An ICP variant with anisotropic weighting to accommodate measurement errors in A-Mode ultrasound-based registration

In computer-assisted surgery, navigation based on pre-operative images and intra-operative tracking requires fusion of data from different coordinate systems. Intra-operative registration is used to determine the spatial relationship between these coordinate systems. Feature-based registration methods rely on reference structures localized both in the pre-operative images and in the surgical site. Optically tracked A-Mode ultrasound (US) allows for non-invasive and cost-efficient digitization of bone surface points needed as input data for registration algorithms. It is especially attractive in combination with surface-based registration algorithms, such as the Iterative Closest Point algorithm and its variants, because they automatically localize the corresponding points, which are covered by soft tissue and, hence, not visible in the site. However, as transcutaneous palpation relies on some assumptions, e.g., regarding the average speed of sound of the scanned soft tissue, that are only partly justified in practice, errors occur that make transcutaneous palpation less reliable than direct palpation. Furthermore, optical tracking causes errors that have to be considered, especially if a so-called dynamic reference base is attached to the patient. The present work investigates how to reduce the effect of important error sources in A-Mode US-based registration. The major contributions are techniques for application-specific error modeling and new methods for surface-based registration with anisotropic weighting. This includes a Newton-like optimization scheme for point-to-point registration and a modified kd-tree-based algorithm for closest point computation. Various combinations of registration algorithms and modeling techniques are tested in a simulation study addressing periacetabular osteotomy, and it is clearly demonstrated that standard methods are not recommendable. On the contrary, the new algorithms allow for a substantial increase in registration accuracy and encourage further research in that field.