کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9500287 1337603 2005 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
Multiscale approximation of piecewise smooth two-dimensional functions using normal triangulated meshes
چکیده انگلیسی
Multiresolution triangulation meshes are widely used in computer graphics for representing three-dimensional (3-d) shapes. We propose to use these tools to represent 2-d piecewise smooth functions such as grayscale images, because triangles have potential to more efficiently approximate the discontinuities between the smooth pieces than other standard tools like wavelets. We show that normal mesh subdivision is an efficient triangulation, thanks to its local adaptivity to the discontinuities. Indeed, we prove that, within a certain function class, the normal mesh representation has an optimal asymptotic error decay rate as the number of terms in the representation grows. This function class is the so-called horizon class comprising constant regions separated by smooth discontinuities, where the line of discontinuity is C2 continuous. This optimal decay rate is possible because normal meshes automatically generate a polyline (piecewise linear) approximation of each discontinuity, unlike the blocky piecewise constant approximation of tensor product wavelets. In this way, the proposed nonlinear multiscale normal mesh decomposition is an anisotropic representation of the 2-d function. The same idea of anisotropic representations lies at the basis of decompositions such as wedgelet and curvelet transforms, but the proposed normal mesh approach has a unique construction.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Applied and Computational Harmonic Analysis - Volume 19, Issue 1, July 2005, Pages 92-130
نویسندگان
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