کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
433813 | 689633 | 2016 | 23 صفحه PDF | دانلود رایگان |
We provide a general notion of a Digital Derivative in 1-dimensional grids, which has real or integer-only versions. From any such masks, a family of masks called skipping masks are defined. We prove general results of multigrid convergence for skipping masks. We propose a few examples of digital derivative masks, including the now well-known binomial mask. The corresponding skipping masks automatically have multigrid convergence properties. We study the cases of parametric curves tangents and curvature. We propose a novel interpretation of digital convolutions as computing points on a smooth curve, the regularity of which depends on the mask. We establish, in the case of binomial and B-spline masks, a close relationship between the derivatives of the smooth curve, and the digital derivatives provided by the mask.
Journal: Theoretical Computer Science - Volume 624, 18 April 2016, Pages 2–24