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

2021/11/01 by Bryce A. Besler, Tannis D. Kemp, Besler, Bryce A. +5
Computer Science · Engineering · Medicine · Physics and Astronomy · #Advanced X-ray Imaging Techniques #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #FOS: Electrical engineering #Hydrocarbon exploration and reservoir analysis #Image and Video Processing (eess.IV) #Medical Image Segmentation Techniques #Medical Imaging Techniques and Applications #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2111.01350

openalex publication_date 2021/11/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Citations

• A new method for the model‐independent assessment of thickness in three‐dimensional images
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow
• A fast sweeping method for Eikonal equations
• Guidelines for assessment of bone microstructure in rodents using micro–computed tomography
• A Threshold Selection Method from Gray-Level Histograms
• Artifacts of Quantization in Distance Transforms
• Local Morphometry of Closed, Implicit Surfaces
• High-Order Signed Distance Transform of Sampled Signals

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