  We investigate solutions to the minimal surface problem with Dirichlet
boundary conditions in the roto-translation group equipped with a subRiemannian
metric. By work of G. Citti and A. Sarti, such solutions are amodal completions
of occluded visual data when using a model of the first layer of the visual
cortex. Using a characterization of smooth minimal surfaces as ruled surfaces,
we give a method to compute a minimal spanning surface given fixed boundary
data presuming such a surface exists. Moreover, we describe a number of
obstructions to existence and uniqueness but also show that under suitable
conditions, smooth minimal spanning surfaces with good properties exist. Not
only does this provide an explicit realization of the disocclusion process for
the neurobiological model, but it also has application to contructing
disocclusion algorithms in digital image processing.
