.. _gradient:

gradient
********


**Syntax:** :code:`gradient(f, spatial sigma, dfdx, dfdy, dfdz, gamma)`

Calculates Gaussian gradient :math:`(\partial f / \partial x, \partial f / \partial y, \partial f / \partial z)` of an image :math:`f`. Each of the derivatives is calculated by convolving the image with the corresponding derivative of the Gaussian function.

This command can be used in the distributed processing mode. Use :ref:`distribute` command to change processing mode from local to distributed.

Arguments
---------

f [input]
~~~~~~~~~

**Data type:** uint8 image, uint16 image, uint32 image, uint64 image, int8 image, int16 image, int32 image, int64 image, float32 image

Image whose gradient is to be calculated.

spatial sigma [input]
~~~~~~~~~~~~~~~~~~~~~

**Data type:** real

Standard deviation of Gaussian kernel.

dfdx [output]
~~~~~~~~~~~~~

**Data type:** float32 image

Derivative in :math:`x`-direction

dfdy [output]
~~~~~~~~~~~~~

**Data type:** float32 image

Derivative in :math:`y`-direction

dfdz [output]
~~~~~~~~~~~~~

**Data type:** float32 image

Derivative in :math:`z`-direction

gamma [input]
~~~~~~~~~~~~~

**Data type:** real

**Default value:** 0

Scale-space scaling exponent according to Lindeberg. Set to zero to disable scaling.

See also
--------

:ref:`derivative`, :ref:`gradientmagnitude`