Robust diffusion of structural flows for volumetric image interpolation

In this paper we propose a set of algorithms that combine the anisotropic smoothing using the heat kernel with the outlier rejection capability of robust statistics. The proposed algorithms are applied on structural vector flows that model the internal shape variation in volumetric images. The 3D shapes are represented by sparse cross-sections along the main axis of the object. The dual directional block matching algorithm is used to initially extract the structural flows. This algorithm uses block matching between pixel blocks from consecutive images representing sparse cross-sections through a volume. Two flows are produced using forward and reverse matching along the main axis of the 3D object. After smoothing, the structural flows are used for slice interpolation. Experimental results provide a comparison among the given algorithms when used for digital 3D reconstruction of an incisor and of two human bones.