Abstract: A method of registering a 3-dimensional (3D) model of a coronary artery tree with 2-dimensional (2D) images includes solving for matrices R, Pi, i=1, . . . , N, that minimize a cost function ?i=1N??iRX?IiPi?2,1 subject to constraints that R?conv(SO(3)), Pi?[0,1]ni×m, and Pi1?1, 1TPi=1, for i?{1, N}, where N is a number of 2D images, R is a rotation matrix, conv(SO(3)) denotes a convex hull of the special orthogonal group in 3 dimensions, X denotes a 3D centerline model of a coronary artery tree, Ii denotes the ith 2D image, ?i denotes a transformation between the 3D centerline model X and the ith 2D image Ii, 1 is an all-ones vector, Pi is a permutation matrix, and rounding a solution R to a nearest orthogonal matrix R* in SO(3), where R* aligns the 3D centerline model X of the coronary artery tree with 2D fluoroscopic images acquired during a percutaneous coronary intervention procedure.

Abstract: A method of registering a 3-dimensional (3D) model of a coronary artery tree with 2-dimensional (2D) images includes solving for matrices R, Pi, i=1, . . . , N, that minimize a cost function ?i=1N??iRX?IiPi?2,1 subject to constraints that R?conv(SO(3)), Pi?[0,1]ni×m, and Pi1?1, 1TPi=1, for i?{1, N}, where N is a number of 2D images, R is a rotation matrix, conv(SO(3)) denotes a convex hull of the special orthogonal group in 3 dimensions, X denotes a 3D centerline model of a coronary artery tree, Ii denotes the ith 2D image, ?i denotes a transformation between the 3D centerline model X and the ith 2D image Ii, 1 is an all-ones vector, Pi is a permutation matrix, and rounding a solution R to a nearest orthogonal matrix R* in SO(3), where R* aligns the 3D centerline model X of the coronary artery tree with 2D fluoroscopic images acquired during a percutaneous coronary intervention procedure.