Making the Sky Searchable: Solving the Blind Astrometry Problem

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Making the Sky Searchable Solving the Blind
Astrometry Problem

• Dustin Lang, Sam Roweis Keir Mierle
• University of Toronto
• David Hogg Michael Blanton
• New York University

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Basic Problem

• You show me a picture of the night sky.
• I tell you where on the sky it came from.

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Rules of the game

• We start with a catalogue of stars in the sky,
  and from it build an index which is used to
  assist us in locating (solving) new test images.

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Rules of the game

• We start with a catalogue of stars in the sky,
  and from it build an index which is used to
  assist us in locating (solving) new test images.

• We can spend as much time as we want building the
  index but solving should be fast.
• Challenges1) The sky is big.2) Both catalogues
  and pictures are noisy.

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Distractors and Dropouts

• Bad newsQuery images may contain some extra
  stars that are not in your index catalogue, and
  some catalogue stars may be missing from the
  image.

• These distractors dropouts mean that naïve
  matching techniques will not work.

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You try
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You try
Hint 1 Missing stars.
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You try
Hint 1 Missing stars.
Hint 2 Extra stars.
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You try
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Solving the search problem

• This is a huge search problem.
• Exhaustive search? Ha!
• There are millions of patches of the scale of a
  typical test image on the sky, plus rotation.

?
The Sky is Big
TM
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Index of Features

• We define features that can be extracted from
  any particular view of the sky (image).
• Our index is a specially chosen subset of the
  features that exist in the catalogue, along with
  a record of the place on the sky each feature
  came from.
• We target each index at a particular range of
  image scales.

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Matching a test image

• When we see a new test image, we compute which
  features are present, and use our index to look
  up which possible views from the catalogue also
  have those features.
• Each feature generates a list of places on the
  sky from which the test image may have come.

The features in our index actas hash codes for
locations on the sky.
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Caching Computation

• The idea of an index is that is pushes the
  computation from search time back to index
  construction time.
• We actually do perform an exhaustive search of
  sorts, but it happens during the building of the
  index and not at search time, so queries can
  still be fast.

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Robust Features for Geometric Hashing

• In simple search domains like text, the indexing
  idea can be applied directly.
• However, in our star matching task, the features
  we chose must be invariant to scale, rotation and
  translation.
• They must also be robust to small positional
  noise.
• Finally, there is the additional problem of
  distractor dropout stars.

The features we use are the relative
positions of nearby quadruples of stars.
(quads)
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Quads as Robust Features

• We encode the relative positions of nearby
  quadruples of stars (ABCD) using a coordinate
  system defined by the most widely separated pair
  (AB).
• Within this coordinate system, the positions of
  the remaining two stars form a 4-dimensional code
  for the shape of the quad.
• Swapping AB or CD reflects the code
  degeneracy.
• We require C,D to lie in the circle with diameter
  AB.

B
C
D
A
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Quads as Robust Features

• This geometric hash code is invariant to scale,
  translationand rotation.
• It has good positional noise properties.
• It also has the property that if stars are
  uniformly distributedin space, codes are
  uniformly distributed in 4D.

B
C
D
A
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Catalogues USNO-B 1.0 TYCHO-2

• USNO-B is an all-sky catalogue compiled from
  scans of old Schmidt plates.Contains about 109
  objects, both stars and galaxies.
• TYCHO-2 is a tiny subset of 2.5Mbrightest stars.

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Making a uniform catalogue

• Starting with USNO TYCHO we cut to get a
  spatially uniform set of the 150M brightest
  stars galaxies.
• We lay down a fine grid and take the brightest K
  objects in each square.
• We split the sky into 12 bite-sized chunks
  (healpixes).

Star density (heat map)
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Building the index

• Start with the cut catalogue.
• Place a fine grid on the sky.
• Within each pixel, identify a valid quad made of
  bright stars whose size is within the target
  range of the index.
• Compute 4D codes for those quads enter them into
  the index along with their original locations.
• Use kd-trees to do it quickly.

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A Typical Final Index

• 144M stars(6 quads/star)
• 205M quads (4-5 arcmin)
• 12 healpixes

Codes in4D
Quadson the sky
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Solving a new test image

• Identify objects (starsgalaxies) in the image
  and create a list of their 2D positions.
• Cycle through all possible valid quads (brightest
  first) and compute their corresponding codes.
• Look up the codes in the index to find matches
  within some tolerance this stage incurs some
  false positive and false negative matches.
• Each code match represents a candidate position,
  rotation and scale on the sky. As soon as N quads
  agree on a candidate, we proceed to verify that
  candidate, using all objects in the image.

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A Real Example from SDSS
Query image(after object detection).
An all-sky catalogue.
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A Real Example from SDSS
Query image(after object detection).
Zoomed in by a factor of 1 million.
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A Real Example from SDSS
Query image(after object detection).
The objects in our index.
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A Real Example from SDSS
All the quads in our index whichare present in
the query image.
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A Real Example from SDSS
A single quad which we happened to try.
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A Real Example from SDSS
The query image scaled, translated rotated as
specified by the quad.
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A Real Example from SDSS
The proposed match, on which we run verification.
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A Real Example from SDSS
The verified answer, overlaid on the original
catalogue.
The proposed match, on which we run verification.
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Final Verification

• After finding N quads that agree about where they
  came from on the sky, we run a slower
  verification process
• Project each object in the test image onto the
  sky according to the matched quad
• Count how many objects in the test image are
  close to objects in the index.
• Simple, but it works.

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Preliminary Results SDSS

• The Sloan Digital Sky Survey (SDSS) covers 1/4 of
  the sky at high resolution in five different
  wavelengths.
• The 2.5 m telescope is located at Apache Point
  Observatory.
• 120 MP, liquid nitrogen cooled camera.
• Fields are 14x9arcmin (10-6 of the sky),
  2048x1361 pixels.

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Preliminary Results SDSS

• 336,554 fieldsscience grade
• 0 false positives
• 99.84 solved 530 unsolved
• 99 solve by looking at just the 60 brightest
  objects

Assume the pixel scale is known to within 5 (to
speed up solving)
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Preliminary Results GALEX

• GALEX is a space-based telescope, seeing only in
  the ultraviolet.
• It was launched in April 2003 by CaltechNASA and
  is just about finished collecting data now.
• It takes huge (80 arcmin) circular fields with
  5arcsec resolution and spectraof all objects.

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Preliminary Results GALEX

• GALEX NUV (near-UV) fields can be solved easily
  using an index built from bright blue USNO stars.

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Preliminary Results GALEX

• GALEX FUV (far-UV) fields are much harder to
  solve using USNO as a source catalogue.

Frequency band(s) of the test images must have
substantial overlap with those of the catalogue.
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Speed/Memory/Disk
SDSS

• Indexing takes 12 hours, uses 2 GB of memory
  and 100 GB of disk.
• Solving a test image almost always takes (not includingobject detection).
• Solving many fields is done by coarse
  parallelization on about 100 shared CPUs.

All the work is in the hardest 10 of fields
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Applications

• Live on the web provide the solver as a service
  to astronomers.
• Monitor telescopes in real time ensure that the
  images and headers make sense.
• Merge large catalogues allow searches for all
  images that cover a region fix up existing
  catalogues.
• Collaborative observing let astronomers add
  their own images to the archive and communicate
  with each other.
• Historical images bring in, eg, the Harvard
  Photographic Plate Archive 500,000 glass plates
  taken 1880-1990.
• Amateur astronomers currently a huge but
  untapped resource for professional astronomers!

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Thanks!

• Time for questions!