| 58 | | astrometry} task is to calibrate the astrometry of an image using |
| 59 | | only the image itself. The broad goal of the \an project was to build |
| 60 | | a system that would allow us to create correct, standards-compliant |
| 61 | | astrometric \metadata for every useful astronomical image ever taken, |
| 62 | | past and future, in any state of archival disarray. This is part of a |
| 63 | | larger effort to organize, annotate and make searchable all the |
| 64 | | world's astronomical information. |
| 65 | | |
| | 58 | astrometric calibration} task is to calibrate an image using only the |
| | 59 | image itself. The broad goal of the \an project was to build a system |
| | 60 | that would allow us to create correct, standards-compliant astrometric |
| | 61 | \metadata for every useful astronomical image ever taken, past and |
| | 62 | future, in any state of archival disarray. This is part of a larger |
| | 63 | effort to organize, annotate and make searchable all the world's |
| | 64 | astronomical information. |
| 806 | | \subsection{The astrometry problem} |
| | 805 | \section{Astrometric calibration as a pattern recognition task} |
| | 806 | |
| | 807 | |
| | 808 | \comment{ |
| | 809 | wget "http://casjobs.sdss.org/ImgCutoutDR7/getjpeg.aspx?ra=166.45&dec=-0.03&scale=1&opt=&width=2000&height=2000" -O ngc3521-orig.jpg |
| | 810 | jpegtopnm ngc3521-orig.jpg | pnmrotate -45 | pnmcut 600 900 1400 1000 | pnmscale -reduce 2 | pnmtojpeg > ngc3521.jpg |
| | 811 | #---> http://live.astrometry.net/status.php?job=alpha-200906-68444159 |
| | 812 | jpegtopnm ngc3521.jpg | ppmtopgm | pnminvert | pnmtojpeg > ngc3521-bw.jpg |
| | 813 | wget "http://live.astrometry.net/status.php?job=alpha-200906-36181848&get=field.xy.fits" -O ngc3521.xy |
| | 814 | wget "http://live.astrometry.net/status.php?job=alpha-200906-36181848&get=index.xy.fits" -O ngc3521-index.xy |
| | 815 | jpegtopnm ngc3521-bw.jpg | plotxy -N 100 -i ngc3521.xy -I - -x 1 -y 1 -C black -b white > ngc3521-sources.png |
| | 816 | jpegtopnm ngc3521-bw.jpg | plotxy -N 100 -i ngc3521.xy -I - -x 1 -y 1 -C black -b white -P | plotxy -I - -i ngc3521-index.xy -x 1 -y 1 -C black -b white -s crosshair -P | plot-constellations -f 18 -w ngc3521.wcs -i - -N -o ngc3521-index.png |
| | 817 | %%% wget "http://live.astrometry.net/status.php?job=alpha-200906-36181848&get=wcs.fits" -O ngc3521.wcs |
| | 818 | %%% scp gmaps:/data2/test-merc/tycho.mkdt.fits . |
| | 819 | wget "http://explore.astrometry.net/tile/get/?layers=tycho,grid,userboundary&arcsinh&wcsfn=alpha/200906/36181848/wcs.fits&gain=-0.5&bb=0,-85,360,85&dashbox=0.1&w=500&h=500&lw=3" -O ngc3521-zoom0.png |
| | 820 | wget "http://explore.astrometry.net/tile/get/?layers=tycho,grid,userboundary&arcsinh&wcsfn=alpha/200906/36181848/wcs.fits&gain=-1&bb=175.533,-17.7621663832,211.533,17.6598478619&dashbox=0.01&w=500&h=500&lw=3" -O ngc3521-zoom1.png |
| | 821 | wget "http://explore.astrometry.net/tile/get/?layers=tycho,grid,userboundary&arcsinh&wcsfn=alpha/200906/36181848/wcs.fits&gain=0.5&bb=191.733,-1.85338140354,195.333,1.74602498613&w=500&h=500&lw=3" -O ngc3521-zoom2.png |
| | 822 | for x in 0 1 2; do |
| | 823 | pngtopnm ngc3521-zoom${x}.png | ppmtopgm | pnminvert | pnmtopng > ngc3521-zoom${x}-bw.png; |
| | 824 | done |
| | 825 | } |
| | 826 | |
| 828 | | \caption{Top: input image (Copyright Volker Wendel, \texttt{http://www.spiegelteam.de/}). |
| 829 | | Middle: sources extracted from the image. |
| 830 | | Bottom: reference sources, transformed into the image coordinate system (green squares). |
| 831 | | Observe that while many of the image and reference sources are aligned, there are |
| 832 | | many image sources without reference sources, and at least one reference source without |
| 833 | | an image source.} |
| 834 | | \label{redgreen} |
| | 849 | \caption{\captionpart{Top:} Input image (credit: Sloan Digital Sky |
| | 850 | Survey). \captionpart{Middle:} The brightest 100 sources extracted |
| | 851 | from the image. \captionpart{Bottom:} Reference sources, transformed |
| | 852 | into the image coordinate system (crosshairs). Many of the image and |
| | 853 | reference sources are aligned, but there are many image sources |
| | 854 | without reference sources. Our system knows about the positions of |
| | 855 | many objects of interest on the sky, and has labelled the galaxy NGC |
| | 856 | 3521.\label{fig:redgreen}} |
| 852 | | \emph{Astrometry} refers to the measurement of the positions and |
| 853 | | motions of celestial bodies. |
| 854 | | |
| 855 | | For modern astronomers, astrometry is often one of the first steps |
| 856 | | toward getting useful information out of an image of the sky. |
| 857 | | Aligning a new image with an \emph{astrometric reference catalog} |
