54,571 research outputs found
Computing largest circles separating two sets of segments
A circle separates two planar sets if it encloses one of the sets and its
open interior disk does not meet the other set. A separating circle is a
largest one if it cannot be locally increased while still separating the two
given sets. An Theta(n log n) optimal algorithm is proposed to find all largest
circles separating two given sets of line segments when line segments are
allowed to meet only at their endpoints. In the general case, when line
segments may intersect times, our algorithm can be adapted to
work in O(n alpha(n) log n) time and O(n \alpha(n)) space, where alpha(n)
represents the extremely slowly growing inverse of the Ackermann function.Comment: 14 pages, 3 figures, abstract presented at 8th Canadian Conference on
Computational Geometry, 199
Spectral Consequences of Deviation from Spherical Composition Symmetry in Type Ia Supernovae
We investigate the prospects for constraining the maximum scale of clumping
in composition that is consistent with observed Type Ia supernova flux spectra.
Synthetic spectra generated without purely spherical composition symmetry
indicate that gross asymmetries make prominent changes to absorption features.
Motivated by this, we consider the case of a single unblended line forming in
an atmosphere with perturbations of different scales and spatial distributions.
Perturbations of about 1% of the area of the photodisk simply weaken the
absorption feature by the same amount independent of the line of sight.
Conversely, perturbations of about 10% of the area of the photodisk introduce
variation in the absorption depth which does depend on the line of sight. Thus,
1% photodisk area perturbations may be consistent with observed profile
homogeneity but 10% photodisk area perturbations can not. Based on this, we
suggest that the absence of significant variation in the depths of Si II 6355
absorption features in normal Type Ia spectra near maximum light indicates that
any composition perturbations in these events are quite small. This also
constrains future three-dimensional explosion models to produce ejecta profiles
with only small scale inhomogeneities.Comment: 11 pages, 6 figure
Enhanced tracking and recognition of moving objects by reasoning about spatio-temporal continuity.
A framework for the logical and statistical analysis and annotation of dynamic scenes containing occlusion and other uncertainties is presented. This framework consists
of three elements; an object tracker module, an object recognition/classification module and a logical consistency, ambiguity and error reasoning engine. The principle behind the object tracker and object recognition modules is to reduce error by increasing ambiguity (by merging objects in close proximity and presenting multiple
hypotheses). The reasoning engine deals with error, ambiguity and occlusion in a unified framework to produce a hypothesis that satisfies fundamental constraints
on the spatio-temporal continuity of objects. Our algorithm finds a globally consistent model of an extended video sequence that is maximally supported by a voting function based on the output of a statistical classifier. The system results
in an annotation that is significantly more accurate than what would be obtained
by frame-by-frame evaluation of the classifier output. The framework has been implemented
and applied successfully to the analysis of team sports with a single
camera.
Key words: Visua
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