  Despite strong stability properties, the persistent homology of filtrations
classically used in Topological Data Analysis, such as, e.g. the Cech or
Vietoris-Rips filtrations, are very sensitive to the presence of outliers in
the data from which they are computed. In this paper, we introduce and study a
new family of filtrations, the DTM-filtrations, built on top of point clouds in
the Euclidean space which are more robust to noise and outliers. The approach
adopted in this work relies on the notion of distance-to-measure functions, and
extends some previous work on the approximation of such functions.