| 858 | | (``solving the astrometry'' of the image) allows the astronomer to |
| 859 | | place the image within a standard coordinate frame. This allows |
| 860 | | stars, galaxies, and other objects (\emph{sources}) in the new image |
| 861 | | to be identified with known sources (which in turn allows astronomers |
| 862 | | to calibrate other properties of the new image), and allows the |
| 863 | | positions of new sources to be described in a meaningful way. |
| 864 | | |
| 865 | | |
| 866 | | Several astrometric reference catalogs exist: one of the largest is |
| 867 | | the USNO-B1.0 catalog, created by the United States Navy Observatory, |
| 868 | | which contains position, motion, and brightness information for over |
| 869 | | one billion objects \cite{usnob,nomad}. |
| 870 | | |
| 871 | | \emph{Blind astrometry} describes the problem of solving the |
| 872 | | astrometry of an image given only the image itself. |
| 873 | | |
| 874 | | % This is equivalent to determining which stars are contained in the image. |
| 875 | | |
| 876 | | As part of the \an project, we are attempting to solve the blind |
| 877 | | astrometry problem for ``every useful astronomical image ever taken, |
| 878 | | past and future, in any state of archival disarray''\cite{an}. As |
| | 877 | For modern astronomers, astrometric calibration is often one of the |
| | 878 | first steps toward getting useful information out of an image of the |
| | 879 | sky. Aligning a new image with an \emph{astrometric reference |
| | 880 | catalog} allows the astronomer to place the image within a standard |
| | 881 | coordinate frame. This allows stars, galaxies, and other objects |
| | 882 | (\emph{sources}) in the new image to be identified with known sources, |
| | 883 | which in turn allows astronomers to calibrate other properties of the |
| | 884 | new image, and allows the positions of new sources to be described in |
| | 885 | a standard reference frame. |
| | 886 | |
| | 887 | |
| | 888 | The task of blind astrometric calibration---automatically finding the |
| | 889 | astrometric calibration of an image, using only the information in the |
| | 890 | image pixels---can be seen as a pattern recognition problem. As |
| 882 | | solve, but one with practical implications for astronomers. Figures |
| 883 | | \ref{redgreen} and \ref{onthesky} show sample results. Given an input |
| 884 | | image, we do some image processing to find sources such as stars and |
| 885 | | galaxies. We build geometric features from these sources and search |
| 886 | | for matching features in a large index. Our approach will be |
| 887 | | described more fully in section \ref{ourapproach}. |
| 888 | | |
| 889 | | |
| 890 | | The blind astrometry problem is challenging for several reasons. |
| 891 | | First, a typical astronomical image covers a tiny fraction of the sky: |
| 892 | | the example image shown above covers about one millionth of the sky. |
| 893 | | Second, both the input image and the reference catalog have positional |
| 894 | | noise-- errors in the measured positions of sources due to turbulence |
| 895 | | of the atmosphere, distortion from the telescope optics, and image |
| 896 | | sensor noise. Third, the input image measures an unknown portion of |
| 897 | | the electromagnetic spectrum (\emph{bandpass}). In many cases filters |
| 898 | | have been used to isolate a narrow window of the spectrum. This |
| 899 | | limits our ability to make use of the brightness of objects, since |
| 900 | | brightness in one band of the spectrum does not imply brightness (or |
| 901 | | even visibility) in another band. Most reference catalogs measure |
| 902 | | brightness in only two or three bands. Fourth, the input image and |
| 903 | | reference catalog have different effective exposure times, so a source |
| 904 | | visible in one may be below the detection threshold in the other. |
| 905 | | Finally, the input image can have nonlinear distortion due to the |
| 906 | | optical properties of the telescope. These distortions are often |
| 907 | | modelled as polynomials up to fourth order, though higher orders are |
| 908 | | occasionally needed. |
| 909 | | |
| 910 | | |
| | 894 | solve, but one with practical implications for astronomers. |
| | 895 | |
| | 896 | |
| | 897 | For the purposes of astrometric calibration, we can think of the sky |
| | 898 | as a large two-dimensional surface: the stars are very distant, so our |
| | 899 | viewpoint is effectively fixed. We are moving, as are the stars, but |
| | 900 | these motions are small relative to the precision at which we |
| | 901 | typically work. The sky contains many stars, galaxies, and other |
