The generalized totally geodesic Radon transform and its application to texture analysis
The generalized totally geodesic Radon transform and its application to texture analysis
复制标题
广义全测地Radon变换及其在纹理分析中的应用
DOI：
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发表时间：
2009
期刊：
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通讯作者：
H. Schaeben
中科院分区：
文献类型：
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作者：
S. Bernstein;R. Hielscher;H. Schaeben
广义全测地Radon变换关联的平均值超过球面环面的函数f上定义的？3、什么是要素？3被认为是代表旋转的四元数。将其引入晶体学择优取向的分析中，并用与角分布函数W相对应的概率密度函数来表示。最终，该通信提出了一种新的方法来从数据采样W恢复f的近似值。同时，它提供了额外的澄清最近建议的方法，应用再生核和径向基函数的启发性洞察其所涉及的几何形状。重点是对应的几何和组功能，而不是映射的功能和他们的空间。版权所有© 2008约翰威利父子有限公司。
The generalized totally geodesic Radon transform associates the mean values over spherical tori to a function f defined on ?3⊂ℍ, where the elements of ?3 are considered as quaternions representing rotations. It is introduced into the analysis of crystallographic preferred orientation and identified with the probability density function corresponding to the angle distribution function W. Eventually, this communication suggests a new approach to recover an approximation of f from data sampling W. At the same time it provides additional clarification of a recently suggested method applying reproducing kernels and radial basis functions by instructive insight into its involved geometry. The focus is on the correspondence of geometrical and group features rather than on the mapping of functions and their spaces. Copyright © 2008 John Wiley & Sons, Ltd.