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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Taylor Optimal Kernel for Derivative Etimation
verfasst von : Henri-Alex Esbelin, Remy Malgouyres
Erschienen in: Discrete Geometry for Computer Imagery
Verlag: Springer International Publishing
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In many geometry processing applications, the estimation of differential geometric quantities such as curvature or normal vector field is an essential step. In this paper, we investigate new estimators for the first and second order derivatives of a real continuous function
f
based on convolution of the values of noisy digitalizations of
f
. More precisely, we provide both proofs of multigrid convergence of the estimators (with a maximal error
$O\left(h^{1-\frac{k}{2n}}\right)$
in the unnoisy case, where
k
= 1 for first order and
k
= 2 for second order derivatives and
n
is a parameter to be choosed
ad libitum
). Then, we use this derivative estimators to provide estimators for normal vectors and curvatures of a planar curve, and give some experimental evidence of the practical usefullness of all these estimators. Notice that these estimators have a better complexity than the ones of the same type previously introduced (cf. [4] and [8]).