  We consider the family of non-local and non-convex functionals introduced by
H. Brezis and H.-M. Nguyen in a recent paper. These functionals Gamma-converge
to a multiple of the Sobolev norm or the total variation, depending on a
summability exponent, but the exact values of the constants are unknown in many
cases.
  We describe a new approach to the Gamma-convergence result that leads in some
special cases to the exact value of the constants, and to the existence of
smooth recovery families.
