Wolfram Language & System 11.0 (2016)|Legacy Documentation

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computes the ni^(th) derivative of image in the vertical and horizontal directions.

computes the derivative at a Gaussian scale of standard deviation σ.

computes the {n1,n2,}^(th) derivative of array.

computes several derivatives der1, der2, .

Details and OptionsDetails and Options

  • DerivativeFilter is a linear filter that renders the derivatives of an image based on a spline interpolation model.
  • DerivativeFilter uses the array coordinate system, where the first coordinate runs from the top to the bottom of image, and the second coordinate increases from right to left.
  • DerivativeFilter works with arbitrary grayscale or multichannel images, operating separately on each channel.
  • DerivativeFilter works with 3D as well as 2D images, and also with data arrays of any rank.
  • DerivativeFilter[image,] gives a real image of the same dimensions as image.
  • DerivativeFilter can take the following options:
  • InterpolationOrderAutomaticinterpolation order up to 8
    Padding"Fixed"padding method
  • The derivation order has to be smaller than the specified interpolation order.
  • Image derivatives are susceptible to noise. To counteract this effect, you can regularize the image or data by a Gaussian kernel of standard deviation σ. The default value is σ=0.
  • The Padding option accepts the settings "Fixed", "Periodic", "Reversed", "Reflected", or a numeric value. A list of these settings can specify different paddings for every dimension of image or data.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

The vertical derivative of an image:

Click for copyable input

The horizontal derivative of an image:

Click for copyable input

The derivative of a list:

Click for copyable input
Click for copyable input
Click for copyable input
Introduced in 2010
| Updated in 2014