An investigation of the non-linear properties of correlation filter synthesis and neural network design

Since the introduction of SDF correlation filters vast amounts of work has been done on improving the filters¿ synthesis. Several different variations of classic SDF filter have been suggested. The objective is to create filters invariant to distortions from rotation, scaling, translation and inclusion of noise. Recently, the use of wavelets as a pre-processing stage of the images has been explored. Additionally, the application of non-linear operations as part of the pre-processing stages seems promising. This paper investigates those non-linear operations in filters like NLDOG SDF filter. We also discuss the newly introduced SDF-MACH filter in this paper. Advances in artificial neural network architectures emerged their wide availability in pattern recognition tasks. We have created a new non-linear neural model able to input analogue patterns. The paper focuses in exploring in detail how any non-linear operations are utilised in our model comparatively to correlation filters. We mathematically prove the non-linear superposition characteristics of the neural network. Finally simulation results are given to demonstrate both, the inside synthesis of SDF type correlation filters and the neural network design under the scope of those non-linear operations. We do not intend to provide an analytical comparison of correlation filters and neural networks rather to focus on the understanding of their underlying working functions.