We propose a geometric approach to extract local properties of digital curves. This approach uses the notion of blurred segment \cite{DEB05} that extends the definition of segment of arithmetic discrete line\cite{REV91} to adapte to noisy curves. A curvature estimator \cite{ND07} for 2D curves in $O(n\log^2n)$ time is proposed relying on this flexible approach. The notion of 2D blurred segment is extended to 3D space. A decomposition of the curve into 3D blurred segments is deduced and allows new curvature and torsion estimators for 3D curves. All these estimators can naturally work with disconnected curves.