Modeling and Analysis of 3D Elongated Shapes with Applications to Long Bone Morphometry
Résumé
This paper presents a geometric model to be used as a framework for the description and analysis of threedimensional(3D) elongated shapes. Elongated shapes can be decomposed into two different parts: a 3D curve (the central axis) and a 3D 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 3D 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 (FDs), each set representing a 2D 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 3D structures. A technique for the reconstruction of the 3D 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 3D shapes, segmentation into 3D primitives, and torsion and curvature analysis. The relevance of the method to morphometry and to clinical applications is discussed.