the sense that a noticeable distortion has been introduced by the system. An example to the distortion introduced by the system is shown in figure 1:
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The distortion was to be corrected either by an automatic correction algorithm or by a solution in the optical domain. The cause to the distortion was to be understood in order to provide any kind of a solution and analysis of the distortion was therefore to be performed. Correction of the distortion would enable the system to be used as a basic building block in various applications such as blind source separation and many others.

The solution
After thorough analysis of the distortion an optical solution was obtained, i.e. a revision of the optical system’s structure. An additional lens was used in order to converge the rays of light before hitting the slide, as shown in figure 2:
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A solution was obtained after realizing that the distortion might have been caused by an aberration of the focus lens. Since some types of distortions caused by lens aberrations are further enhanced when the rays of light are far from being parallel, it was suggested that addition of a lens after the source of light might improve the performance of the system. Addition of such a lens and rearrangement of the system’s structure has indeed provided an extreme improvement in the results, as shown in figure 3:
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Tools
Tools used in the project include Matlab, a video capturing device and a dedicated video workstation.

Conclusions
The problem was solved using an optical solution rather than an automatic correction of the distortion. This has improved the stability of the system and will enable a much more convenient array to be used in future applications. This optical solution is obviously preferred over automatic correction of the distortion using a computer since it does not require any kind of post processing and images can be captured directly and independently.

Acknowledgments
We would like to thank our project supervisor Eli Appelboim for his help and guidance throughout this work and wish to express our gratitude to the rest of VISL staff for their support and availability.