Dynamic Planar Embeddings of Dynamic Graphs

We present an algorithm to support the dynamic embedding in the plane of a dynamic graph. An edge can be inserted across a face between two vertices on the face boundary (we call such a vertex pair linkable), and edges can be deleted. The planar embedding can also be changed locally by flipping components that are connected to the rest of the graph by at most two vertices. Given vertices $u,v$, linkable$(u,v)$ decides whether $u$ and $v$ are linkable in the current embedding, and if so, returns a list of suggestions for the placement of $(u,v)$ in the embedding. For non-linkable vertices $u,v$, we define a new query, one-flip-linkable$(u,v)$ providing a suggestion for a flip that will make them linkable if one exists. We support all updates and queries in O(log$^2 n$) time. Our time bounds match those of Italiano et al. for a static (flipless) embedding of a dynamic graph. Our new algorithm is simpler, exploiting that the complement of a spanning tree of a connected plane graph is a spanning tree of the dual graph. The primal and dual trees are interpreted as having the same Euler tour, and a main idea of the new algorithm is an elegant interaction between top trees over the two trees via their common Euler tour.Comment: Announced at STACS'1

In-home and remote use of robotic body surrogates by people with profound motor deficits

By controlling robots comparable to the human body, people with profound motor deficits could potentially perform a variety of physical tasks for themselves, improving their quality of life. The extent to which this is achievable has been unclear due to the lack of suitable interfaces by which to control robotic body surrogates and a dearth of studies involving substantial numbers of people with profound motor deficits. We developed a novel, web-based augmented reality interface that enables people with profound motor deficits to remotely control a PR2 mobile manipulator from Willow Garage, which is a human-scale, wheeled robot with two arms. We then conducted two studies to investigate the use of robotic body surrogates. In the first study, 15 novice users with profound motor deficits from across the United States controlled a PR2 in Atlanta, GA to perform a modified Action Research Arm Test (ARAT) and a simulated self-care task. Participants achieved clinically meaningful improvements on the ARAT and 12 of 15 participants (80%) successfully completed the simulated self-care task. Participants agreed that the robotic system was easy to use, was useful, and would provide a meaningful improvement in their lives. In the second study, one expert user with profound motor deficits had free use of a PR2 in his home for seven days. He performed a variety of self-care and household tasks, and also used the robot in novel ways. Taking both studies together, our results suggest that people with profound motor deficits can improve their quality of life using robotic body surrogates, and that they can gain benefit with only low-level robot autonomy and without invasive interfaces. However, methods to reduce the rate of errors and increase operational speed merit further investigation.Comment: 43 Pages, 13 Figure

Curve Reconstruction via the Global Statistics of Natural Curves

Reconstructing the missing parts of a curve has been the subject of much computational research, with applications in image inpainting, object synthesis, etc. Different approaches for solving that problem are typically based on processes that seek visually pleasing or perceptually plausible completions. In this work we focus on reconstructing the underlying physically likely shape by utilizing the global statistics of natural curves. More specifically, we develop a reconstruction model that seeks the mean physical curve for a given inducer configuration. This simple model is both straightforward to compute and it is receptive to diverse additional information, but it requires enough samples for all curve configurations, a practical requirement that limits its effective utilization. To address this practical issue we explore and exploit statistical geometrical properties of natural curves, and in particular, we show that in many cases the mean curve is scale invariant and oftentimes it is extensible. This, in turn, allows to boost the number of examples and thus the robustness of the statistics and its applicability. The reconstruction results are not only more physically plausible but they also lead to important insights on the reconstruction problem, including an elegant explanation why certain inducer configurations are more likely to yield consistent perceptual completions than others.Comment: CVPR versio

A distributed camera system for multi-resolution surveillance

We describe an architecture for a multi-camera, multi-resolution surveillance system. The aim is to support a set of distributed static and pan-tilt-zoom (PTZ) cameras and visual tracking algorithms, together with a central supervisor unit. Each camera (and possibly pan-tilt device) has a dedicated process and processor. Asynchronous interprocess communications and archiving of data are achieved in a simple and effective way via a central repository, implemented using an SQL database. Visual tracking data from static views are stored dynamically into tables in the database via client calls to the SQL server. A supervisor process running on the SQL server determines if active zoom cameras should be dispatched to observe a particular target, and this message is effected via writing demands into another database table. We show results from a real implementation of the system comprising one static camera overviewing the environment under consideration and a PTZ camera operating under closed-loop velocity control, which uses a fast and robust level-set-based region tracker. Experiments demonstrate the effectiveness of our approach and its feasibility to multi-camera systems for intelligent surveillance

Combinatorial and Geometric Properties of Planar Laman Graphs

Laman graphs naturally arise in structural mechanics and rigidity theory. Specifically, they characterize minimally rigid planar bar-and-joint systems which are frequently needed in robotics, as well as in molecular chemistry and polymer physics. We introduce three new combinatorial structures for planar Laman graphs: angular structures, angle labelings, and edge labelings. The latter two structures are related to Schnyder realizers for maximally planar graphs. We prove that planar Laman graphs are exactly the class of graphs that have an angular structure that is a tree, called angular tree, and that every angular tree has a corresponding angle labeling and edge labeling. Using a combination of these powerful combinatorial structures, we show that every planar Laman graph has an L-contact representation, that is, planar Laman graphs are contact graphs of axis-aligned L-shapes. Moreover, we show that planar Laman graphs and their subgraphs are the only graphs that can be represented this way. We present efficient algorithms that compute, for every planar Laman graph G, an angular tree, angle labeling, edge labeling, and finally an L-contact representation of G. The overall running time is O(n^2), where n is the number of vertices of G, and the L-contact representation is realized on the n x n grid.Comment: 17 pages, 11 figures, SODA 201