29 July 1993 Geometrical models for the analysis of 3D anatomic shapes: application to bone structures
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This paper presents a framework for the description and the analysis of three-dimensional (3D) elongated shapes based on appropriate geometrical models. Its application to the analysis of long bone structures like ulna and radius is described. Elongated shapes can be decomposed into a space curve (the medial axis) and a space surface (the straight surface). The medial axis is described by means of curvature and torsion. A novel torsion image is presented which avoids computing any third derivative. The description of the straight surface is based on an ordered set of series of Fourier descriptors, each series representing a 2D contour of the structure. These descriptors are endowed with completeness, continuity and stability properties, and with some geometrical invariances. Various applications are derived from this model: compression and reconstruction of the shape, comparison of 3D shapes, and segmentation into 3D primitives.
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Christian Roux, Christian Roux, V. Burdin, V. Burdin, Christian Lefevre, Christian Lefevre, } "Geometrical models for the analysis of 3D anatomic shapes: application to bone structures", Proc. SPIE 1905, Biomedical Image Processing and Biomedical Visualization, (29 July 1993); doi: 10.1117/12.148678; https://doi.org/10.1117/12.148678

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