machinevisiontoolbox.ImageSpatial.Kernel.Gauss

static Kernel.Gauss(sigma, h=None)[source]

Gaussian kernel

Parameters:

sigma (float) – standard deviation of Gaussian kernel
h (integer, optional) – half width of the kernel

Returns:

Gaussian kernel

Return type:

ndarray(2h+1, 2h+1)

Return the 2-dimensional Gaussian kernel of standard deviation sigma

\[\mathbf{K} = \frac{1}{2\pi \sigma^2} e^{-(u^2 + v^2) / 2 \sigma^2}\]

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
>>> K = Kernel.Gauss(sigma=1, h=2)
>>> K.shape
(5, 5)
>>> K
array([[0.003 , 0.0133, 0.0219, 0.0133, 0.003 ],
       [0.0133, 0.0596, 0.0983, 0.0596, 0.0133],
       [0.0219, 0.0983, 0.1621, 0.0983, 0.0219],
       [0.0133, 0.0596, 0.0983, 0.0596, 0.0133],
       [0.003 , 0.0133, 0.0219, 0.0133, 0.003 ]])
>>> K = Kernel.Gauss(sigma=2)
>>> K.shape
(13, 13)

Note:

The volume under the Gaussian kernel is one.
If the kernel is strongly truncated, ie. it is non-zero at the edges of the window then the volume will be less than one.

References:

Robotics, Vision & Control for Python, Section 11.5.1.1, P. Corke, Springer 2023.

Seealso:

DGauss