High fidelity fiber orientation density functions from fiber ball imaging

2021 ◽  
Author(s):  
Hunter G. Moss ◽  
Jens H. Jensen
Keyword(s):  
Fiber Orientation ◽  
Density Functions ◽  
High Fidelity ◽  
Orientation Density ◽  
Fiber Ball

scholarly journals Optimized rectification of fiber orientation density function

2020 ◽  
Vol 85 (1) ◽  
pp. 444-455
Author(s):  
Hunter G. Moss ◽  
Jens H. Jensen
Keyword(s):  
Density Function ◽  
Fiber Orientation ◽  
Orientation Density

Orientation Analysis

2021 ◽  
Vol 1016 ◽  
pp. 605-610
Author(s):  
Janos Imhof
Keyword(s):  
Density Function ◽  
Initial Function ◽  
Minimum Principle ◽  
Density Functions ◽  
Pole Density ◽  
Orientation Analysis ◽  
Euler Space ◽  
Orientation Density ◽  
Basic Concepts ◽  
The Relationship

Simple figures illustrate the basic concepts: orientation, Euler angles, Euler space, orientation density function, pole density function. The iteration that decisively influenced the development of orientation analysis follows directly from the relationship between the two density functions. The minimum principle defines the initial function and the structure of the iteration. Using model orientation density function, we prove that this kind of orientation analysis is extremely effective.

On the entropy to texture index relationship in quantitative texture analysis

2007 ◽  
Vol 40 (2) ◽  
pp. 371-375 ◽  
Author(s):  
R. Hielscher ◽  
H. Schaeben ◽  
D. Chateigner
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Texture Analysis ◽  
Sharp Inequality ◽  
Probability Density Functions ◽  
Density Functions ◽  
Orientation Space ◽  
Reconstruction Software ◽  
Orientation Density

This communication demonstrates a sharp inequality between the L^{2}-norm and the entropy of probability density functions. This inequality is applied to texture analysis, and the relationship between the entropy and the texture index of an orientation density function is characterized. More precisely, the orientation space is shown to allow for texture index and entropy variations of orientation probability density functions between an upper and a lower bound for the entropy. In this way, it is proved that there is no functional relationship between entropy and texture index of an orientation probability density function as conjectured previously on the basis of practical numerical texture analyses using the widely used pole-to-orientation probability density function reconstruction softwareWIMV, known by the initials of its authors and their ancestors (Williams–Imhof–Matthies–Vinel). Synthetic orientation probability density functions were then synthesized, covering a large domain of variation for texture index and entropy, and used to check the numerical results of the same software package.

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