کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1894890 1044252 2012 13 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Discrete spherical means of directional derivatives and Veronese maps
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Discrete spherical means of directional derivatives and Veronese maps
چکیده انگلیسی

We describe and study geometric properties of discrete circular and spherical means of directional derivatives of functions, as well as discrete approximations of higher order differential operators. For an arbitrary dimension, we present a general construction for obtaining discrete spherical means of directional derivatives. The construction is based on using Minkowski’s existence theorem and Veronese maps. Approximating the directional derivatives by appropriate finite differences allows one to obtain finite difference operators with good rotation invariance properties. In particular, we use discrete circular and spherical means to derive discrete approximations of various linear and nonlinear first- and second-order differential operators, including discrete Laplacians. A practical potential of our approach is demonstrated by considering applications to nonlinear filtering of digital images and surface curvature estimation.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Geometry and Physics - Volume 62, Issue 1, January 2012, Pages 124–136
نویسندگان
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