Algorithm 1.

Algorithm for finding gravity-induced deformations using ICP registration

1.	Initialize by transforming preoperative chest wall contours to intraoperative space using transformation from “Rigid alignment”
2.	Perform an ICP registration between MR chest wall surface and iUS chest wall contours
3.	Extract the rotation matrix from the final transformation and apply to the gravity vector in intraoperative space
	$\Delta g=R\ast g_{intraop}\left(2\right)$
	where gintraop is a 3 × 1 vector containing the unit direction normal to the patient bed in intraoperative space