4,449 research outputs found
Polygonal Complexes and Graphs for Crystallographic Groups
The paper surveys highlights of the ongoing program to classify discrete
polyhedral structures in Euclidean 3-space by distinguished transitivity
properties of their symmetry groups, focussing in particular on various aspects
of the classification of regular polygonal complexes, chiral polyhedra, and
more generally, two-orbit polyhedra.Comment: 21 pages; In: Symmetry and Rigidity, (eds. R.Connelly, A.Ivic Weiss
and W.Whiteley), Fields Institute Communications, to appea
Hoodsquare: Modeling and Recommending Neighborhoods in Location-based Social Networks
Information garnered from activity on location-based social networks can be
harnessed to characterize urban spaces and organize them into neighborhoods. In
this work, we adopt a data-driven approach to the identification and modeling
of urban neighborhoods using location-based social networks. We represent
geographic points in the city using spatio-temporal information about
Foursquare user check-ins and semantic information about places, with the goal
of developing features to input into a novel neighborhood detection algorithm.
The algorithm first employs a similarity metric that assesses the homogeneity
of a geographic area, and then with a simple mechanism of geographic
navigation, it detects the boundaries of a city's neighborhoods. The models and
algorithms devised are subsequently integrated into a publicly available,
map-based tool named Hoodsquare that allows users to explore activities and
neighborhoods in cities around the world.
Finally, we evaluate Hoodsquare in the context of a recommendation
application where user profiles are matched to urban neighborhoods. By
comparing with a number of baselines, we demonstrate how Hoodsquare can be used
to accurately predict the home neighborhood of Twitter users. We also show that
we are able to suggest neighborhoods geographically constrained in size, a
desirable property in mobile recommendation scenarios for which geographical
precision is key.Comment: ASE/IEEE SocialCom 201
Unbounded Orbits for Outer Billiards
Outer billiards is a basic dynamical system, defined relative to a planar
convex shape. This system was introduced in the 1950's by B.H. Neumann and
later popularized in the 1970's by J. Moser. All along, one of the central
questions has been: is there an outer billiards system with an unbounded orbit.
We answer this question by proving that outer billiards defined relative to the
Penrose Kite has an unbounded orbit. The Penrose kite is the quadrilateral that
appears in the famous Penrose tiling. We also analyze some of the finer orbit
structure of outer billiards on the penrose kite. This analysis shows that
there is an uncountable set of unbounded orbits. Our method of proof relates
the problem to self-similar tilings, polygon exchange maps, and arithmetic
dynamics.Comment: 65 pages, computer-aided proof. Auxilliary program, Billiard King,
available from author's website. Latest version is essentially the same as
earlier versions, but with minor improvements and many typos fixe
Automatic Image Registration in Infrared-Visible Videos using Polygon Vertices
In this paper, an automatic method is proposed to perform image registration
in visible and infrared pair of video sequences for multiple targets. In
multimodal image analysis like image fusion systems, color and IR sensors are
placed close to each other and capture a same scene simultaneously, but the
videos are not properly aligned by default because of different fields of view,
image capturing information, working principle and other camera specifications.
Because the scenes are usually not planar, alignment needs to be performed
continuously by extracting relevant common information. In this paper, we
approximate the shape of the targets by polygons and use affine transformation
for aligning the two video sequences. After background subtraction, keypoints
on the contour of the foreground blobs are detected using DCE (Discrete Curve
Evolution)technique. These keypoints are then described by the local shape at
each point of the obtained polygon. The keypoints are matched based on the
convexity of polygon's vertices and Euclidean distance between them. Only good
matches for each local shape polygon in a frame, are kept. To achieve a global
affine transformation that maximises the overlapping of infrared and visible
foreground pixels, the matched keypoints of each local shape polygon are stored
temporally in a buffer for a few number of frames. The matrix is evaluated at
each frame using the temporal buffer and the best matrix is selected, based on
an overlapping ratio criterion. Our experimental results demonstrate that this
method can provide highly accurate registered images and that we outperform a
previous related method
Computing the Similarity Between Moving Curves
In this paper we study similarity measures for moving curves which can, for
example, model changing coastlines or retreating glacier termini. Points on a
moving curve have two parameters, namely the position along the curve as well
as time. We therefore focus on similarity measures for surfaces, specifically
the Fr\'echet distance between surfaces. While the Fr\'echet distance between
surfaces is not even known to be computable, we show for variants arising in
the context of moving curves that they are polynomial-time solvable or
NP-complete depending on the restrictions imposed on how the moving curves are
matched. We achieve the polynomial-time solutions by a novel approach for
computing a surface in the so-called free-space diagram based on max-flow
min-cut duality
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