Height Ridge Computation and Filtering for Visualization

Motivated by the growing interest in the use of ridges in scientific visualization, we analyze the two height ridge definitions by Eberly and Lindeberg. We propose a raw feature definition leading to a superset of the ridge points as obtained by these two definitions. The set of raw feature points has the correct dimensionality, and it can be narrowed down to either Eberly's or Lindeberg's ridges by using Boolean filters which we formulate. While the straight-forward computation of height ridges requires explicit eigenvalue calculation, this can be avoided by using an equivalent definition of the raw feature set, for which we give a derivation. We describe efficient algorithms for two special cases, height ridges of dimension one and of co-dimension one. As an alternative to the aforementioned filters, we propose a new criterion for filtering raw features based on the distance between contours which generally makes better decisions, as we demonstrate on a few synthetic fields, a topographical dataset, and a fluid flow simulation dataset. The same set of test data shows that it is unavoidable to use further filters to eliminate false positives. For this purpose, we use the angle between feature tangent and slope line as a quality measure and, based on this, formalize a previously published filter.