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   -> Volume 10, Issue 4


Preprint: Reversing subdivision and constructing multiresolutions
 
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Richard Bartels (rhbartel@shaw.ca)
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PostPosted: Wed Nov 21, 2001 11:51 pm    
Subject: Preprint: Reversing subdivision and constructing multiresolutions
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#9 Preprint: Reversing subdivision and constructing multiresolutions

#1:
Authors
-------
Bartels, R., Samavati, F.,

Title
-----
Reversing Subdivision Rules:
Local Linear Conditions and
Observations on Inner Products

Appearing in
------------
Journal of Computational and Applied Mathematics
vol. 119, nos. 1-2, July, 2000, pages 29-67

Also available at
-----------------
http://www.cgl.uwaterloo.ca/~rhbartel/Papers/LocalLS.pdf
http://pages.cpsc.ucalgary.ca/~samavati/papers/LocalLS.pdf

Abstract
--------
In this work we study biorthogonal systems based upon
subdivision rules and local least squares fitting problems
that reverse the subdivision. We are able to produce
multiresolution structures for some common subdivision
rules that have both finite reconstruction and
decompositions filters. We observe that each biorthogonal
system we produce can be interpreted as a semiorthogonal
system with an inner product induced on the multiresolution
that is quite different from that normally used. Some examples
of the use of this approach on images and geometry are given.

#2:
Authors
-------
Samavati, F., and Bartels, R.

Title
-----
Reversing Subdivision Using Local Linear Conditions:
Generating Multiresolutions on Regular Triangular Meshes

Available at
-----------------
http://www.cgl.uwaterloo.ca/~rhbartel/Papers/TriMesh.pdf
http://pages.cpsc.ucalgary.ca/~samavati/papers/Butterfly.pdf

Abstract
--------
We extended the results of paper #1 to non-tensor-product surfaces
(specifically: regular, triangular-mesh surfaces).
The local matrix approach of #1 is replaced by an approach based upon
masks.
To demonstrate the generality of the approach, examples of finite
multiresolution
filters are generated for Butterfly and Loop subdivision and for
a subdivision recently proposed by Litke, Schroeder, et al.

Richard Bartels
University of Waterloo
Waterloo, Ontario
Canada

Faramarz Samavati
University of Calgary
Calgary, Alberta
Canada
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