Cardiac catheterization is carried out by inserting a multi-electrode probe into a heart, constructing a position map of the electrodes, and simulating a 3-dimensional surface of the heart. The method is further carried out by placing the position map in registration with an acquired image of the heart, constructing, based on the position map, a mesh that models the 3-dimensional surface of the heart, and adjusting positions of vertices of the mesh relative to mapped points in the position map to improve a registration of the mesh with the acquired image.