Groupwise Rigid Registration of Wrist Bones

We present an extension of the symmetric ICP algorithm that is unbiased for an arbitrary number (N > or = 2) of shapes, using rigid transformations and scaling. The method 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 (see text for symbol)(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.