Constructing High-Order Signed Distance Maps from Computed Tomography Data with Application to Bone Morphometry

TL;DR

This paper introduces a high-order signed distance field construction algorithm for computed tomography data, enabling accurate surface localization, phase density estimation, and morphometry in bone imaging.

Contribution

It presents a novel high-order method that reduces quantization artifacts in signed distance maps from CT data, improving accuracy in morphometric analysis.

Findings

Validated on bovine trabecular bone samples

Achieved accurate surface localization and phase density estimation

Enabled precise curvature and morphometry calculations

Abstract

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.