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

arXiv: https://arxiv.org/abs/2111.01350 · HTML: https://mlsanity.com/paper/2111.01350/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 42 references that are in the map.
- First posted on arXiv 2 Nov 2021.

## Builds on (most cited first, 3 of 3)

- [Artifacts of Quantization in Distance Transforms](https://mlsanity.com/paper/2011.08880/) (2020)
- [Local Morphometry of Closed, Implicit Surfaces](https://mlsanity.com/paper/2108.04354/) (2021)
- [High-Order Signed Distance Transform of Sampled Signals](https://mlsanity.com/paper/2110.13354/) (2021)

## Abstract (arXiv)

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.