Next: A System for Web-based Access to the HSOS Database
Up: Software Applications
Previous: ATV: An Image-Display Tool for IDL
Table of Contents -
Subject Index -
Author Index -
Search -
PS reprint -
PDF reprint
Thiebaut, C. & Boër, M. 2001, in ASP Conf. Ser., Vol. 238, Astronomical Data Analysis Software and Systems X, eds. F. R. Harnden, Jr., F. A. Primini, & H. E. Payne (San Francisco: ASP), 388
A New Field-Matching Method for Astronomical Images
C. Thiebaut, M. Boër
Centre d'Etude Spatiale des Rayonnements (CESR-CNRS), BP
4346, 31028 Toulouse Cedex 4, France
Abstract:
We propose a new Field-Matching algorithm for astronomical images.
This new method is based on a multiresolution analysis. We tried
two cases: first, we compared the test image with a synthetic
image built from a point source catalog; second, we used a reference
image of the relevant portion of the sky. Structures of images are
obtained at different scales by applying the wavelet transform.
An appropriate thresholding of the wavelet coefficients gives the
significant pixels in the Wavelet Transform Space. In order to
compare the selected coefficients between the test and the reference
images we used a genetic algorithm. We applied this method on
images taken by the automatic TAROT (Rapid Action
Telescope for Transient Object) telescope. The reference data are
taken from the USNO-A2.0 Catalog and from the Digital Sky Survey.
The results are more robust and reliable than those obtained
with the FOCAS algorithm. Moreover, the new algorithm is faster
than FOCAS.
The field-matching consists in recognizing the field of an
image with unknown coordinates in a reference image taken from a catalog.
The existing field-matching methods, like FOCAS,
require good knowledge of the approximated centroïd position. We have
developed a new method of field-matching which takes into account
the geometrical characteristics of the test image and tries to compare these
characteristics with those of a reference image. To do this, we
use a multiresolution analysis which will give us the details of
the image at the different scales. First, we use Mallat's
analysis, which is anisotropic. Because the
images we study are quite isotropic (astronomical objects: stars,
galaxies etc.) we try to use an isotropic analysis too: the
``à trous'' algorithm. After having obtained the different wavelet
plans, we have to threshold the coefficients in order to keep the
most significant ones. The pixels we keep represent the image structure.
We obtain two structures that we match using a genetic algorithm.
It will give us the vertical and horizontal offsets between the two
structures and then, the offset between the two original images.
Thanks to a multiresolution analysis, we obtain the details of an
image at different scales by applying a wavelet transform.
Mallat introduced this concept in 1989, which led to the discrete
wavelet transform (Mallat, 1989).
Mallat's Analysis
This analysis is a non-redundant one because the amount of data
is divided by two at each scale: this is called a dyadic
analysis. In two dimensions, Mallat's analysis uses three
wavelets which leads to an anisotropic analysis. We obtain the
horizontal, diagonal and vertical details of the image at each
scale. We used the Daubechies wavelet of degree four. However,
the astronomical objects are usually isotropic and without privileged directions.
That is why we use the so called ``à trous'' algorithm (Starck et al. 1995).
The ``à trous'' Algorithm
This analysis is isotropic but redundant. The image is smoothed
on the different scales. Because of the redundancy, this
algorithm is not as fast as Mallat's algorithm.
When we have obtained the structures at the different scales, we
have to keep only the significant wavelet coefficients. Because
of the wavelet form, the best coefficients of Mallat's analysis
are the most negative and positive ones, whereas the best
coefficients of the ``à trous'' analysis are the most positive ones. As
a consequence, we take the absolute value of the wavelet plans
from the first analysis and we keep the 20 best coefficients of these
images. For the ``à trous'' analysis, we keep the 20 best
coefficients of the original wavelet plans.
At each scale and for each details image, we have 20 significant pixels. The set we obtain
is called the structure of the studied image. We apply one of the
algorithms on the test image and on the reference image and we
obtain two structures. Finally, we have to match both structures
and find the original offset between the two images.
To match both obtained structures we use a genetic algorithm (Houck et al. 1995).
These algorithms are inspired by natural evolution theory: they
maintain and manipulate a family or a population of solutions
and implement a ``survival of the fittest'' strategy in their
search for better solution. Those algorithms have been shown to
solve linear and nonlinear problems by exploring all regions of
the state space and exponentially exploiting promising areas
through mutation, crossover, and selection functions applied to
individuals in the population.
Here we want to find the vertical and horizontal offsets between
the two original images. The population of our algorithm is a
vertical and horizontal offset pair to apply to one of the
structures. The algorithm will converge to the best offset pair.
Taking into account the scale of the studied structure, we can
find the original offset by multiplying by the relevant factor.
We want to find the offset position between the astronomical
images taken by the automatic TAROT telescope (Boër et al. 2001) and a reference image. The reference image of a relevant
portion of the sky is an image taken from the Digitized Sky
Survey. The second reference image is built from the point source
catalog USNO-A2.0. The pixel image is convolved with a Gaussian
which represents the Point Spread Function of the TAROT telescope.
We made a Matlab implementation of the algorithms. For the
genetic algorithm, we took a population of 100 offset pairs, the
selection function was a tournament. We only used two crossover
and two mutation functions. With a convergence time of 40s, the
Mallat's analysis is faster than the ``à trous'' algorithm (120s).
We then decided to use the anisotropic method. We matched the
horizontal and vertical details images of the third scale.
Then, we compare the matching with the DSS images and the one
with the USNO-A2.0 catalog images. In Table 1, we give the original vertical
and horizontal offset, and those found after the convergence.
Finally, we show the results of the FOCAS method (matching with
the USNO catalog): we give the number of matched stars and the
number of stars found on the image.
For the DSS images, 30 images of 31 are matched. For the only
non-matched image, we took the structures of the second scale.
The new found offset is (
40,64), and
the matching is then done. For
the USNO images, only 13 of 31 images are matched.
The matching with the USNO images is not as good as the one with
DSS images, which is very good. In fact, a multiresolution
analysis is perhaps not well adapted to such constructed images, which
present no structure. We could apply the genetic algorithm
directly to the brightest objects of both images.
Nevertheless, the new method is faster and more robust than other
methods. It does not require a good knowledge of the centroïd
coordinates.
References
Boër, M. et al. 2001, this volume,
111
Valdes, F., Campusano, L., Velasquez, J., & Stetson, P. 1995, PASP, 107, 1119
Starck, J.-L., Murtagh, F., & Bijaoui, A. 1995,
in ASP Conf. Ser., Vol. 77, Astronomical Data Analysis
Software and Systems IV, ed. R. A. Shaw, H. E. Payne, & J. J. E. Hayes
(San Francisco: ASP), 279
Lega, E., Bijaoui, A., Alimi, J. M., & Scholl, H. 1996,
A&A, 309, 23
Houck, C., Joines, J., & Kay, M. 1995, NCSU-IE TR
95-09
Mallat, S. 1989, IEEE Trans on Pattern Anal. and
Math. Intel., 11, 7
© Copyright 2001 Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, California 94112, USA
Next: A System for Web-based Access to the HSOS Database
Up: Software Applications
Previous: ATV: An Image-Display Tool for IDL
Table of Contents -
Subject Index -
Author Index -
Search -
PS reprint -
PDF reprint
adass-editors@head-cfa.harvard.edu