# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# DerivativeFilter

DerivativeFilter[image,{n1,n2}]
computes the derivative of image in the vertical and horizontal directions.

DerivativeFilter[image,{n1,n2},σ]
computes the derivative at a Gaussian scale of standard deviation σ.

DerivativeFilter[array,{n1,n2,}]
computes the derivative of array.

DerivativeFilter[,{der1,der2,},]
computes several derivatives , , .

## 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:
•  InterpolationOrder Automatic interpolation 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 , , , , 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:

 In[1]:=
 Out[1]=

The horizontal derivative of an image:

 In[1]:=
 Out[1]=

The derivative of a list:

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