Transcript Scan matching in the Hough domain

Università La Sapienza
Rome, Italy
Scan matching
in the Hough domain
Andrea Censi, Luca Iocchi, Giorgio Grisetti
lastname @ dis.uniroma1.it
www.dis.uniroma1.it/~lastname
SIED Lab
www.dis.uniroma1.it/~multirob/sied/
Scan matching
• 2D scan matching (geometric interpretation): find a rotation
 and a translation T who maximize overlapping of two
sets of 2D data.
Map portion
Sensor scan
• 2D scan matching (probabilistic interpretation):
approximate a pdf of the robot pose; ex: p(xt|xt-1, ut-1, yt, yt1)
or others...
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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]
– A.
extensive
correlation [Konolige-Chou ‘99]
Censi, L. search:
Iocchi, G.2D
Grisetti
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Hough Scan Matching (HSM)
• Our approach:
– works in unstructured environments and with noisy
range finders (we don’t 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
– A.
given
an estimate , estimate T via cross-correlation4 of
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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()x+sin()y = r
corresponds to point ( , r) in the Hough Domain.

r

HT
r


(x,y) cartesian plane
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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.


Cartesian plane (x,y).
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Hough Domain (, )
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Feature detection with the HT
HT


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Expressiveness of the HT
HT

HT-1
“features distributions”

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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)
HT[i]
i
HT
HSg[i]
g
• The spectrum is a a
function of  with 180°
period.
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Hough Spectrum properties
• it is invariant to input translation
• it shifts on input rotation

T
T

(same spectrum)
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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.
HSg[i’]
HSg[i]

T
cross
correlation

+180
°
The peaks of the cross correlation are estimates for .
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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.
result of
Example:
Input data
correlation
histogram
of surface
angles
Hough
spectrum
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HSM: estimating T
translation T
T
HT
HT



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|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.
linear
constraints
d
d'
T
d'
Td
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~ p(T| )
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Example with real data
Map portion
First solution (exact)
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Laser scan
Second solution
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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
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L. Iocchi,
G. Grisetti
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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 @ dis.uniroma1.it
www.dis.uniroma1.it/~lastname
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