Geodesic based registration of sensor data and anatomical surface image data

This paper presents two related methods for registering an image of an anatomical object with data from sensors arranged on the object. One method is described with reference to a test case involving a rectangular electrode plaque disposed on a heart surface, which is imaged with MRI. Data from the electrodes is fused with the MRI image at the appropriate locations. The registration scheme involves four parts. First, selected landmarks on a data surface (e.g., electrode plaque) are registered to known locations on a target anatomical surface image. Second, the anatomical surface is represented numerically with a spherical harmonic expansion. Third, given the registration of the select data surface landmarks, the location of the outer four corners of the rectangular electrode plaque are located on the anatomical surface. Fourth, a quasi-evenly spaced grid within these four corners is formed on the anatomical surface. The third and fourth steps involve calculating geodesics on the anatomical surface, preferably by utilizing the spherical harmonic expansion. According to the second registration method, spherical harmonics and geodesics are used to extract a mesh from the anatomical surface. Laplace's equation is solved on this mesh to generate a mapping from the anatomical surface to the data surface (electrode plaque).