Handout17

Handout17 - 1 Course 18.327 and 1.130 Wavelets and Filter...

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Unformatted text preview: 1 Course 18.327 and 1.130 Wavelets and Filter Banks Wavelets and subdivision: nonuniform grids; multiresolution for triangular meshes; representation and compression of surfaces. 2 Wavelets on Surfaces in R 3 Construction by Schrder and Sweldens uses lifting scaling functions are interpolating in most straightforward case typically work with triangular mesh generated by subdivision k 1 k 2 k 3 k 4 k 5 k 6 m 1 m 2 m 3 m 4 m 5 m 6 k K(j) = {k, k 1 , k 2 , k 3 , k 4 , k 5 , k 6 , } M(j) = {m 1 , m 2 , m 3 , m 4 , m 5 , m 6 , } mesh describing surface S 2 3 Notation: K(j) = all vertices at resolution j K(j + 1) = all vertices at resolution j + 1 M(j) = vertices obtained by subdividing the resolution j mesh to produce the resolution j + 1 mesh So K(j + 1) = K(j) \ M(j) Interpolating property means that scalings functions satisfy 1 if x = x k k K(j) 0 if x = x k k K(j) k k x = position vector of a point on S....
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Handout17 - 1 Course 18.327 and 1.130 Wavelets and Filter...

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