  An algorithm is presented for constructing high-order signed distance fields
for two phase materials imaged with computed tomography. The signed distance
field is high-order in that it is free of the quantization artifact associated
with the distance transform of sampled signals. The narrowband is solved using
a closest point algorithm extended for implicit embeddings that are not a
signed distance field. The high-order fast sweeping algorithm is used to extend
the narrowband to the remainder of the domain. The order of accuracy of the
narrowband and extension methods are verified on ideal implicit surfaces. The
method is applied to ten excised cubes of bovine trabecular bone. Localization
of the surface, estimation of phase densities, and local morphometry is
validated with these subjects. Since the embedding is high-order, gradients and
thus curvatures can be accurately estimated locally in the image data.
