Further, the traditional way to learn the parameters of a deep architecture is to minimize an objective function by computing the gradient over all the parameters using the backpropagation algorithm [14] with a nonlinear optimizer.
A voxel-wise approximation of the surface normal was obtained by computing the gradient direction for each voxel within a scalar field derived by a combination of these distance functions (ФWM– ФPBS).
Often it is helpful to interpret MEG fields measured by magnetometers (and axial gradiometers, e.g., Gross et al. 2012) after transforming the data to a planar gradient configuration, that is, by computing the gradient tangential to the scalp.
By rewriting the matrix quadratic form in the log-likelihood term of (34) as a vector quadratic form in terms of h ̲ ( f ) and by computing the gradient of Q G and equating it to zero, we obtain h ̲ ( f ) = γ Σ h ̲ − 1 ( f ) + 1 σ b 2 ( f ) ∑ n = 1 N ( R ̂ s ( n, f ) ⊗ I I ) T − 1 × γ Σ h ̲ − 1 ( f ) μ h ̲ ( f ) + 1 σ b 2 ( f ) ∑ n = 1 N vec ( R ̂ xs ( n, f ) ) (35).
This is achieved by computing the gradient (vec{g}) and the Hessian H (or its approximation) at each iteration of the nonlinear regression.
Ruiz et al. [26] presented a texture orientation detection algorithm by computing the dominant gradient and reducing the unnecessary directional candidate modes in the RDO process, saving average time of 30.1% compared with HM 14.0.
We simplify the local variation in the gradient by computing its descriptive statistics, i.e., mean (mu ), standard deviation (sigma ), median m and maximum (mathcal {M}).
As in references, we therefore quantified the Wilson ventricular gradient by computing the spatial dispersion of ventricular repolarization.
At each iteration, the deformation field is updated by computing local forces using the intensity gradient and the difference of the intensities of the two images.
The quantity n x /n (h d c d) is the kernel density estimate f̂ U (x) (where U means the uniform kernel ) computed with the hypersphere S h(x), and thus we can write expression (4) as: which yields, Expression (7) shows that an estimate of the normalized gradient can be obtained by computing the sample mean shift in a uniform kernel centered on x.
