Groupwise rigid registration of wrist bones

Abstract

We present an extension of the symmetric ICP algorithm that is unbiased for an arbitrary number (N ≥ 2) of shapes, using rigid transformations and scaling. Themethod does not require the selection of a reference shape or registration order and hence it is unbiased towards any of the registered shapes. The functional to be minimized is non-linear in the transformation parameters and thus computationally complex.We therefore propose a first order approximation that estimates the transformation parameters in a closed form, with computational complexity O(N2). Using a set of wrist bones, we show that the least-squares minimization and the proposed approximation converge to the same solution. Experiments also show that the proposed algorithms lead to smaller registration errors than algorithms that select a reference shape or register to an evolving mean shape. The low computational cost and trivial parallelization enable the alignment of large numbers of bones.