Computing contour trees in all dimensions

AbstractWe show that contour trees can be computed in all dimensions by a simple algorithm that merges two trees. Our algorithm extends, simplifies, and improves work of Tarasov and Vyalyi and of van Kreveld et al

Flexible isosurfaces: Simplifying and displaying scalar topology using the contour tree

The contour tree is an abstraction of a scalar field that encodes the nesting relationships of isosurfaces. We show how to use the contour tree to represent individual contours of a scalar field, how to simplify both the contour tree and the topology of the scalar field, how to compute and store geometric properties for all possible contours in the contour tree, and how to use the simplified contour tree as an interface for exploratory visualization

Topological Galleries: A High Level User Interface for Topology Controlled Volume Rendering

Existing topological interfaces to volume rendering are limited by their reliance on sophisticated knowledge of topology by the user. We extend previous work by describing topological galleries, an interface for novice users that is based on the design galleries approach. We report three contributions: an interface based on hierarchical thumbnail galleries to display the containment relationships between topologically identifiable features, the use of the pruning hierarchy instead of branch decomposition for contour tree simplification, and drag-and-drop transfer function assignment for individual components. Initial results suggest that this approach suffers from limitations due to rapid drop-off of feature size in the pruning hierarchy. We explore these limitations by providing statistics of feature size as function of depth in the pruning hierarchy of the contour tree

Strain fields in twisted bilayer graphene

Van der Waals heteroepitaxy allows deterministic control over lattice mismatch or azimuthal orientation between atomic layers to produce long wavelength superlattices. The resulting electronic phases depend critically on the superlattice periodicity as well as localized structural deformations that introduce disorder and strain. Here, we introduce Bragg interferometry, based on four-dimensional scanning transmission electron microscopy, to capture atomic displacement fields in twisted bilayer graphene with twist angles < 2{\deg}. Nanoscale spatial fluctuations in twist angle and uniaxial heterostrain are statistically evaluated, revealing the prevalence of short-range disorder in this class of materials. By quantitatively mapping strain tensor fields we uncover two distinct regimes of structural relaxation -- in contrast to previous models depicting a single continuous process -- and we disentangle the electronic contributions of the rotation modes that comprise this relaxation. Further, we find that applied heterostrain accumulates anisotropically in saddle point regions to generate distinctive striped shear strain phases. Our results thus establish the reconstruction mechanics underpinning the twist angle dependent electronic behaviour of twisted bilayer graphene, and provide a new framework for directly visualizing structural relaxation, disorder, and strain in any moir\'e material.Comment: 29 pages, 6 figures plus supporting information (42 pages, 28 figures

Visualisation of urban airborne laser scanning data with occlusion images

Airborne Laser Scanning (ALS) was introduced to provide rapid, high resolution scans of landforms for computational processing. More recently, ALS has been adapted for scanning urban areas. The greater complexity of urban scenes necessitates the development of novel methods to exploit urban ALS to best advantage. This paper presents occlusion images: a novel technique that exploits the geometric complexity of the urban environment to improve visualisation of small details for better feature recognition. The algorithm is based on an inversion of traditional occlusion techniques

Clinical outcomes and response to treatment of patients receiving topical treatments for pyoderma gangrenosum: a prospective cohort study

Background: pyoderma gangrenosum (PG) is an uncommon dermatosis with a limited evidence base for treatment. Objective: to estimate the effectiveness of topical therapies in the treatment of PG. Methods: prospective cohort study of UK secondary care patients with a clinical diagnosis of PG suitable for topical treatment (recruited July 2009 to June 2012). Participants received topical therapy following normal clinical practice (mainly Class I-III topical corticosteroids, tacrolimus 0.03% or 0.1%). Primary outcome: speed of healing at 6 weeks. Secondary outcomes: proportion healed by 6 months; time to healing; global assessment; inflammation; pain; quality-of-life; treatment failure and recurrence. Results: Sixty-six patients (22 to 85 years) were enrolled. Clobetasol propionate 0.05% was the most commonly prescribed therapy. Overall, 28/66 (43.8%) of ulcers healed by 6 months. Median time-to-healing was 145 days (95% CI: 96 days, ∞). Initial ulcer size was a significant predictor of time-to-healing (hazard ratio 0.94 (0.88;80 1.00); p = 0.043). Four patients (15%) had a recurrence. Limitations: No randomised comparator Conclusion: Topical therapy is potentially an effective first-line treatment for PG that avoids possible side effects associated with systemic therapy. It remains unclear whether more severe disease will respond adequately to topical therapy alone