  We describe a convex programming framework for pose estimation in 2D/3D
point-set registration with unknown point correspondences. We give two
mixed-integer nonlinear program (MINP) formulations of the 2D/3D registration
problem when there are multiple 2D images, and propose convex relaxations for
both of the MINPs to semidefinite programs (SDP) that can be solved efficiently
by interior point methods. Our approach to the 2D/3D registration problem is
non-iterative in nature as we jointly solve for pose and correspondence.
Furthermore, these convex programs can readily incorporate feature descriptors
of points to enhance registration results. We prove that the convex programs
exactly recover the solution to the original nonconvex 2D/3D registration
problem under noiseless condition. We apply these formulations to the
registration of 3D models of coronary vessels to their 2D projections obtained
from multiple intra-operative fluoroscopic images. For this application, we
experimentally corroborate the exact recovery property in the absence of noise
and further demonstrate robustness of the convex programs in the presence of
noise.
