The former is developed so as to find the most representative features while the latter is developed to provide a set of rotation-invariant features for texture characterization.
Initialization is performed in a similar way as the proposed method and results in a set of rotations and translations, one of which approximately aligns the two coordinate systems.
A "conjugate pair" corresponds to the coordinate of the fixed point in 2D sensor coordinate system, a set of PH10M rotation angles, and the coordinate got from the CMM optical scales.
As it lacked the artificial intelligence, or the control link with a pilot on the ground, it reached a given destination by using a set of propeller rotation and a gyroscope.
Then, a set of small rotations of rotary axes are used to decouple the squareness errors of linear and rotary axes.
The basic idea is to use a set of large rotations of rotary axes to prolong the moving distance of linear axes when squareness errors of linear axes are identified.
Instead, we minimize the above equation for a set of possible rotations Θ = { θ1, θ2,..., θ Q}: (21) θ b = argmin θ i PSSD θ i, i ∈ [ 1, Q ], from which we obtain d b = argmin d PSSD θ b.
Based on such a decomposition, the intensity distribution of all the voxels in shell V j (x i ) can then be described by a set of L rotation-invariant features { s jl | l=1,…, L} Kazhdan et al., 2003) as follows: (7) Such features are calculated for all the M shells.
The mean rotation for a set of 3-D rotations, M, is a commonly used measure of center which is defined as the rotation that maximizes (text {trace}(mathbf {M}^{T} bar {mathbf {O}})), where (bar {mathbf {O}}=frac {1}{n}sum _{i=1}^{n} mathbf {O}_{i}) (Khatri and Mardia 1977; Leoń et al. 2006; Bingham et al. 2009a).
A set of translation, symmetry, rotation and scaling operations have been applied to the bucket sections of the Savonius rotor by means of transforming the initial cylindrical buckets into topological surfaces with an organic shape.
The input for this step is the set Q of residue positions that are modeled as flexible using backrubs and rotamers, and a set of allowed primary rotation angles.
