Nonlinear, local and highly parallel algorithms can perform several simple but important visual computations. Specific classes of algorithms can be considered in an abstract way. I study here the class of polynomial algorithms to exemplify some of the important issues for visual processing like linear vs. nonlinear and local vs. global. Polynomial algorithms are a natural extension of Perceptrons to time dependent grey level images.. Although they share most of the limitations of Perceptrons, they are powerful parallel computational devices. Several of their properties are characterized and especially (a) their equivalence with Perceptrons for geometrical figures and (b) the synthesis of non-linear algorithms (mappings) via associative learning. Finally, the paper considers how algorithms of this type could be implemented in nervous hardware, in terms of synaptic interactions strategically located in a dendritic tree.