On the local properties of digital curves

Thanh Phuong Nguyen (1) , Isabelle Debled-Rennesson (1)

1 ADAGIO - Applying Discrete Algorithms to Genomics and Imagery

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.

Mots clés: torsion; curvature

Domaines: Géométrie algorithmique [cs.CG]

Thanh Phuong Nguyen, Isabelle Debled-Rennesson. On the local properties of digital curves. International Journal of Shape Modeling, 2008, pp.105-125. ⟨10.1142/S0218654308001105⟩. ⟨hal-00437304⟩