On the ICP algorithm

We present upper and lower bounds for the number of iterations performed by the Iterative Closest Point (ICP) algorithm. This algorithm has been proposed by Besl and McKay [4] as a successful heuristics for pattern matching under translation, where the input consists of two point sets in d-space, for d 1, but so far it seems not to have been rigorously analyzed. The considered (standard) measure of resemblance that the algorithm attempts to optimize is the RMS (root mean squared distance). We show that the number of iterations performed by the algorithm is polynomial in the number of input points. In particular, this bound is quadratic in the one-dimensional problem, for which we present a lower bound construction of (n log n) iterations, where n is the overall size of the input. We also present several structural geometric properties of the algorithm. We show that at each iteration of the algorithm the cost function monotonically and strictly decreases along the vector t of the rela...

• Type: Conference
• Year: 2006
• Where: COMPGEOM
• Authors: Esther Ezra, Micha Sharir, Alon Efrat
• Keywords: Algorithm, COMPGEOM 2006, Discrete Geometry, Lower Bound, Relative Translations