Online reconstruction of 3D objects from arbitrary cross-sections

We describe a simple algorithm to reconstruct the surface of smooth three-dimensional multilabeled objects from sampled planar cross-sections of arbitrary orientation. The algorithm has the unique ability to handle crosssections in which regions are classified as being inside the object, outside the object, or unknown. This is achieved by constructing a scalar function on R3, whose zero set is the desired surface. The function is constructed independently inside every cell of the arrangement of the cross-section planes using transfinite interpolation techniques based on barycentric coordinates. These guarantee that the function is smooth, and its zero set interpolates the cross-sections. The algorithm is highly parallelizable and may be implemented as an incremental update as each new cross-section is introduced. This leads to an efficient online version, performed on a GPU, which is suitable for interactive medical applications.