Hierarchical Hashing for Pattern Search in 3D Vector Fields

Abstract

The expressiveness of many visualization methods for 3D vector fields is often limited by occlusion, i.e., interesting flow patterns hide each other or are hidden by laminar flow. Automatic detection of patterns in 3D vector fields has gained attention recently, since it allows to highlight user-defined patterns and separate the wheat from the chaff. We propose an algorithm which is able to detect 3D flow patterns of arbitrary extent in a robust manner. We encode the local flow behavior in scale space using a sequence of hierarchical base descriptors, which are pre-computed and hashed into a number of hash tables. This ensures a fast fetching of similar occurrences in the flow and requires only a constant number of table lookups. In contrast to many previous approaches, our method supports patterns of arbitrary shape and extent. We achieve this by assembling these patterns using several smaller spheres. The results are independent of translation, rotation, and scaling. Our experiments show that our approach encompasses the state of the art with respect to both the computational costs and the accuracy.