Extremal feature extraction from 3-D vector and noisy scalar fields
Chi–Keung Tang, Gérard G. Medioni · 1998
We are interested in feature extraction from volume data in terms of coherent surfaces and 3-D space curves. The input can be an inaccurate scalar or vector field, sampled densely or sparsely on a regular 3-D grid, in which poor resolution and the presence of spurious noisy samples make traditional iso-surface techniques inappropriate. In this paper, we present a general-purpose methodology to extract surfaces or curves from a digital 3-D potential vector field {(s,v̄)}, in which each voxel holds a scalar s designating strength, and a vector v̄ indicating direction. For scalar, sparse or low resolution data, we `vectorize' and `densify' the volume by Tensor Voting to produce dense vector fields suitable as input to our algorithms, the Extremal Surface and Curve Algorithms. Both algorithms extract, with sub-voxel precision, coherent features representing local extrema in the given vector field. These coherent features are a hole-free triangulation mesh (in the surface case), and a set of connected, oriented, and non-intersecting polyline segments (in the curve case). We demonstrate the general usefulness of both extremal algorithms on a variety of real data by properly extracting their inherent extremal properties, such as (a) shock waves induced by abrupt velocity or direction changes in a flow field, (b) interacting vortex cores and vorticity lines in a velocity field, (c) crestlines and ridges implicit in a digital terrain map, and (d) grooves, anatomical lines and complex surfaces from noisy dental data.