How to Walk Your Dog in the Mountains with No Magic Leash

We describe a $O(\log n )$-approximation algorithm for computing the homotopic \Frechet distance between two polygonal curves that lie on the boundary of a triangulated topological disk. Prior to this work, algorithms were known only for curves on the Euclidean plane with polygonal obstacles. A key technical ingredient in our analysis is a $O(\log n)$-approximation algorithm for computing the minimum height of a homotopy between two curves. No algorithms were previously known for approximating this parameter. Surprisingly, it is not even known if computing either the homotopic \Frechet distance, or the minimum height of a homotopy, is in NP

Visualization of Tensor Fields in Mechanics

Tensors are used to describe complex physical processes in many applications. Examples include the distribution of stresses in technical materials, acting forces during seismic events, or remodeling of biological tissues. While tensors encode such complex information mathematically precisely, the semantic interpretation of a tensor is challenging. Visualization can be beneficial here and is frequently used by domain experts. Typical strategies include the use of glyphs, color plots, lines, and isosurfaces. However, data complexity is nowadays accompanied by the sheer amount of data produced by large-scale simulations and adds another level of obstruction between user and data. Given the limitations of traditional methods, and the extra cognitive effort of simple methods, more advanced tensor field visualization approaches have been the focus of this work. This survey aims to provide an overview of recent research results with a strong application-oriented focus, targeting applications based on continuum mechanics, namely the fields of structural, bio-, and geomechanics. As such, the survey is complementing and extending previously published surveys. Its utility is twofold: (i) It serves as basis for the visualization community to get an overview of recent visualization techniques. (ii) It emphasizes and explains the necessity for further research for visualizations in this context

3D Polarized Light Imaging Portrayed: Visualization of Fiber Architecture Derived from 3D-PLI

3D polarized light imaging (3D-PLI) is a neuroimaging technique that has recently opened up new avenues to study the complex architecture of nerve fibers in postmortem brains at microscopic scales. In a specific voxel-based analysis, each voxel is assigned a single 3D fiber orientation vector. This leads to comprehensive 3D vector fields. In order to inspect and analyze such high-resolution fiber orientation vector field, also in combination with complementary microscopy measurements, appropriate visualization techniques are essential to overcome several challenges, such as the massive data sizes, the large amount of both unique and redundant information at different scales, or the occlusion issues of inner structures by outer layers. Here, we introduce a comprehensive software tool that is able to visualize all information of a typical 3D-PLI dataset in an adequate and sophisticated manner. This includes the visualization of (i) anatomic structural and fiber architectonic data in one representation, (ii) a large-scale fiber orientation vector field, and (iii) a clustered version of the field. Alignment of a 3D-PLI dataset to an appropriate brain atlas provides expert-based delineation, segmentation, and, ultimately, visualization of selected anatomical structures. By means of these techniques, a detailed analysis of the complex fiber architecture in 3D is feasible

Mobile Wound Assessment and 3D Modeling from a Single Image

The prevalence of camera-enabled mobile phones have made mobile wound assessment a viable treatment option for millions of previously difficult to reach patients. We have designed a complete mobile wound assessment platform to ameliorate the many challenges related to chronic wound care. Chronic wounds and infections are the most severe, costly and fatal types of wounds, placing them at the center of mobile wound assessment. Wound physicians assess thousands of single-view wound images from all over the world, and it may be difficult to determine the location of the wound on the body, for example, if the wound is taken at close range. In our solution, end-users capture an image of the wound by taking a picture with their mobile camera. The wound image is segmented and classified using modern convolution neural networks, and is stored securely in the cloud for remote tracking. We use an interactive semi-automated approach to allow users to specify the location of the wound on the body. To accomplish this we have created, to the best our knowledge, the first 3D human surface anatomy labeling system, based off the current NYU and Anatomy Mapper labeling systems. To interactively view wounds in 3D, we have presented an efficient projective texture mapping algorithm for texturing wounds onto a 3D human anatomy model. In so doing, we have demonstrated an approach to 3D wound reconstruction that works even for a single wound image

A Neural Model of Visually Guided Steering, Obstacle Avoidance, and Route Selection

A neural model is developed to explain how humans can approach a goal object on foot while steering around obstacles to avoid collisions in a cluttered environment. The model uses optic flow from a 3D virtual reality environment to determine the position of objects based on motion discotinuities, and computes heading direction, or the direction of self-motion, from global optic flow. The cortical representation of heading interacts with the representations of a goal and obstacles such that the goal acts as an attractor of heading, while obstacles act as repellers. In addition the model maintains fixation on the goal object by generating smooth pursuit eye movements. Eye rotations can distort the optic flow field, complicating heading perception, and the model uses extraretinal signals to correct for this distortion and accurately represent heading. The model explains how motion processing mechanisms in cortical areas MT, MST, and VIP can be used to guide steering. The model quantitatively simulates human psychophysical data about visually-guided steering, obstacle avoidance, and route selection.Air Force Office of Scientific Research (F4960-01-1-0397); National Geospatial-Intelligence Agency (NMA201-01-1-2016); National Science Foundation (NSF SBE-0354378); Office of Naval Research (N00014-01-1-0624