Back to wavelets and MRA
Analysis of Scalar Data on Multiresolution Geometric Models. (G.P. Bonneau, A. Gerussi)
Key words:
multiresolution analysis, irregular meshes, visualization.
Abstract of the paper:
Recently, multi-resolution methods based on non-nested spaces were introduced to allow the visualization and approximation of functions defined on irregular triangulations [1,2,3]. This paper comes back to these methods and shows more precisely how the subdivision/prediction/correction scheme of ordinary wavelet-based multi-resolution analysis (MRA)is also present in that framework. As an illustration, it is demonstrated how it can be applied in two of the classical issues of MRA: compression and level-of-detail editing. We also show that the framework can be used for the analysis and approximation of scalar data defined on meshes with arbitrary topology, thus extending our previous results in the plane and the sphere. Here again, the link with the corresponding classical multi-resolution scheme of [4] as well as decimation methods is made.
[1] Bonneau, G.P., Multiresolution analysis on irregular surface meshes, IEEE Transactions on Visualization and Computer Graphics, vol 4, no 4 (1998), 365-378.
[2] Gerussi, A. and Bonneau, G.P., Level of detail visualization of scalar datasets on irregular surface meshes, Proceedings of the IEEE Vis'98, October 18-23 (1998), 73-77.
[3] Bonneau, G.P. and Gerussi, A., Hierarchical decomposition of datasets on irregular surface meshes, Proceedings of CGI'98, Hannover, June 98 (1998)
[4] Certain, A., Popovic, J., DeRose, T., Duchamp, T., Salesin, D. and Stuetzle, W., Interactive multiresolution surface viewing, Computer Graphics Proceedings (SIGGRAPH), 1996, 91-98.