deposit_your_work

Multiscale Approximation of Piecewise Smooth Two-Dimensional Function using Normal Triangulated Meshes

Files in this item

Files Size Format View
Jan2005Jul1Multiscale.PDF 1.111Mb application/pdf Thumbnail

Show full item record

Item Metadata

Title: Multiscale Approximation of Piecewise Smooth Two-Dimensional Function using Normal Triangulated Meshes
Author: Jansen, Maarten; Baraniuk, Richard G.; Lavu, Sridhar
Type: Journal Paper
Keywords: Normal offsets; Mesh; Image; Multiresolution; Wavelet; Approximation
Citation: M. Jansen, R. G. Baraniuk and S. Lavu, "Multiscale Approximation of Piecewise Smooth Two-Dimensional Function using Normal Triangulated Meshes," Journal of Applied and Computational Harmonic Analysis, vol. 19, no. 1, pp. 92-130, 2005.
Abstract: 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.
Date Published: 2005-07-01

This item appears in the following Collection(s)

  • ECE Publications [1032 items]
    Publications by Rice University Electrical and Computer Engineering faculty and graduate students
  • DSP Publications [508 items]
    Publications by Rice Faculty and graduate students in digital signal processing.