Endstopped operators based on iterated nonlinear center-surround inhibition

In this paper we analyze the properties of a repeated isotropic center-sunound inhibition which includes simple nonlinearities like half-wave rectification and saturation. Our simulation results show that such operations, here implemented as iterated nonlinear differences and ratios of Gaussians (INDOG and INROG), lead to endstopping. The benefits of the approach are twofold. Firstly, the INDOG can be used to design simple endstopped operators, e.g., corner detectors. Secondly, the results can explain how endstopping might arise in a neural network with purely isotropic characteristics. The iteration can be implemented as cascades by feeding the output of one NDOG to a next stage of NDOG. Alternatively, the INDOG mechanism can be activated in a feedback loop. In the latter case, the resulting spatio-temporal response properties are not separable and the response becomes spatially endstopped if the input is transient. Finally, we show that ON- and OFF-type INDOG outputs can be integrated spatially to result in quasi-topological image features like open versus closed and the number of components.