32,272 research outputs found
Arcfinder: An algorithm for the automatic detection of gravitational arcs
We present an efficient algorithm designed for and capable of detecting
elongated, thin features such as lines and curves in astronomical images, and
its application to the automatic detection of gravitational arcs. The algorithm
is sufficiently robust to detect such features even if their surface brightness
is near the pixel noise in the image, yet the amount of spurious detections is
low. The algorithm subdivides the image into a grid of overlapping cells which
are iteratively shifted towards a local centre of brightness in their immediate
neighbourhood. It then computes the ellipticity for each cell, and combines
cells with correlated ellipticities into objects. These are combined to graphs
in a next step, which are then further processed to determine properties of the
detected objects. We demonstrate the operation and the efficiency of the
algorithm applying it to HST images of galaxy clusters known to contain
gravitational arcs. The algorithm completes the analysis of an image with
3000x3000 pixels in about 4 seconds on an ordinary desktop PC. We discuss
further applications, the method's remaining problems and possible approaches
to their solution.Comment: 12 pages, 12 figure
Automated Generation of Geometric Theorems from Images of Diagrams
We propose an approach to generate geometric theorems from electronic images
of diagrams automatically. The approach makes use of techniques of Hough
transform to recognize geometric objects and their labels and of numeric
verification to mine basic geometric relations. Candidate propositions are
generated from the retrieved information by using six strategies and geometric
theorems are obtained from the candidates via algebraic computation.
Experiments with a preliminary implementation illustrate the effectiveness and
efficiency of the proposed approach for generating nontrivial theorems from
images of diagrams. This work demonstrates the feasibility of automated
discovery of profound geometric knowledge from simple image data and has
potential applications in geometric knowledge management and education.Comment: 31 pages. Submitted to Annals of Mathematics and Artificial
Intelligence (special issue on Geometric Reasoning
Wavelet-based cross-correlation analysis of structure scaling in turbulent clouds
We propose a statistical tool to compare the scaling behaviour of turbulence
in pairs of molecular cloud maps. Using artificial maps with well defined
spatial properties, we calibrate the method and test its limitations to
ultimately apply it to a set of observed maps. We develop the wavelet-based
weighted cross-correlation (WWCC) method to study the relative contribution of
structures of different sizes and their degree of correlation in two maps as a
function of spatial scale, and the mutual displacement of structures in the
molecular cloud maps. We test the WWCC for circular structures having a single
prominent scale and fractal structures showing a self-similar behavior without
prominent scales. Observational noise and a finite map size limit the scales
where the cross-correlation coefficients and displacement vectors can be
reliably measured. For fractal maps containing many structures on all scales,
the limitation from the observational noise is negligible for signal-to-noise
ratios >5. (abbrev). Application of the WWCC to the observed line maps of the
giant molecular cloud G333 allows to add specific scale information to the
results obtained earlier using the principle component analysis. It confirms
the chemical and excitation similarity of CO and CO on all
scales, but shows a deviation of HCN at scales of up to 7' (~7 pc). This can be
interpreted as a chemical transition scale. The largest structures also show a
systematic offset along the filament, probably due to a large-scale density
gradient. The WWCC can compare correlated structures in different maps of
molecular clouds identifying scales that represent structural changes such as
chemical and phase transitions and prominent or enhanced dimensions.Comment: 26 pages, 41 figures, accepted to A&
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