High-throughput feature extraction for measuring attributes of deforming open-cell foams

Towards replacing physical testing of granular materials with a Topology-based Model

“…The Morse-Smale complex, in particular, encodes the gradient flow features of a scalar function, including those of interest in porous media: minima, basins, valley lines, 1-saddles, and the interfaces between basins. These same topological features form the basis for the analysis of: electronic potentials in quantum chemistry [3,34], the filamentary and dark matter structure in cosmology [40]; the formation of bubbles in mixing fluids [29]; the core structure of open cell foams [20,35]; lithium diffusion pathways [21,22]; and many others [6,7,37]. For extracting the pore structure for porous materials, Homberg et al [24,25] described computing the pores and throats of porous materials in terms of the Morse complex of the distance function.…”

Improving the Usability of Virtual Reality Neuron Tracing with Topological Elements

“…For example, these components define features in the electron density field in the quantum theory of atoms in molecules: maxima occur at atom locations; 2saddle-maximum arcs are covalent bonds; and descending 3-manifolds are atomic basins [6]. In other domains, specially selected subsets of the MSC can be used to extract features: descending 2-manifolds represent bubbles in mixing fluids [32]; 2-saddle-maximum arcs can be used to extract the core of a porous solid [24] as well as the filamentary structure of galaxies [63] or structural materials [54]; descending 2-and 1-manifolds identify lithium diffusion pathways [25]; and ascending 2-manifolds define burning regions in combustion simulations [12]. In each application, the features of interest were computed by identifying the appropriate topological abstraction, and then selecting a subset of the topological features that correspond to the quantities under study.…”

GPU Parallel Computation of Morse-Smale Complexes

“…It represents a decomposition of the domain of the scalar field into regions with uniform gradient flow behavior. Applications to feature-driven analysis and visualization of data from a diverse set of application domains including material science [16,21], cosmology [25], and chemistry [6,11] have clearly demonstrated the utility of this topological structure. A sound theoretical framework for identification of features, a principled approach to measuring the size of features, controlled simplification, and support for noise removal are key reasons for the wide use of this topological structure.…”