machinevisiontoolbox.ImageSpatial.Kernel.DGauss
- static Kernel.DGauss(sigma, h=None)[source]
Derivative of Gaussian kernel
- Parameters:
sigma (float) – standard deviation of first Gaussian kernel
h (int, optional) – half-width of kernel
- Returns:
kernel
- Return type:
ndarray(2h+1, 2h+1)
Returns a 2-dimensional derivative of Gaussian kernel with standard deviation
sigma\[\mathbf{K} = \frac{-x}{2\pi \sigma^2} e^{-(x^2 + y^2) / 2 \sigma^2}\]The kernel is centred within a square array with side length given by:
\(2 \mbox{ceil}(3 \sigma) + 1\), or
\(2\mathtt{h} + 1\)
Example:
>>> from machinevisiontoolbox import Kernel >>> Kernel.DGauss(1) array([[ 0.0001, 0.0005, 0.0011, -0. , -0.0011, -0.0005, -0.0001], [ 0.0007, 0.0058, 0.0131, -0. , -0.0131, -0.0058, -0.0007], [ 0.0032, 0.0261, 0.0585, -0. , -0.0585, -0.0261, -0.0032], [ 0.0053, 0.0431, 0.0965, -0. , -0.0965, -0.0431, -0.0053], [ 0.0032, 0.0261, 0.0585, -0. , -0.0585, -0.0261, -0.0032], [ 0.0007, 0.0058, 0.0131, -0. , -0.0131, -0.0058, -0.0007], [ 0.0001, 0.0005, 0.0011, -0. , -0.0011, -0.0005, -0.0001]])
- Note:
This kernel is the horizontal derivative of the Gaussian, \(dG/dx\).
The vertical derivative, \(dG/dy\), is the transpose of this kernel.
This kernel is an effective edge detector.
- References:
Robotics, Vision & Control for Python, Section 11.5.1.3, P. Corke, Springer 2023.
- Seealso: