@InProceedings{Zetzsche2013,
  author    = {C. Zetzsche and K. Gadzicki and T. Kluth},
  title     = {Statistical Invariants of Spatial Form: From Local AND to Numerosity},
  booktitle = {Proceedings of the Second Interdisciplinary Workshop The Shape of Things},
  year      = {2013},
  pages     = {163-172},
  month     = {apr},
  publisher = {CEUR-WS.org},
  abstract  = {Abstract Theories of the processing and representation of spatial form have to take into account recent results on the importance of holistic properties. Numerous experiments showed the importance of “set properties”, “ensemble representations” and “summary statistics”, ranging from the “gist of a scene ” to something like “numerosity”. These results are sometimes difficult to interpret, since we do not exactly know how and on which level they can be computed by the neural machinery of the cortex. According to the standard model of a local-to-global neural hierarchy with a gradual increase of scale and complexity, the ensemble properties have to be regarded as high-level features. But empirical results indicate that many of them are primary perceptual properties and may thus be attributed to earlier processing stages. Here we investigate the prerequisites and the neurobiological plausibility for the computation of ensemble properties. We show that the cortex can easily compute common statistical functions, like a probability distribution function or an autocorrelation function, and that it can also compute abstract invariants, like the number of items in a set. These computations can be performed on fairly early levels and require only two well-accepted properties of cortical neurons, linear summation of afferent inputs and variants of nonlinear cortical gain control.},
}