Multiresolution Tiling

Abstract

This paper describes an efficient method for constructing a tiling between a pair of planar contours. The problem is of interest in a number of domains, including medical imaging, biological research and geological reconstructions. Our method, based on ideas from multiresolution analysis and wavelets, requires O(n) space and appears to require O(n log n) time for average inputs, compared to the O(n2) space and O(n2 log n) time required by the optimizing algorithm of Fuchs, Kedem and Uselton1. The results computed by our algorithm are in many cases nearly the same as those of the optimizing algorithm, but at a small fraction of the computational cost. The performance improvement makes the algorithm usable for large contours in an interactive system. The use of multiresolution analysis provides an efficient mechanism for data compression by discarding wavelet coefficients smaller than a threshold value during reconstruction. The amount of detail lost can be controlled by appropriate choice of the threshold value. The use of lower resolution approximations to the original contours yields significant savings in the time required to display a reconstructed object, and in the space required to store it.