Kernel.LoG#

classmethod Kernel.LoG(sigma, h=None)[source]#

Laplacian of Gaussian kernel

Parameters:

sigma (float) – standard deviation of first Gaussian kernel
h (int, optional) – half-width of kernel

Returns:

2h+1 x 2h+1 kernel

Return type:

Kernel

Return a 2-dimensional Laplacian of Gaussian kernel with standard deviation sigma

\[\mathbf{K} = \frac{1}{\pi \sigma^4} \left(\frac{u^2 + v^2}{2 \sigma^2} -1\right) e^{-(u^2 + v^2) / 2 \sigma^2}\]

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.LoG(1)
>>> K
Kernel: 7x7, min=-0.32, max=0.043, mean=9.6e-20, SYMMETRIC (LoG σ=1)
>>> K.print()
  0.00  0.00  0.01  0.01  0.01  0.00  0.00
  0.00  0.02  0.04  0.04  0.04  0.02  0.00
  0.01  0.04  0.00 -0.10  0.00  0.04  0.01
  0.01  0.04 -0.10 -0.32 -0.10  0.04  0.01
  0.01  0.04  0.00 -0.10  0.00  0.04  0.01
  0.00  0.02  0.04  0.04  0.04  0.02  0.00
  0.00  0.00  0.01  0.01  0.01  0.00  0.00