54,571 research outputs found

    Computing largest circles separating two sets of segments

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    A circle CC 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 Ω(n2)\Omega(n^2) 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

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    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.

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    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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