  In this paper we study the problem of the convergence in variation for the
generalized sampling series based upon averaged-type kernels in the
multidimensional setting. As a crucial tool, we introduce a family of operators
of sampling-Kantorovich type for which we prove convergence in L^p on a
subspace of L^p(R^N): therefore we obtain the convergence in variation for the
multidimensional generalized sampling series by means of a relation between the
partial derivatives of such operators acting on an absolutely continuous
function f and the sampling-Kantorovich type operators acting on the partial
derivatives of f. Applications to digital image processing are also furnished.
