Systems and methods for determining a surface geometry

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.