Efficient geometric techniques for reconstructing 3D vessel trees from biplane image

Diagnosis and treatment of cardiovascular disease relies heavily on interventional procedures. Typically, these procedures allow only limited visibility of the vessels; thus determination of the three-dimensional configuration of the vasculature is important for visualization and the planning and delivery of treatment. Currently, the primary method used for the determination of the 3D configuration of the vessel network during such interventional procedures is biplane imaging. In biplane imaging, two projection images of the 3D objects of interest are acquired. The focal spots are taken as the origins of their respective coordinate systems (see schematic diagram of a biplane system in Figure 1). The approximate relative translation and rotation between the two imaging planes is obtained from the gantry angles of the imaging system. The approximate 3D information of the vasculature can thus be recovered from these two images. However, if the information regarding the relative translation and rotation between the imaging planes is inaccurate, the reconstructed 3D could be far from accurate. A key problem (called Imaging Geometry Determination or IGD) is thus to determine the relative rotation matrix R and translation vector t between the two imaging planes, in the presence of random noise and system error, such that accurate 3D vasculature can be reconstructed and be used reliably in clinical decision making. The IGD problem can be defined as follows. Given a problem instance I comprising two sets of 2D points Left = {lp1 , lp2 , . . . , lpn} and Right = {rp1 , rp2 , . . . , rpn} on the left and right image planes where each lpi and rpi are the cor∗This work was supported in part by NIH Grant HL 52567 and Toshiba Medical Systems Corporation.