Superquadric glyphs for symmetric second-order tensors

Symmetric second-order tensor fields play a central role in scientific and biomedical studies as well as in image analysis and feature-extraction methods. The utility of displaying tensor field samples has driven the development of visualization techniques that encode the tensor shape and orientation into the geometry of a tensor glyph. With some exceptions, these methods work only for positive-definite tensors (i.e. having positive eigenvalues, such as diffusion tensors). We expand the scope of tensor glyphs to all symmetric second-order tensors in two and three dimensions, gracefully and unambiguously depicting any combination of positive and negative eigenvalues. We generalize a previous method of superquadric glyphs for positive-definite tensors by drawing upon a larger portion of the superquadric shape space, supplemented with a coloring that indicates the quadratic form (including eigenvalue sign). We show that encoding arbitrary eigenvalue magnitudes requires design choices that differ fundamentally from those in previous work on traceless tensors that arise in the study of liquid crystals. Our method starts with a design of 2-D tensor glyphs guided by principles of scale-preservation and symmetry, and creates 3-D glyphs that include the 2-D glyphs in their axis-aligned cross-sections. A key ingredient of our method is a novel way of mapping from the shape space of three-dimensional symmetric second-order tensors to the unit square. We apply our new glyphs to stress tensors from mechanics, geometry tensors and Hessians from image analysis, and rate-of-deformation tensors in computational fluid dynamics.     

Crease Surfaces: From Theory to Extraction and Application to Diffusion Tensor MRI

Crease surfaces are two-dimensional manifolds along which a scalar field assumes a local maximum (ridge) or a local minimum (valley) in a constrained space. Unlike isosurfaces, they are able to capture extremal structures in the data. Creases have a long tradition in image processing and computer vision, and have recently become a popular tool for visualization. When extracting crease surfaces, degeneracies of the Hessian (i.e., lines along which two eigenvalues are equal) have so far been ignored. We show that these loci, however, have two important consequences for the topology of crease surfaces: First, creases are bounded not only by a side constraint on eigenvalue sign, but also by Hessian degeneracies. Second, crease surfaces are not, in general, orientable. We describe an efficient algorithm for the extraction of crease surfaces which takes these insights into account and demonstrate that it produces more accurate results than previous approaches. Finally, we show that diffusion tensor magnetic resonance imaging (DT-MRI) stream surfaces, which were previously used for the analysis of planar regions in diffusion tensor MRI data, are mathematically ill-defined. As an example application of our method, creases in a measure of planarity are presented as a viable substitute.     

Coupling and comparing a spatially- and temporally-detailed eutrophication model with an ecosystem network model: An initial application to Chesapeake Bay

Coastal waters are modeled for a variety of purposes including eutrophication remediation and fisheries management. Combining these two approaches provides insights which are not available from either approach independently. Coupling is confounded, however, by differences in model formulations and “currencies.” We present here an initial coupling of a spatially- and temporally-detailed eutrophication model, CE-QUAL-ICM, with a network fisheries model, Ecopath. We list commonalities between the models and present algorithms and software for the exchange of information. The models are applied to the central portion of Chesapeake Bay for a contemporary summer period. After comparison of the representations of Chesapeake Bay by the two models, an illustrative example one-way, off-line, coupling is presented. In an initial examination of a 20% increase in predation on phytoplankton by a small, highly-exploited fish (Atlantic menhaden, Brevoortia tyrannus), computed reduction in phytoplankton biomass is accompanied by increased production due to enhanced nutrient recycling. Minimal impact on the structure of the food web or on biomass of higher-trophic level organisms is computed. The algorithms and software can be adapted to alternate eutrophication models and Ecopath applications and provide the first, necessary, steps for subsequent coupling with the time-variable Ecosim model.     

A high-density multi-point LAPS set-up using a VCSEL array and FPGA control

A new LAPS (light-addressable potentiometric sensor) set-up will be introduced, in which the light sources are miniaturised by the utilisation of a VCSEL (vertical-cavity surface-emitting laser) array to increase the measurement spot density. An FPGA (field-programmable gate array) is used to generate modulation signals for individual illumination of each measurement spot of the LAPS. The new set-up can operate a large number of measurement spots simultaneously by reading out the sum photocurrent and separate the signals of the individual measurement spots by an FFT analysis. The frequency, amplitude and offset of the modulation signal can be configured for each measurement spot by software. The new system can be combined with a positioning stage allowing the parallel read out of a single line of measurement spots and a scan perpendicular to that line in a similar manner, like for an optical scanner set-up. First measurements demonstrate the functionality of the new LAPS set-up as a chemical imaging system.     

Branch-and-Bound Methods for Euclidean Registration Problems

In this paper, we propose a practical and efficient method for finding the globally optimal solution to the problem of determining the pose of an object. We present a framework that allows us to use point-to-point, point-to-line, and point-to-plane correspondences for solving various types of pose and registration problems involving euclidean (or similarity) transformations. Traditional methods such as the iterative closest point algorithm or bundle adjustment methods for camera pose may get trapped in local minima due to the nonconvexity of the corresponding optimization problem. Our approach of solving the mathematical optimization problems guarantees global optimality. The optimization scheme is based on ideas from global optimization theory, in particular convex underestimators in combination with branch-and-bound methods. We provide a provably optimal algorithm and demonstrate good performance on both synthetic and real data. We also give examples of where traditional methods fail due to the local minima problem.     

Discovery of sound sources by an autonomous mobile robot

In this work, we describe an autonomous mobile robotic system for finding, investigating, and modeling ambient noise sources in the environment. The system has been fully implemented in two different environments, using two different robotic platforms and a variety of sound source types. Making use of a two-step approach to autonomous exploration of the auditory scene, the robot first quickly moves through the environment to find and roughly localize unknown sound sources using the auditory evidence grid algorithm. Then, using the knowledge gained from the initial exploration, the robot investigates each source in more depth, improving upon the initial localization accuracy, identifying volume and directivity, and, finally, building a classification vector useful for detecting the sound source in the future.     

A Unified Variational Volume Registration Method Based on Automatically Learned Brain Structures

We introduce a new volumetric registration technique that effectively combines active surfaces with the finite element method. The method simultaneously aligns multi-label automatic structural segmentation results, which can be obtained by the application of existing segmentation software, to produce an anatomically accurate 3D registration. This registration is obtained by the minimization of a single energy functional. Just like registering raw images, obtaining a 3D registration this way still requires solving a fundamentally ill-posed problem. We explain through academic examples as well as an MRI dataset with manual anatomical labels, which are hidden from the registration method, how the quality of a registration method can be measured and the advantages our approach offers.     

Racing to the precipice: a model of artificial intelligence development

This paper presents a simple model of an AI (artificial intelligence) arms race, where several development teams race to build the first AI. Under the assumption that the first AI will be very powerful and transformative, each team is incentivised to finish first—by skimping on safety precautions if need be. This paper presents the Nash equilibrium of this process, where each team takes the correct amount of safety precautions in the arms race. Having extra development teams and extra enmity between teams can increase the danger of an AI disaster, especially if risk-taking is more important than skill in developing the AI. Surprisingly, information also increases the risks: the more teams know about each others’ capabilities (and about their own), the more the danger increases. Should these results persist in more realistic models and analysis, it points the way to methods of increasing the chance of the safe development of AI.