Newton's method on Riemannian manifolds and a geometric model for the human spine
Newton's method on Riemannian manifolds and a geometric model for the human spine
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DOI：
10.1093/imanum/22.3.359
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发表时间：
2002-07
影响因子：
2.1
通讯作者：
R. Adler;J. Dedieu;J. Margulies;M. Martens;M. Shub
中科院分区：
文献类型：
--
作者：
R. Adler;J. Dedieu;J. Margulies;M. Martens;M. Shub
为了研究人体脊柱的几何模型，我们找到了定义在特殊正交群积上的实值函数的约束极小值。为了充分利用它的李群结构，我们在这个流形上考虑牛顿法。测量的脊柱和计算的脊柱之间的比较表明了这种方法的针对性。
To study a geometric model of the human spine we are led to finding a constrained minimum of a real valued function defined on a product of special orthogonal groups. To take advantge of its Lie group structure we consider Newton's method on this manifold. Comparisons between measured spines and computed spines show the pertinence of this approach.