Three-dimensional interpolation for brain MR images

In this paper, we propose a new directional 3-dimensional interpolation algorithm for brain magnetic resonance (MR) images. Typically, brain images consist of a number of two-dimensional images. In order to reconstruct 3 dimensional objects from slices of 2 dimensional images, interpolation operation is required. In most interpolation algorithms in the three-dimensional space, the interpolation operation is performed separately in each coordinate that is orthogonal to each other. However, since the shape of the brain is roughly a sphere, interpolation along these three orthogonal coordinates may result in some information loss, particularly when gradients of pixel values have directions similar to the directions of the coordinates. In order to address this problem, we propose a new directional interpolation algorithm. In the proposed algorithm, we first perform the interpolation along two orthogonal coordinates. Typically, the two orthogonal coordinates would be the coordinates of the two dimensional images. And then, in order to find the best interpolation in the remaining coordinate, we search various directions that are not orthogonal to the two orthogonal coordinates using cost functions. Experiments show promising results.