  We introduce a method for generating a continuous, mass-conserving and
high-order differentiable density field from a discrete point distribution such
as particles or halos from an N-body simulation or galaxies from a
spectroscopic survey. The method consists on generating an ensemble of point
realizations by perturbing the original point set following the geometric
constraints imposed by the Delaunay tessellation in the vicinity of each point
in the set. By computing the mean field of the ensemble we are able to
significantly reduce artifacts arising from the Delaunay tessellation in poorly
sampled regions while conserving the features in the point distribution. Our
implementation is based on the Delaunay Tessellation Field Estimation (DTFE)
method, however other tessellation techniques are possible. The method
presented here shares the same advantages of the DTFE method such as
self-adaptive scale, mass conservation and continuity, while being able to
reconstruct even the faintest structures of the point distribution usually
dominated by artifacts in Delaunay-based methods. Additionally, we also present
preliminary results of an application of this method to image denoising and
artifact removal, highlighting the broad applicability of the technique
introduced here.
