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Title: Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry

Abstract

This paper presents a geometric model to be used as a framework for the description and analysis of three-dimensional (3-D) elongated shapes. Elongated shapes can be decomposed into two different parts: a 3-D curve (the central axis) and a 3-D surface (the straight surface). The central axis is described in terms of curvature and torsion. A novel concept of torsion image is introduced which allows the user to study the torsion of some relevant 3-D structures such as the medulla of long bones, without computing the third derivative. The description of the straight surface is based on an ordered set of Fourier Descriptors (FD`s), each set representing a 2-D slice of the structure. These descriptors possess completeness, continuity, and stability properties, and some geometrical invariancies. A polar diagram is built which contains the anatomical information of the straight surface and can be used as a tool for the analysis and discrimination of 3-D structures. A technique for the reconstruction of the 3-D surface from the model`s two components is presented. Various applications to the analysis of long bone structures, such as the ulna and radius, are derived from the model, namely, data compression, comparison of 3-D shapes, segmentation into 3-Dmore » primitives, and torsion and curvature analysis. The relevance of the method to morphometry and to clinical applications is discussed.« less

Authors:
;  [1]; ;  [2]
  1. Telecom Bretagne-LATIM, Brest (France). Dept. Image et Traitement de l`Information
  2. Centre Hospitalier Regional Univ. de Brest-LATIM (France). Service Orthopedie et Traumatologie
Publication Date:
OSTI Identifier:
207911
Resource Type:
Journal Article
Journal Name:
IEEE Transactions on Medical Imaging
Additional Journal Information:
Journal Volume: 15; Journal Issue: 1; Other Information: PBD: Feb 1996
Country of Publication:
United States
Language:
English
Subject:
55 BIOLOGY AND MEDICINE, BASIC STUDIES; ARMS; IMAGE PROCESSING; LEGS; THREE-DIMENSIONAL CALCULATIONS; MATHEMATICAL MODELS; SKELETON

Citation Formats

Burdin, V, Roux, C, Lefevre, C, and Stindel, E. Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry. United States: N. p., 1996. Web. doi:10.1109/42.481443.
Burdin, V, Roux, C, Lefevre, C, & Stindel, E. Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry. United States. https://doi.org/10.1109/42.481443
Burdin, V, Roux, C, Lefevre, C, and Stindel, E. 1996. "Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry". United States. https://doi.org/10.1109/42.481443.
@article{osti_207911,
title = {Modeling and analysis of 3-D elongated shapes with applications to long bone morphometry},
author = {Burdin, V and Roux, C and Lefevre, C and Stindel, E},
abstractNote = {This paper presents a geometric model to be used as a framework for the description and analysis of three-dimensional (3-D) elongated shapes. Elongated shapes can be decomposed into two different parts: a 3-D curve (the central axis) and a 3-D surface (the straight surface). The central axis is described in terms of curvature and torsion. A novel concept of torsion image is introduced which allows the user to study the torsion of some relevant 3-D structures such as the medulla of long bones, without computing the third derivative. The description of the straight surface is based on an ordered set of Fourier Descriptors (FD`s), each set representing a 2-D slice of the structure. These descriptors possess completeness, continuity, and stability properties, and some geometrical invariancies. A polar diagram is built which contains the anatomical information of the straight surface and can be used as a tool for the analysis and discrimination of 3-D structures. A technique for the reconstruction of the 3-D surface from the model`s two components is presented. Various applications to the analysis of long bone structures, such as the ulna and radius, are derived from the model, namely, data compression, comparison of 3-D shapes, segmentation into 3-D primitives, and torsion and curvature analysis. The relevance of the method to morphometry and to clinical applications is discussed.},
doi = {10.1109/42.481443},
url = {https://www.osti.gov/biblio/207911}, journal = {IEEE Transactions on Medical Imaging},
number = 1,
volume = 15,
place = {United States},
year = {Thu Feb 01 00:00:00 EST 1996},
month = {Thu Feb 01 00:00:00 EST 1996}
}