  Autonomous ultrasound (US) imaging has gained increased interest recently,
and it has been seen as a potential solution to overcome the limitations of
free-hand US examinations, such as inter-operator variations. However, it is
still challenging to accurately map planned paths from a generic atlas to
individual patients, particularly for thoracic applications with high
acoustic-impedance bone structures under the skin. To address this challenge, a
graph-based non-rigid registration is proposed to enable transferring planned
paths from the atlas to the current setup by explicitly considering
subcutaneous bone surface features instead of the skin surface. To this end,
the sternum and cartilage branches are segmented using a template matching to
assist coarse alignment of US and CT point clouds. Afterward, a directed graph
is generated based on the CT template. Then, the self-organizing map using
geographical distance is successively performed twice to extract the optimal
graph representations for CT and US point clouds, individually. To evaluate the
proposed approach, five cartilage point clouds from distinct patients are
employed. The results demonstrate that the proposed graph-based registration
can effectively map trajectories from CT to the current setup for displaying US
views through limited intercostal space. The non-rigid registration results in
terms of Hausdorff distance (Mean$\pm$SD) is 9.48$\pm$0.27 mm and the path
transferring error in terms of Euclidean distance is 2.21$\pm$1.11 mm.
