DerivativeFilter

DerivativeFilter[data,{n1,n2,}]

computes the ni^(th) derivative of data at level i.

DerivativeFilter[data,{n1,n2,},σ]

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

DerivativeFilter[data,{der1,der2,},]

computes several derivatives der1, der2, .

Details and Options

  • DerivativeFilter is a linear filter that computes the derivatives of data based on a spline interpolation model. Regularization with a Gaussian kernel of standard deviation σ (default value is σ=0) can be used to reduce susceptibility to noise.
  • The data can be any of the following:
  • listarbitrary-rank numerical array
    tseriestemporal data such as TimeSeries, TemporalData,
    imagearbitrary Image or Image3D object
    audioan Audio object
  • DerivativeFilter operates separately on each level of data.
  • DerivativeFilter[image,] uses the array coordinate system, where the first coordinate runs from the top to the bottom of image, and the second coordinate increases from left to right.
  • DerivativeFilter gives a result with the same dimensions as data.
  • DerivativeFilter can take the following options:
  • InterpolationOrderAutomaticinterpolation order up to 8
    Padding"Fixed"padding method
  • With Padding->{pad1,pad2,}, different padding schemes can be used for every dimension of data.
  • The derivative order has to be smaller than the specified interpolation order.

Examples

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Basic Examples  (3)

Derivative of a numeric list:

In[1]:=
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In[2]:=
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Out[2]=
In[3]:=
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Out[3]=

A horizontal derivative of an image:

In[1]:=
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Out[1]=

A regularized horizontal derivative of an image:

In[1]:=
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Out[1]=

Scope  (13)

Options  (3)

Applications  (5)

Properties & Relations  (4)

See Also

GaussianFilter  Derivative  RidgeFilter  DifferentiatorFilter

Introduced in 2010
(8.0)
| Updated in 2016
(11.0)