Derivative

Gradient filter but using predefined kernels.

🖼️ Image options and parameters of derivative method

Derivative filter is a special case of a gradient filter, therefore it uses gradient algorithm. However, the key difference are the kernels used in this very algorithm. In ImageJS there are three distinguished kernels: Sobel, Scharr and Prewitt.

Source:LennaBarbaraStandard boatMandrillPeppersHouse

Ran in 0.00μs (Infinity ops/s)

Parameters and default values

• options

Options

Property	Required	Default value
bitDepth	no	image.bitDepth
borderType	no	replicate
borderValue	no	0
filter	no	sobel

• Sobel kernel

$KernelX = \begin{bmatrix} -1 & 0 & 1 \\ -2 & 0 & 2 \\ -1 & 0 & 1 \end{bmatrix}$

$KernelY = \begin{bmatrix} -1 & -2 & -1 \\ 0 & 0 & 0 \\ 1 & 2 & 1 \end{bmatrix}$

• Scharr kernel

$KernelX = \begin{bmatrix} 3 & 0 & -3 \\ 10 & 0 & -10 \\ 3 & 0 & -3 \end{bmatrix}$

$KernelY = \begin{bmatrix} 3 & 10 & 3 \\ 0 & 0 & 0 \\ -3 & -10 & -3 \end{bmatrix}$

• Prewitt kernel

$KernelX = \begin{bmatrix} 1 & 0 & -1 \\ 1 & 0 & -1 \\ 1 & 0 & -1 \end{bmatrix}$

$KernelY = \begin{bmatrix} 1 & 1 & 1 \\ 0 & 0 & 0 \\ -1 & -1 & -1 \end{bmatrix}$

info

As was mentioned, derivative filter is a type of gradient filter. Therefore using the same kernels with gradient filter will provide the same image output. Derivative filter simplifies some kernel's application.

Applying Sobel kernel using gradient filter

return image.gradientFilter({
  kernelX: [
    [-1, 0, 1],
    [-2, 0, 2],
    [-1, 0, 1],
  ],
  kernelY: [
    [-1, -2, -1],
    [0, 0, 0],
    [1, 2, 1],
  ],
});

Applying Sobel kernel using derivative filter

return image.derivativeFilter({ filter: 'sobel' });