9 March 2011 Affine invariant parameterization to assess local shape in abdominal organs
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We present a novel method for three-dimensional (3D) shape parameterization. The approach is affine invariant and is applied to comparing local shape across abdominal organs. The inherent structure of the abdominal organs is used to generate a regular sampling of the organ's surface. 'Planar-convexity' is defined for a general 3D closed object as the property that there exists a set of parallel planes which cover the 3D space such that every intersection of a plane with the object is a singular closed planar curve. We show that this parameterization, combined with the 3D analogue of a 2D shape descriptor, successfully shown to be invariant under affine transformations and noise, can be effectively used to compare features of two closed 3D surfaces point-to-point. The technique avoids common problems with the parameterization of concave surfaces and shows great potential for analyzing and improving the automatic modeling and segmentation of abdominal organs.
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Jeremy M. Watt, Marius George Linguraru, Ronald M. Summers, "Affine invariant parameterization to assess local shape in abdominal organs", Proc. SPIE 7965, Medical Imaging 2011: Biomedical Applications in Molecular, Structural, and Functional Imaging, 79650F (9 March 2011); doi: 10.1117/12.877589; https://doi.org/10.1117/12.877589

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