Roland Vollgraf, Michael Scholz, Ian Meinertzhagen, Klaus Obermayer
Nonlinear (cid:12)ltering can solve very complex problems, but typically involve very time consuming calculations. Here we show that for (cid:12)lters that are constructed as a RBF network with Gaussian basis functions, a decomposition into linear (cid:12)lters exists, which can be computed e(cid:14)ciently in the frequency domain, yielding dramatic improvement in speed. We present an application of this idea to image processing. In electron micrograph images of photoreceptor terminals of the fruit (cid:13)y, Drosophila, synaptic vesicles containing neurotransmitter should be detected and labeled automatically. We use hand labels, provided by human experts, to learn a RBF (cid:12)lter using Support Vector Regression with Gaussian kernels. We will show that the resulting nonlinear (cid:12)lter solves the task to a degree of accuracy, which is close to what can be achieved by human experts. This allows the very time consuming task of data evaluation to be done e(cid:14)ciently.