Pythagorean Mean Images for Efficient Groupwise Registration

Groupwise registration is a powerful technique allowing to simultaneously align multiple images using an unbiased approach. Its need arises from population studies or motion estimation across dynamic sequences. An often used class of efficient groupwise metrics measures similarity as the sum of the pairwise similarities between the images and a template image, commonly chosen to be the arithmetic mean image in the current iteration. However, arithmetic averaging in intensity space limits the applications to closely related modalities, and may produce fuzzy images compromising the performance of the metric. Geometric and harmonic averaging is capable of handling range and scale differences without adding computational complexity. Groupwise similarity metrics based on mutual information and the three Pythagorean means were investigated. Experiments performed on monomodal and multimodal data demonstrated superior performance of geometric and harmonic over arithmetic averaging and the corresponding pairwise registration.