Wavelet representation of contour sets

Abstract: We present a new wavelet compression and mul-tiresolution modeling approach for sets of contours (level sets). In contrast to previous wavelet schemes, our algorithm creates a parametrization of a scalar field induced by its contours and com-pactly stores this parametrization rather than function values sam-pled on a regular grid. Our representation is based on hierarchical polygon meshes with subdivision connectivity whose vertices are transformed into wavelet coefficients. From this sparse set of co-efficients, every set of contours can be efficiently reconstructed at multiple levels of resolution. When applying lossy compression, introducing high quantization errors, our method preserves contour topology, in contrast to compression methods applied to the cor-responding field function. We provide numerical results for scalar fields defined on planar domains. Our approach generalizes to vol-umetric domains, time-varying contours, and level sets of vector fields