A generalized 3D shape sampling method and file format for storage or indexing

Abstract

Several ways of 2D shape (or contour) description in terms of Fourier and wavelet transform coefficients have been proposed. They provide data compression capability, and some of the descriptors are invariant under scaling, rotation, and choice of the starting point for contour tracing. Several methods for 3D shape description also exist. However, they lack either the simplicity, the generality, or the data compression ability comparable to the 2D methods. We propose a generalized sampling method for efficient description of free-form 3D shape surfaces. The key idea is to warp a 3D spherical coordinate system onto the 3D surface, so that the spatial coordinates of each point on the surface may be represented parametrically as {x(/spl alpha/,/spl beta/), y(/spl alpha/,/spl beta/), z(/spl alpha/,/spl beta/)}, where /spl les//spl alpha//spl les/2/spl pi/ and 0/spl les//spl beta//spl les//spl pi/ with /spl alpha/ and /spl beta/ giving normalized arc lengths on the 3D surface. Fourier, wavelet, or other 2D transforms can then be applied to the three coordinate functions for purposes of data compression, database storage, or indexing. Simulations show that wavelet-based method yields efficient 3D shape compression based on this generalized sampling approach.