università la sapienza rome, italy scan matching in the hough domain andrea censi, luca iocchi,...
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![Page 1: Università La Sapienza Rome, Italy Scan matching in the Hough domain Andrea Censi, Luca Iocchi, Giorgio Grisetti lastname @ dis.uniroma1.it](https://reader035.vdocuments.site/reader035/viewer/2022062407/56649d555503460f94a33024/html5/thumbnails/1.jpg)
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/
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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(xt|xt-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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• 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– given an estimate , estimate T via cross-correlation of
the HT
Hough Scan Matching (HSM)
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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.
(x,y) cartesian plane Hough Domain (, )
HT
r
r
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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). Hough Domain (, )
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HT
Feature detection with the HT
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Expressiveness of the HT
HT-1HT
“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
HT[i]i
• The spectrum is a a function of with 180° period.
HSg[i]g
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Hough Spectrum properties• it is invariant to input translation • it shifts on input rotation
(same spectrum)
T
T
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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
HSg[i] HSg[i’]
The peaks of the cross correlation are estimates for .
+180°
cross correlation
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Handling ambiguities• Multi-modal global search can detect
ambiguities
result ofcorrelation
Input data
Houghspectrum
multiple hypotheses for
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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:
Input data
Houghspectrum
histogramof surfaceangles
result ofcorrelation
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HSM: estimating T
HT
|T|
HT
Ttranslation T
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T
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.
d~ p(T| )
d'
T
linearconstraints
d'
d
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Example with real data
Map portion Laser scan
First solution (exact) 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 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 Grisettilastname @ dis.uniroma1.it
www.dis.uniroma1.it/~lastname