This is documentation for Mathematica 8, which was
based on an earlier version of the Wolfram Language.

# DerivativeFilter

 DerivativeFilter computes the derivative of image in the vertical and horizontal directions. DerivativeFiltercomputes the derivative at a Gaussian scale of standard deviation . DerivativeFiltercomputes the derivative of array.
• 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.
• Possible settings for the InterpolationOrder option are 1, 3, 5, 7, or 9. The derivation order has to be smaller than the specified interpolation order.
• Image derivatives are susceptible to noise. To counteract this effect, one can regularize the image or data by a Gaussian kernel of standard deviation . The default value is =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.
The vertical derivative of an image:
The horizontal derivative of an image:
The vertical derivative of an image:
 Out[1]=

The horizontal derivative of an image:
 Out[1]=
 Applications   (2)
Ridge detection at scale :
T-junction filter:
New in 8