Systems and methods for determining a surface geometry
Methods and systems for determining a surface geometry of an object, including determining a first projection matrix based on a first imaging device, determining a second projection matrix based on a second imaging device, obtaining at least one first two-dimensional (2D) image of the object using the first imaging device, obtaining at least one second 2D image of the object using the second imaging device, determining a contour of the object in the first 2D image and the second 2D image, and, based on the at least two contours, the first projection matrix, and the second projection matrix, reconstructing 3D data associated with the surface of the object. In one embodiment, the object can be a heart.
1. A method for computing epicardial surface electric potentials based on measured body surface electric potentials, the method comprising:
generating a multidimensional matrix, the matrix representing at least one geometric relationship between at least one body surface electric potential measuring system and the epicardial surface, the multidimensional matrix being based on:
at least one first two-dimensional (2D) image of the epicardium using a first imaging device,
at least one second 2D image of the epicardium using a second imaging device,
a first projection matrix associated with the first imaging device,
a second projection matrix associated with the second imaging device,
a computed contour of the outer surface of the heart formed from contours identified in the at least one first 2D image and the at least one second 2D image,
a computed contour of the electric potential measuring system, and,
a boundary element method based on the computed contour of the outer surface of the heart and the computed contour of the electric potential measuring system,
using a Generalized Minimum Residual (GMRes) method to estimate an inverse of the multidimensional matrix, and,
based on the inverse matrix and the measured body surface potentials, determining the epicardial surface electric potentials.
2. A method according to claim 1 , where representing includes measuring the position of the at least one body surface electric potential measuring system.
3. A method according to claim 1 , where using a GMRes method includes determining a number of iterations for the GMRes method.
4. A method according to claim 3 , where using a GMRes method includes providing a maximum number of iterations for the GMRes method, and based on the data from the maximum number of iterations, determining a number of iterations for the GMRes method.
5. A method according to claim 3 , where determining a number of iterations includes comparing residual error to a Hessenberg matrix condition, and computing at least one of a corner of a condition L curve and a maximum curvature of a condition L curve.
6. A method according to claim 3 , where determining a number of iterations includes determining a number of iterations based on at least one of: a corner of a condition L curve, a corner of an L curve, an increase in spatial frequency of a reconstructed potential map, and an increase in amplitude of a solution norm.
7. A method according to claim 1 , where using a GMRes method includes providing an initial condition of zero.
8. A method according to claim 1 , where using a GMRes method includes providing an initial condition based on a Tikhonov regularization of the multidimensional matrix.