<title>Three-dimensional wavelet transform and multiresolution surface reconstruction from volume data</title>

Abstract

Multiresolution surface reconstruction from volume data is very useful in medical imaging, data compression and multiresolution modeling. This paper presents a hierarchical structure for extracting multiresolution surfaces from volume data by using a 3-D wavelet transform. The hierarchical scheme is used to visualize different levels of detail of the surface and allows a user to explore different features of the surface at different scales. We use 3-D surface curvature as a smoothness condition to control the hierarchical level and the distance error between the reconstructed surface and the original data as the stopping criteria. A 3-D wavelet transform provides an appropriate hierarchical structure to build the volume pyramid. It can be constructed by the tensor products of 1-D wavelet transforms in three subspaces. We choose the symmetric and smoothing filters such as Haar, linear, pseudoCoiflet, cubic B-spline and their corresponding orthogonal wavelets to build the volume pyramid. The surface is reconstructed at each level of volume data by using the cell interpolation method. Some experimental results are shown through the comparison of the different filters based on the distance errors of the surfaces.© (1995) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.