A varifold-type estimation for data sampled on a rectifiable set
We investigate the inference of varifold structures in a statistical framework: assuming that we have
access to i.i.d. samples in Rn obtained from an underlying d–dimensional shape S endowed with a possibly non
uniform density θ, we propose and analyse an estimator of the varifold structure associated to S. The shape S
is assumed to be piecewise C1,a in a sense that allows for a singular set whose small enlargements are of small
d–dimensional measure. The estimators are kernel–based both for infering the density and the tangent spaces and
the convergence result holds for the bounded Lipschitz distance between varifolds, in expectation and in a noiseless
model. The mean convergence rate involves the dimension d of S, its regularity through a ∈ (0, 1] and the regularity
of the density θ.