The groundbreaking work of Hubel and Wiesel has been instrumental in shaping our understanding of V1, leading to modeling neural responses as cascades of linear and nonlinear processes in what has come to be known as the “standard model” of vision. Under this formulation, however, some dendritic properties cannot be represented in a practical manner, while extensive evidence indicates that dendritic processes are an indispensable element of key neural behaviours. As a result, current V1 models fail to explain neural responses in a number of scenarios. In this work, we propose an implicit model for V1 that considers nonlinear dendritic integration and backpropagation of action potentials from the soma to the dendrites. This is a parsimonious scheme that minimizes an energy, allows for a better conceptual understanding of neural processes, and explains several neurophysiological phenomena that have challenged classical approaches.