A spatial approach to morphological feature extraction from irregularly sampled scalar fields

Abstract

Several algorithms have recently been introduced for morphological analysis of scalar fields (terrains, static and dynamic volume data) based on a discrete version of Morse theory. However, despite the applicability of the theory to very general discretized domains, memory constraints have limited its practical usage to scalar fields defined on regular grids, or to relatively small simplicial complexes. We propose an efficient and effective data structure for the extraction of morphological features, such as critical points and their regions of influence, based on the PR-star octree data structure [24], which uses a spatial index over the embedding space of the complex to locally reconstruct the connectivity among its cells. We demonstrate the effectiveness and scalability of our approach over irregular simplicial meshes in 2D and in 3D with a set of streaming algorithms which extract topological features of the associated scalar field from its locally computed discrete gradient field. Specifically, we extract the critical points of the scalar field, their corresponding regions in the Morse decomposition of the field domain induced by the gradient field, and their connectivity.