A neural net for reconstruction of multiple curves with a visual grammar

A neural net has been derived for reconstructing a set of curves from ungrouped dot locations. The network performs Bayesian inference on a visual grammar, which serves as a probabilistic model of the image formation process, by means of a quadratic matching objective function. The steps involved in the derivation are: (1) formulate a stochastic grammar; (2) derive its probability distribution on images, along with the partition function which is a configuration space integral over both discrete and continuous variables; (3) change variables by exploiting the structure of the original grammar; (4) use mean field theory to derive an objective function whose optimization permits the approximation of averages under the distribution; and (5) introduce optimizing neural net dynamics, possibly after transforming the objective function to decrease the size of the network