| | 902 | astronomical sources. The stars and distant galaxies are effectively |
| | 903 | point sources, while closer galaxies can be resolved. Astrometric |
| | 904 | reference catalogs list the positions, motions, and brightnesses of |
| | 905 | these sources and serve as the ``ground truth'' or database of known |
| | 906 | (reference) objects. The USNO-B1 catalog \cite{usnob, nomad}, for |
| | 907 | example, lists over one billion objects. As many as a few percent of |
| | 908 | these are false detections or other artifacts \cite{barroncleaning}, |
| | 909 | and some objects that should be visible are missing. |
| | 910 | |
| | 911 | |
| | 912 | The images to be recognized are subregions of the sky. Image sizes |
| | 913 | range from nearly half the celestial sphere down to $10^{-7}$ of the |
| | 914 | area and smaller. The input images measure unknown bands of the |
| | 915 | electromagnetic spectrum, and various nonlinear functions may have |
| | 916 | been applied to the pixel values. We cannot rely on absolute |
| | 917 | brightness or color to recognize individual stars or galaxies. At |
| | 918 | best we can hope that there is some positive correlation in the |
| | 919 | relative brightness ordering of objects in the image and the |
| | 920 | corresponding objects in our catalog. |
| | 921 | |
| | 922 | |
| | 923 | Blind astrometric calibration is an ideal task for exploring geometric |
| | 924 | ideas in pattern recognition. Most celestial objects are effectively |
| | 925 | point sources, and can be found and localized to sub-pixel accuracy |
| | 926 | using relatively simple image-processing procedures. But since the |
| | 927 | individual features are characterized only by their positions and |
| | 928 | brightnesses, we must examine collections of features in order to |
| | 929 | build distinctive patterns. In \chapref{chap:techreport} we present |
| | 930 | \an, which applies the geometric hashing framework to the task of |
| | 931 | blind astrometric calibration. An example of our results in shown in |
| | 932 | \figs \ref{fig:redgreen} and \ref{fig:onthesky}. |
| | 933 | |
| | 934 | |
| | 935 | \comment{ |
| 961 | | \begin{center} |
| 962 | | \includegraphics[width=3.3in]{moon} \\ |
| 963 | | \includegraphics[width=3.3in]{saturated} |
| 964 | | \end{center} |
| 965 | | \caption{Astronomical images with occlusion. Top: the moon occludes the stars |
| 966 | | behind it (image copyright Johannes Schedler, \texttt{http://panther-observatory.com}). Bottom: |
| 967 | | saturation and diffraction spikes due to bright objects can obscure nearby objects.} |
| | 976 | \begin{center} |
| | 977 | %\begin{tabular}{c@{\hspace{1pt}}c@{\hspace{1pt}}c} |
| | 978 | \includegraphics[width=\figunit]{moon} \\ |
| | 979 | \includegraphics[width=\figunit]{saturated} |
| | 980 | %\end{tabular} |
| | 981 | \end{center} |
| | 982 | \caption{Astronomical images with occlusion. \captionpart{Top:} The |
| | 983 | moon, buildings, and mountains occlude the stars behind them (image |
| | 984 | copyright Johannes Schedler, \texttt{http://panther-observatory.com}). |
| | 985 | \captionpart{Bottom:} Saturation and diffraction spikes due to bright |
| | 986 | objects can obscure nearby objects.} |
| 970 | | |
| 971 | | The blind astrometry problem can be seen as a somewhat peculiar visual |
| 972 | | pattern recognition problem. The images to be recognized are |
| 973 | | subregions of a large two-dimensional surface (for our purposes). On |
| 974 | | this dark surface are many luminous objects, many of which are |
| 975 | | effectively point sources, and some of which are extended or nebulous. |
| 976 | | Unlike many object recognition tasks, we do not have ready access to |
| 977 | | these objects, so we must use existing information in the form of an |
| 978 | | astrometric reference catalog compiled by astronomers. The number of |
| 979 | | objects listed in the catalog is of order $10^9$, but as many as a few |
| 980 | | percent are false detections or other artifacts, and some objects that |
| 981 | | should be visible are missing. |
| 982 | | |
| 983 | | %The cameras that generate the images which we are to recognize have unknown wavelength |
| 984 | | %bandpasses and various nonlinear functions may have been applied to the pixel values. |
| 985 | | % |
| 986 | | The input images measure unknown bands of the electromagnetic |
| 987 | | spectrum, and various nonlinear functions may have been applied to the |
| 988 | | pixel values. We cannot therefore rely on absolute brightness or |
| 989 | | color. At best we can hope that there is some positive correlation in |
| 990 | | the relative brightness ordering of objects in the image and the |
| 991 | | corresponding objects in our catalog. |
| 992 | | |
