Additionally, in robotic arm kinematics, the chapter is interested in the forward transformation as well as inverse (backward) transformation.
For HEVC forward and backward transformation, we need to consider the data range and the center value in computing matrix multiplications, unlike SAD and SATD implementations.
Backward transformation in correlation coefficients resulted in a moderate association between impairment and disability (r = 0.60; r2 = 36%) and a weak association between impairment and HRQL (r = 0.36; r2 = 13%).
However, because the voxel-by-voxel analysis showed that values correspond well after forward and backward transformations, it suggests that the corresponding transformation is practically invertible.
For non-linear systems, in general only the approximated NNM manifolds are obtainable in practice, so different base points may lead to different forms of NNM oscillators and different normalization schemes lead to different forward and backward transformations which in turn affect the numerical computation errors.
The relationships between the generic backward cloud transformation algorithms are further studied, which help reach the finding that the two backward cloud transformation algorithms presented by Wang and Xu [26,34] are two special cases of the 2nd-GBCT.
Then, a backward state transformation problem is studied which allows us to reconstruct the original state vector of the system.
Our proposed architecture is divided into two units: the warping arithmetic performs backward coordinate transformation and the bilinear interpolation.
Whereafter, an ideal backward cloud transformation algorithm of the 2nd-order generic normal cloud model (2nd-GIBCT) is designed based on the mutually inverse features of FCT and BCT, in which the distribution of all the cloud drops generated in 2nd-GFCT is used.
Meanwhile, a 2nd-order generic backward cloud transformation algorithm (2nd-GBCT), which does not use the distribution of cloud drops, is also proposed to solve real life problems since it is impossible to know the distribution of all the cloud drops in advance in real life applications.
Therefore, by using both the forward and the backward state transformations, state observers for time-delay systems can be systematically designed.
