187,521 research outputs found
Finding and Maintaining Rigid Components
We give the first complete analysis that the complexity of finding and maintaining rigid components of planar bar-and-joint frameworks and arbitrary d-dimensional body-and-bar frameworks, using a family of algorithms called pebble games, is O(n2). To this end, we intro- duce a new data structure problem called union pair- find, which maintains disjoint edge sets and supports pair-find queries of whether two vertices are spanned by a set. We present solutions that apply to generalizations of the pebble game algorithms, beyond the original rigidity motivation
Word matching using single closed contours for indexing handwritten historical documents
Effective indexing is crucial for providing convenient access to scanned versions of large collections of historically valuable handwritten manuscripts. Since traditional handwriting recognizers based on optical character recognition (OCR) do not perform well on historical documents, recently a holistic word recognition approach has gained in popularity as an attractive and more straightforward solution (Lavrenko et al. in proc. document Image Analysis for Libraries (DIAL’04), pp. 278–287, 2004). Such techniques attempt to recognize words based on scalar and profile-based features extracted from whole word images. In this paper, we propose a new approach to holistic word recognition for historical handwritten manuscripts based on matching word contours instead of whole images or word profiles. The new method consists of robust extraction of closed word contours and the application of an elastic contour matching technique proposed originally for general shapes (Adamek and O’Connor in IEEE Trans Circuits Syst Video Technol 5:2004). We demonstrate that multiscale contour-based descriptors can effectively capture intrinsic word features avoiding any segmentation of words into smaller subunits. Our experiments show a recognition accuracy of 83%, which considerably exceeds the performance of other systems reported in the literature
Prediction of stable walking for a toy that cannot stand
Previous experiments [M. J. Coleman and A. Ruina, Phys. Rev. Lett. 80, 3658
(1998)] showed that a gravity-powered toy with no control and which has no
statically stable near-standing configurations can walk stably. We show here
that a simple rigid-body statically-unstable mathematical model based loosely
on the physical toy can predict stable limit-cycle walking motions. These
calculations add to the repertoire of rigid-body mechanism behaviors as well as
further implicating passive-dynamics as a possible contributor to stability of
animal motions.Comment: Note: only corrections so far have been fixing typo's in these
comments. 3 pages, 2 eps figures, uses epsf.tex, revtex.sty, amsfonts.sty,
aps.sty, aps10.sty, prabib.sty; Accepted for publication in Phys. Rev. E.
4/9/2001 ; information about Andy Ruina's lab (including Coleman's, Garcia's
and Ruina's other publications and associated video clips) can be found at:
http://www.tam.cornell.edu/~ruina/hplab/index.html and more about Georg
Bock's Simulation Group with whom Katja Mombaur is affiliated can be found at
http://www.iwr.uni-heidelberg.de/~agboc
Non-iterative and exact method for constraining particles in a linear geometry
We present a practical numerical method for evaluating the Lagrange
multipliers necessary for maintaining a constrained linear geometry of
particles in dynamical simulations. The method involves no iterations, and is
limited in accuracy only by the numerical methods for solving small systems of
linear equations. As a result of the non-iterative and exact (within numerical
accuracy) nature of the procedure there is no drift in the constrained
geometry, and the method is therefore readily applied to molecular dynamics
simulations of, e.g., rigid linear molecules or materials of non-spherical
grains. We illustrate the approach through implementation in the commonly used
second-order velocity explicit Verlet method.Comment: 12 pages, 2 figure
Stable Camera Motion Estimation Using Convex Programming
We study the inverse problem of estimating n locations (up to
global scale, translation and negation) in from noisy measurements of a
subset of the (unsigned) pairwise lines that connect them, that is, from noisy
measurements of for some pairs (i,j) (where the
signs are unknown). This problem is at the core of the structure from motion
(SfM) problem in computer vision, where the 's represent camera locations
in . The noiseless version of the problem, with exact line measurements,
has been considered previously under the general title of parallel rigidity
theory, mainly in order to characterize the conditions for unique realization
of locations. For noisy pairwise line measurements, current methods tend to
produce spurious solutions that are clustered around a few locations. This
sensitivity of the location estimates is a well-known problem in SfM,
especially for large, irregular collections of images.
In this paper we introduce a semidefinite programming (SDP) formulation,
specially tailored to overcome the clustering phenomenon. We further identify
the implications of parallel rigidity theory for the location estimation
problem to be well-posed, and prove exact (in the noiseless case) and stable
location recovery results. We also formulate an alternating direction method to
solve the resulting semidefinite program, and provide a distributed version of
our formulation for large numbers of locations. Specifically for the camera
location estimation problem, we formulate a pairwise line estimation method
based on robust camera orientation and subspace estimation. Lastly, we
demonstrate the utility of our algorithm through experiments on real images.Comment: 40 pages, 12 figures, 6 tables; notation and some unclear parts
updated, some typos correcte
Algorithms for detecting dependencies and rigid subsystems for CAD
Geometric constraint systems underly popular Computer Aided Design soft-
ware. Automated approaches for detecting dependencies in a design are critical
for developing robust solvers and providing informative user feedback, and we
provide algorithms for two types of dependencies. First, we give a pebble game
algorithm for detecting generic dependencies. Then, we focus on identifying the
"special positions" of a design in which generically independent constraints
become dependent. We present combinatorial algorithms for identifying subgraphs
associated to factors of a particular polynomial, whose vanishing indicates a
special position and resulting dependency. Further factoring in the Grassmann-
Cayley algebra may allow a geometric interpretation giving conditions (e.g.,
"these two lines being parallel cause a dependency") determining the special
position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract
based on v1
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