Symmetric Radial Basis Function Networks and their application to video de-interlacing

Abstract

Video technology is one of the most advanced fields of modern electronics. The degree of interaction between different disciplines is simply extraordinary. In particular, the introduction of digital signal processing has revolutionised video technology. Sophisticated mathematical techniques are applied at several points in the video chain. One of the most common tasks in video processing is de-interlacing, i.e. the conversion from an interlaced format to a progressive format. De-interlacing can be considered as a form of interpolation, where the even lines of a frame in a video are estimated by interpolating the odd lines in the frame. De-interlacing is a task that is often required in real time, therefore the amount of computation required is a critical parameter. A straightforward way of achieving this task is by employing some form of linear interpolation. Linear techniques are fast, robust, and theoretically tractable. Unfortunately, the results are often unsatisfactory in terms of image quality. A more sophisticated approach is offered by the implementation of non-linear techniques. When dealing with non-linear methods, two main factors must be considered: the amount of computation required and the tendency to over-fit the data (generalisation). In this work two non-linear techniques are investigated, the Volterra series and the Radial Basis Function Networks (RBFN). Volterra series can be considered as an extension of the linear model to a polynomial series. RBFN is a functional series that creates arbitrary interpolation mappings due to its localisation properties. It is shown how both techniques produce results that are superior compared to linear techniques in terms of image quality. However great care must be taken and proper training procedures must be devised in order to maintain the computational load to an acceptable level and to avoid over-fitting. In this thesis a novel approach is devised to reduce the computational load in RBFN at the same time increasing the generalisation ability of the network by exploiting the symmetries arising in the input space when the sampling lattice is symmetric. Symmetrisation is initially developed for linear techniques, where an analytic derivation leads to a reduction in the number of operations required. Successively this technique is extended to RBFN by devising a mathematical approach that is both intuitive and rigorous. It is shown how symmetrisation leads to a reduction of the computational load required at the same time increasing the generalisation ability of the interpolation.

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