Universit La Sapienza Rome Italy Scan matching in

Università La Sapienza Rome, Italy Scan matching in the Hough domain Andrea Censi, Luca Iocchi, Giorgio Grisetti lastname @ dis. uniroma 1. it www. dis. uniroma 1. it/~lastname SIED Lab www. dis. uniroma 1. it/~multirob/sied/

Scan matching • 2 D scan matching (geometric interpretation): find a rotation and a translation T who maximize overlapping of two sets of 2 D data. Map portion Sensor scan • 2 D scan matching (probabilistic interpretation): approximate a pdf of the robot pose; ex: p(xt|xt-1, ut-1, yt 1) or others. . . A. Censi, L. Iocchi, G. Grisetti 2 of 16

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] 3 of 16 Censi, L. search: Iocchi, G. 2 D Grisetti

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-correlation 4 of Censi, L. Iocchi, G. Grisetti of 16

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 A. Censi, L. Iocchi, G. Grisetti Hough Domain ( , ) 5 of 16

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). A. Censi, L. Iocchi, G. Grisetti Hough Domain ( , ) 6 of 16

Feature detection with the HT HT A. Censi, L. Iocchi, G. Grisetti 7 of 16

Expressiveness of the HT HT HT-1 “features distributions” A. Censi, L. Iocchi, G. Grisetti 8 of 16

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. A. Censi, L. Iocchi, G. Grisetti 9 of 16

Hough Spectrum properties • it is invariant to input translation • it shifts on input rotation T T (same spectrum) A. Censi, L. Iocchi, G. Grisetti 10 of 16

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 . A. Censi, L. Iocchi, G. Grisetti 11 of 16

Handling ambiguities • Multi-modal global search can detect ambiguities multiple hypotheses for Input data Hough spectrum result of correlation A. Censi, L. Iocchi, G. Grisetti 12 of 16

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 A. Censi, L. Iocchi, G. Grisetti 13 of 16

HSM: estimating T translation T T HT HT A. Censi, L. Iocchi, G. Grisetti |T| 14 of 16

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 A. Censi, L. Iocchi, G. Grisetti ~ p(T| ) 15 of 16

Example with real data Map portion First solution (exact) A. Censi, L. Iocchi, G. Grisetti Laser scan Second solution 16 of 16

Summary • Operating in the Hough space allows to decouple the search of the rotation from the translation (3 D search 3 x 1 D 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 3 D for dealing with 3 D noisy sensors (stereo camera). A. Censi, L. Iocchi, G. Grisetti 17 of 16

Thanks for your attention • Slides and an extended version of the paper available at www. dis. uniroma 1. it/~censi Andrea Censi, Luca Iocchi, Giorgio Grisetti lastname @ dis. uniroma 1. it www. dis. uniroma 1. it/~lastname A. Censi, L. Iocchi, G. Grisetti 18 of 16