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Wavelets on Planar Tessellations

  • Author(s): Bertram, Martin
  • Duchaineau, Mark A.
  • Hamann, Bernd
  • Joy, Ken
  • Editor(s): Arabnia, H. R.
  • Coudoux, F.-X.
  • Mun, Y.
  • Power, G.P.
  • Sarfraz, M.
  • Zhu, Q.
  • et al.
Abstract

We present a new technique for progressive C0-continuous approximation and compression of polygonal objects in images. Our technique uses local parametrizations defined by meshes of convex polygons in the plane. We generalize a lifted biorthogonal wavelet transform to polygonal domains to perform multiresolution analysis and compression of image regions. The advantage of our technique over conventional wavelet methods is that the domain is an arbitrary tesselation rather than a rectilinear grid. We expect that this technique has many applications image compression, progressive transmission, radiosity, virtual reality, and image morphing.

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