By Topic

Worst-case and Smoothed Analysis of the ICP Algorithm, with an Application to the k-means Method

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Arthur, D. ; Stanford Univ., CA ; Vassilvitskii, S.

We show a worst-case lower bound and a smoothed upper bound on the number of iterations performed by the iterative closest point (ICP) algorithm. First proposed by Besl and McKay, the algorithm is widely used in computational geometry where it is known for its simplicity and its observed speed. The theoretical study of ICP was initiated by Ezra, Sharir and Efrat, who bounded its worst-case running time between Omega(n log n) and O(n2d)d. We substantially tighten this gap by improving the lower bound to Omega(n/d)d+1 . To help reconcile this bound with the algorithm's observed speed, we also show the smoothed complexity of ICP is polynomial, independent of the dimensionality of the data. Using similar methods, we improve the best known smoothed upper bound for the popular k-means method to nO(k) once again independent of the dimension

Published in:

Foundations of Computer Science, 2006. FOCS '06. 47th Annual IEEE Symposium on

Date of Conference:

Oct. 2006