In the case of linear evolution, the nonlinear term in the numerator, expressed by the convolution, may be removed.
Generally, the Hilbert transform is expressed using the convolution representation as follows: (3).
An image is represented as a one-parameter family of smoothed images, the scale-space representation, parameterized by the size of the Gaussian smoothing kernel (Lindeberg, 1994): Given a subtomogram, f, a Gaussian smoothing can be expressed as the convolution between f and : In the smoothed subtomogram, all features with a size smaller than σ are filtered out, whereas others are preserved.
The equation of a linear unidimensional acoustic system, expressed by means of the convolution integral relating pressure and velocity, p t) = ∫0∞ h(t′)v(t−t′ dt′≡h ∗ v, (a), can be transformed [1] into the equation p = Z0v+r∗ (p+Z0v), (b), where r(t) is the FT−1 of r̂f = (Z−Z0)(Z−Z0).
This approach is built on the statistical continuum theories developed by Kroner that express the localization of the response field at the microscale using a series of highly complex convolution integrals, which have historically been evaluated analytically.
The diffusion is expressed by a convolution of the diffusion matrix D m with the filter matrix F element-wise multiplied by the layout map matrix L: (4).
The response is expressed by a convolution of the dawn-to-dusk electric field and some response function and not by the electric field itself. .
The response is expressed by a convolution of the dawn-to-dusk electric field and some response function and not by the electric field itself.
The proposed NNGVF snake expresses the gradient vector flow (GVF) as a convolution with a neighborhood-extending Laplacian operator augmented by a noise-smoothing mask.
We denote by ∗ the convolution.
