Continuous medial representation for anatomical structures
Continuous medial representation for anatomical structures
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DOI：
10.1109/tmi.2006.884634
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发表时间：
2006-12-01
影响因子：
10.6
通讯作者：
Gee, James C.
中科院分区：
文献类型：
--
作者：
Yushkevich, Paul A.;Zhang, Hui;Gee, James C.
Pizer 等人首创的 m-rep 方法。 (2003) 是一个强大的形态学工具，使得在形状分析中使用源自内侧位点（骨架）的特征成为可能。本文将中间表示范式扩展到连续领域，将三维对象的骨架和边界建模为连续参数流形，同时还保持这些流形之间正确的几何关系。边界-中间关系的参数化表示使得基于形状的坐标系适合对象的内部成为可能，为形状和外观的组合统计分析提供了框架。我们的方法利用了逆骨架化的思想，其中首先定义对象的骨架，然后从骨架分析得出对象的边界。本文推导了一组确保单流形骨架逆骨架化适定的充分条件，并建立了一个其解满足充分条件的偏微分方程。描述了一种使用连续内侧表示进行可变形模板建模的有效变分算法，并用于将模板拟合到来自精神分裂症研究的 87 名受试者的海马体中，具有亚体素精度和 95% 的平均重叠度。
The m-rep approach pioneered by Pizer et al. (2003) is a powerful morphological tool that makes it possible to employ features derived from medial loci (skeletons) in shape analysis. This paper extends the medial representation paradigm into the continuous realm, modeling skeletons and boundaries of three-dimensional objects as continuous parametric manifolds, while also maintaining the proper geometric relationship between these manifolds. The parametric representation of the boundary-medial relationship makes it possible to fit shape-based coordinate systems to the interiors of objects, providing a framework for combined statistical analysis of shape and appearance. Our approach leverages the idea of inverse skeletonization, where the skeleton of an object is defined first and the object's boundary is derived analytically from the skeleton. This paper derives a set of sufficient conditions ensuring that inverse skeletonization is well-posed for single-manifold skeletons and formulates a partial differential equation whose solutions satisfy the sufficient conditions. An efficient variational algorithm for deformable template modeling using the continuous medial representation is described and used to fit a template to the hippocampus in 87 subjects from a schizophrenia study with sub-voxel accuracy and 95% mean overlap.