Binomial Convolutions and Derivatives Estimation from Noisy Discretizations

Rémy Malgouyres, Florent Brunet, Sébastien Fourey

Discrete Geometry for Computer Imagery (DGCI), Lyon, April 2008

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.

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