Linear Programming in Linear Time When the Dimension Is Fixed
Journal of the ACM (JACM)
Geometrical parameters extraction from discrete paths
DCGA '96 Proceedings of the 6th International Workshop on Discrete Geometry for Computer Imagery
Fast, accurate and convergent tangent estimation on digital contours
Image and Vision Computing
An elementary digital plane recognition algorithm
Discrete Applied Mathematics - Special issue: IWCIA 2003 - Ninth international workshop on combinatorial image analysis
Binomial convolutions and derivatives estimation from noisy discretizations
DGCI'08 Proceedings of the 14th IAPR international conference on Discrete geometry for computer imagery
Convergence of binomial-based derivative estimation for C2noisy discretized curves
DGCI'09 Proceedings of the 15th IAPR international conference on Discrete geometry for computer imagery
Maximal digital straight segments and convergence of discrete geometric estimators
SCIA'05 Proceedings of the 14th Scandinavian conference on Image Analysis
Integral based curvature estimators in digital geometry
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Efficient robust digital annulus fitting with bounded error
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Convergence of level-wise convolution differential estimators
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
Multigrid convergent curvature estimator
DGCI'13 Proceedings of the 17th IAPR international conference on Discrete Geometry for Computer Imagery
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We provide a new method to estimate the derivatives of a digital function by linear programming or other geometrical algorithms. Knowing the digitization of a real continuous function f with a resolution h, this approach provides an approximation of the kth derivative f(k)(x) with a maximal error in O(h1/1+k) where the constant depends on an upper bound of the absolute value of the (k + 1)th derivative of f in a neighborhood of x. This convergence rate 1/k+1 should be compared to the two other methods already providing such uniform convergence results, namely 1/3 from Lachaud et. al (only for the first order derivative) and (2/3)k from Malgouyres et al..