On a more mechanistic level, some electrophysiological recordings of individual neurons in animal cortex appear consistent with a probabilistic weighing of sense data (Ma, Beck, Latham, & Pouget,
2006; Mazurek, Roitman, Ditterich, & Shadlen,
2003; Murray, Kersten, Olshausen, Schrater, & Woods,
2002). We might speculate that some cortical neurons could be tuned to encode feature probabilities. For instance, complex cells in primary visual cortex are excited by edges irrespective of polarity and precise location of those edges (Hubel & Wiesel,
1962) and are especially sensitive to phase alignment caused frequently by object boundaries in natural images (Felsen, Touryan, Han, & Dan,
2005). We might therefore wish to describe a rudimentary complex cell as encoding the probability that an edge passes through two points in its receptive field, irrespective of which side of the edge is brighter. In our formalism, this corresponds to an object membership function
_{edge} = {1∣2}. Assuming that objects have Gaussian distribution intensities and the image sensors have some additive Gaussian noise, the probability of an edge given the intensity difference Δ across space is
P(
_{edge}∣Δ) = [1 +
k exp(−
βΔ
^{2})]
^{−1}, where
k and
β are positive constants that depend on the spatial scale, overall image contrast, and sensor noise. This function resembles the contrast energy model of complex cells (Adelson & Bergen,
1985) with a saturating non-linearity. Thus, we might interpret complex cell activity as encoding the probability of a local edge in a world of objects. It will be interesting to explore such a model more thoroughly and to see if other neurons have properties that map nicely onto representations of still more complex features within the dead leaves model. Since synaptic connections are modified by neural correlations, and the occlusion model explains stimulus correlations, the model may also help generate predictions about cortical circuitry that has matured in the natural world.