Kernel.DGauss

classmethod Kernel.DGauss(sigma, h=None)

Derivative of Gaussian kernel

Parameters:

• sigma (float) – standard deviation of Gaussian kernel

• h (int, optional) – half-width of kernel

Returns:

2h+1 x 2h+1 kernel

Return type:

Kernel

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
>>> K = Kernel.DGauss(1)
>>> K
Kernel: 7x7, min=-0.097, max=0.097, mean=-4.3e-19 (DGauss σ=1)
>>> K.print()
  0.00  0.00  0.00 -0.00 -0.00 -0.00 -0.00
  0.00  0.01  0.01 -0.00 -0.01 -0.01 -0.00
  0.00  0.03  0.06 -0.00 -0.06 -0.03 -0.00
  0.01  0.04  0.10 -0.00 -0.10 -0.04 -0.01
  0.00  0.03  0.06 -0.00 -0.06 -0.03 -0.00
  0.00  0.01  0.01 -0.00 -0.01 -0.01 -0.00
  0.00  0.00  0.00 -0.00 -0.00 -0.00 -0.00

Example:

>>> Kernel.DGauss(5, 15).disp3d()

(Source code, png, hires.png, pdf)

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:

• P. Corke, Robotics, Vision & Control for Python, Springer, 2023, Section 11.5.1.3.

Seealso:

HGauss Gauss Sobel