Scan matching in the Hough domain

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Scan matching in the Hough domain

• Andrea Censi, Luca Iocchi, Giorgio Grisetti
• lastname _at_ dis.uniroma1.it
• www.dis.uniroma1.it/lastname

SIED Lab www.dis.uniroma1.it/multirob/sie
d/
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Scan matching

• 2D scan matching (geometric interpretation) find
  a rotation ? and a translation T who maximize
  overlapping of two sets of 2D data.
• 2D scan matching (probabilistic interpretation)
  approximate a pdf of the robot pose ex
  p(xtxt-1, ut-1, yt, yt-1) or others...

Map portion
Sensor scan
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Previous research

• Existing methods differ by
• assumptions about environment (ex features?)
• assumptions about sensing devices (noise, FOV)
• assumptions about the search domain (local vs.
  global)
• representation of uncertainty (multi-hypothesis,
  continuous pdf)
• Methods performing a local search
• features based ex Guttman 96, Lingemann 04
• ICP family Lu-Milios 94, several
  extensions/optimizations
• gradient-based iterative methods ex Hähnel 02,
  Biber 03
• Methods performing a global search
• feature based many ex us, 2002
• histogram of surface angles ex Weiß 94
• extensive search 2D correlation Konolige-Chou
  99

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Hough Scan Matching (HSM)

• Our approach
• works in unstructured environments and with noisy
  range finders (we dont do feature detection,
  we work with features distributions)
• global search (but if a guess is available, it
  performs efficient local search) and
  multi-modality (detects ambiguities)
• completeness if an exact match exists, it will
  be included in the solution set (works in
  practice with very different data).
• Algorithm. Given reference and sensor data
• compute the Hough Transform (HT) for both
• compute the Hough Spectrum (HS) from the HT
• find hypotheses for ? via the cross-correlation
  of the HS
• given an estimate ?, estimate T via
  cross-correlation of the HT

andrea decoupling
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7 - The Hough Transform (HT)

• The simplest HT transforms the cartesian space
  X-Y into the Hough Domain (?, ?). The straight
  line
• cos(?)xsin(?)y r
• corresponds to point (? , r) in the Hough Domain.

Andrea Censi si può fare in modo formale
?
r
?
HT
r
?
?
(x,y) cartesian plane
Hough Domain (?, ?)
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7 - The Hough Transform (HT)

• A point in the cartesian plane ? a sinusoid in
  the Hough domain
• Sinusoids of collinear points intersects.

Andrea Censi si può fare in modo formale
?
?
Cartesian plane (x,y).
Hough Domain (?, ?)
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Feature detection with the HT
andrea in you algorithm
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Expressiveness of the HT
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Definition of Hough Spectrum

• We compute a spectrum from the Hough Transform
  (applying a translation-invariant functional g to
  the columns of the HT)

i
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Hough Spectrum properties

• it is invariant to input translation
• it shifts on input rotation

Andrea Censi anche alla scala
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HSM finding the rotation ?

• The spectrum of an input transformed by (?,Tx,Ty)
  is shifted by ? regardless of T we can estimate
  ? by correlating the two spectra.

?
T
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Handling ambiguities

• Multi-modal global search can detect ambiguities

multiple hypotheses for ?
Input data
Hough spectrum
result of correlation
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Comparison with circular histogram

• The histogram of surface angles has similar
  properties, but
• HS works with noisier data (does not need
  orientation information)
• HS can handle cases when the circular histogram
  fails. Example

Andrea Censi anche alla scala
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HSM estimating T
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HSM how to estimate T

• Given an estimate of ? , we can get linear
  constraints for T comparing columns of the HT
  (directions of alignment). We choose the
  directions with higher expected energy peaks of
  the spectrum.

T
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Example with real data
Map portion
Laser scan
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Summary

• Operating in the Hough space allows to decouple
  the search of the rotation ? from the translation
  (3D search ? 3 x 1D searches )
• Does not rely on the existence of features.
• Multi-modal and global search (efficient local
  search).
• Experimental simulation results
• Good results in curved enviroments if sensor is
  accurate.
• Reliability to different kinds of sensor noise
  (except for high discretization).
• Future (hard) work extension to 3D for dealing
  with 3D noisy sensors (stereo camera).

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Thanks for your attention

• Slides and an extended version of the paper
  available at www.dis.uniroma1.it/censi

Andrea Censi, Luca Iocchi, Giorgio
Grisetti lastname _at_ dis.uniroma1.it www.dis.unirom
a1.it/lastname