Smooth Shape-Based Interpolation using the Conjugate Gradient Method

In this paper a novel technique for smooth shapebased interpolation of volume data is introduced. Previously simple linear interpolation of signed distance maps has been used in practice. As it will be shown, this approach results in artifacts, since sharp edges appear along the original slices. In order to obtain a smooth 3D implicit function generated by interpolating 2D distance maps, we use a global interpolation method instead of a higher order local technique. The global curvature of the implicit function representing an isosurface is minimized using an iterative conjugate gradient method. Because of the iterative approach the user can easily control the trade-off between the smoothness of the isosurface and the computational cost of the refinement. As opposed to previous techniques, like variational interpolation, our method can generate a reasonably good approximation of the ideal solution in a significantly shorter time.