Binomial Convolutions and Derivatives Estimation from Noisy Discretizations

Rémy Malgouyres (1) , Florent Brunet (1) , Sébastien Fourey (2)

1 LLAIC1 - Laboratoire de Logique, Algorithmique et Informatique
2 Equipe Image - Laboratoire GREYC - UMR6072

We present a new method to estimate derivatives of digitized functions. Even with noisy data, this approach is convergent and can be computed by using only the arithmetic operations. Moreover, higher order derivatives can also be estimated. To deal with parametrized curves, we introduce a new notion which solves the problem of correspondence between the parametrization of a continuous curve and the pixels numbering of a discrete object.

Mots clés: convolution; binomial coefficients; derivative estimation

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Rémy Malgouyres, Florent Brunet, Sébastien Fourey. Binomial Convolutions and Derivatives Estimation from Noisy Discretizations. Discrete Geometry for Computer Imagery, Apr 2008, Lyon, France. pp.370-379, ⟨10.1007/978-3-540-79126-3_33⟩. ⟨hal-00333776⟩