4,847 research outputs found
A fixed-parameter tractable algorithm for combinatorial filter reduction
What is the minimal information that a robot must retain to achieve its task?
To design economical robots, the literature dealing with reduction of
combinatorial filters approaches this problem algorithmically. As lossless
state compression is NP-hard, prior work has examined, along with minimization
algorithms, a variety of special cases in which specific properties enable
efficient solution. Complementing those findings, this paper refines the
present understanding from the perspective of parameterized complexity. We give
a fixed-parameter tractable algorithm for the general reduction problem by
exploiting a transformation into minimal clique covering. The transformation
introduces new constraints that arise from sequential dependencies encoded
within the input filter -- some of these constraints can be repaired, others
are treated through enumeration. Through this approach, we identify parameters
affecting filter reduction that are based upon inter-constraint couplings
(expressed as a notion of their height and width), which add to the structural
parameters present in the unconstrained problem of minimal clique covering.Comment: 8 pages, 4 figure
Catalog Matching with Astrometric Correction and its Application to the Hubble Legacy Archive
Object cross-identification in multiple observations is often complicated by
the uncertainties in their astrometric calibration. Due to the lack of standard
reference objects, an image with a small field of view can have significantly
larger errors in its absolute positioning than the relative precision of the
detected sources within. We present a new general solution for the relative
astrometry that quickly refines the World Coordinate System of overlapping
fields. The efficiency is obtained through the use of infinitesimal 3-D
rotations on the celestial sphere, which do not involve trigonometric
functions. They also enable an analytic solution to an important step in making
the astrometric corrections. In cases with many overlapping images, the correct
identification of detections that match together across different images is
difficult to determine. We describe a new greedy Bayesian approach for
selecting the best object matches across a large number of overlapping images.
The methods are developed and demonstrated on the Hubble Legacy Archive, one of
the most challenging data sets today. We describe a novel catalog compiled from
many Hubble Space Telescope observations, where the detections are combined
into a searchable collection of matches that link the individual detections.
The matches provide descriptions of astronomical objects involving multiple
wavelengths and epochs. High relative positional accuracy of objects is
achieved across the Hubble images, often sub-pixel precision in the order of
just a few milli-arcseconds. The result is a reliable set of high-quality
associations that are publicly available online.Comment: 9 pages, 9 figures, accepted for publication in the Astrophysical
Journa
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