Rigid Point-Surface Registration using Oriented Points and an EM Variant of ICP for Computer Guided Oral Implantology

Sébastien Granger (1) , Xavier Pennec , Alexis Roche

1 EPIDAURE - Medical imaging and robotics

We investigate in this research report the rigid registration of a set of points with a surface for computer-guided oral implants surgery. We first formulate the Iterative Closest Point (ICP) algorithm as a Maximum Likelihood (ML) estimation of the transformation and the matches. Then, considering matches as a hidden random variable, we show that the ML estimatio- n of the transformation alone leads to a criterion efficiently solved using an Expectation-Maximisation (EM) algorithm. This algorithm implies a new parameter, based on the standard-deviation of the noise on points position. We demonstrate that, for small values, the algorithm behaves like the accurate ICP, while, for high values, the algorithm robustly aligns the barycenter and inertia moments. Finaly, this parameter is decreased using an annealing scheme, which can be seen as a kind of multi-scale scheme. We present besides an efficient way to use oriented points - like surface points with their normals - instead of points with ICP and EM algorithms. The experimental section provides evidences that the EM algorithm is far more robust and more accurate than ICP and reaches a global accuracy of 0.2 mm with computation times compatible with a per-operative system. Another important property is that the criterion analysis enables an easy distinction between correct results and false postives.

Mots clés: MEDICAL IMAGING; RIGID REGISTRATION; ICP ALGORITHM; EM ALGORITHM

Domaines: Autre [cs.OH]

Sébastien Granger, Xavier Pennec, Alexis Roche. Rigid Point-Surface Registration using Oriented Points and an EM Variant of ICP for Computer Guided Oral Implantology. RR-4169, INRIA. 2001. ⟨inria-00072453⟩