Applications of Optical Transformations to Visual Navigation

Navigational systems performing real-time tasks involve many image related procedures, such as: acquisition, processing, and information extraction. Various components of these procedures consist of mathematical transformations that can be implemented optically. By using specially designed lenses these transformations can be provided at image acquisition time, and therefore, speed up execution time. This study addresses the optical implementation of the log-polar mapping and of different correlators based on Fourier transform and Mellin transform. In addition, the fractional versions of these correlators are defined and analyzed here. Correlators are well familiar for their role in object recognition. Here, their possible applications to motion related topics were investigated. We have shown that when the motion is assumed to consist of rotation and scaling, the Mellin based correlator can be used to compute time-to-impact. In addition, the Fractional Fourier based correlator can be used to control ranges of translation, while the Fractional Mellin based correlator, introduced here, can be used to control ranges of rotation and scaling. The log-polar mapping is typically incorporated into navigational systems when a large field of view is of interest, especially where real-time motion estimation related tasks are needed. In contrast to its optical version, if a log-polar mapping is to be computed from planar images, the resulted image is of sparse density, and interpolation is usually needed. Here, it has been verified that this transformation can be implemented optically, and the resulted log-polar image has indeed proven to be of high density. Based on the experimental results, the optical implementation of all three aspects of navigational tasks discussed here (i.e. computation of time-to-impact, control of movement within specific range, and log-polar mapping) can indeed play a significant role in speeding up execution time.