Quaternions are used to represent orientations of a rigid body in the 3-dimensional space eliminating the problem of singularities.
Gabor features and PC features show remarkable advantages in representing orientation and gradient information of images.
These statistics also allow representing orientation coherence patterns typical of the observed nanostructure.
These models begin by defining an input space, with some coordinates being linear (representing position or spatial frequency) and others circular (representing orientation), need to be mapped to the two-dimensional plane in some optimal fashion [61], [62], [64], [116], [122] [126].
More specifically, here the angle of each filament relative to the horizontal is set to a normally distributed value with mean 0 and a certain standard deviation (representing orientation dispersion).
Figures 5(a)- 5(b) show the orientation distribution functions (ODFs, f as determined at each depth of the hip and knee samples. The angle β represents orientation of individual molecular chains with respect to the mean preferential orientation (θ p ).
Third, preliminary data showed shifts in the balance of represented orientations within the map.
The clear result seen in Fig. 5, that Lanczos 3 and B-spline outperform the other interpolation methods, is drastically reduced when the training data is somewhat more heterogeneous in terms of represented orientations.
