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scipy.ndimage.

# gaussian_filter

scipy.ndimage.gaussian_filter(input, sigma, order=0, output=None, mode='reflect', cval=0.0, truncate=4.0, *, radius=None, axes=None)

  Multidimensional Gaussian filter.

  Parameters:
    input array_like

      The input array.

    sigma scalar or sequence of scalars

      Standard deviation for Gaussian kernel. The standard deviations of the Gaussian filter are given for each axis as a sequence, or as a single number, in which case it is equal for all axes.

    order int or sequence of ints, optional

      The order of the filter along each axis is given as a sequence of integers, or as a single number. An order of 0 corresponds to convolution with a Gaussian kernel. A positive order corresponds to convolution with that derivative of a Gaussian.

    output array or dtype, optional

      The array in which to place the output, or the dtype of the returned array. By default an array of the same dtype as input will be created.

    mode str or sequence, optional

      The mode parameter determines how the input array is extended when the filter overlaps a border. By passing a sequence of modes with length equal to the number of dimensions of the input array, different modes can be specified along each axis. Default value is ‘reflect’. The valid values and their behavior is as follows:

      ‘reflect’ (d c b a | a b c d | d c b a)

        The input is extended by reflecting about the edge of the last pixel. This mode is also sometimes referred to as half-sample symmetric.

      ‘constant’ (k k k k | a b c d | k k k k)

        The input is extended by filling all values beyond the edge with the same constant value, defined by the cval parameter.

      ‘nearest’ (a a a a | a b c d | d d d d)

        The input is extended by replicating the last pixel.

      ‘mirror’ (d c b | a b c d | c b a)

        The input is extended by reflecting about the center of the last pixel. This mode is also sometimes referred to as whole-sample symmetric.

      ‘wrap’ (a b c d | a b c d | a b c d)

        The input is extended by wrapping around to the opposite edge.

      For consistency with the interpolation functions, the following mode names can also be used:

      ‘grid-constant’

        This is a synonym for ‘constant’.

      ‘grid-mirror’

        This is a synonym for ‘reflect’.

      ‘grid-wrap’

        This is a synonym for ‘wrap’.

    cval scalar, optional

      Value to fill past edges of input if mode is ‘constant’. Default is 0.0.

    truncate float, optional

      Truncate the filter at this many standard deviations. Default is 4.0.

    radius None or int or sequence of ints, optional

      Radius of the Gaussian kernel. The radius are given for each axis as a sequence, or as a single number, in which case it is equal for all axes. If specified, the size of the kernel along each axis will be `2*radius + 1`, and truncate is ignored. Default is None.

    axes tuple of int or None, optional

      If None, input is filtered along all axes. Otherwise, input is filtered along the specified axes. When axes is specified, any tuples used for sigma, order, mode and/or radius must match the length of axes. The ith entry in any of these tuples corresponds to the ith entry in axes.

  Returns:
    gaussian_filter ndarray

      Returned array of same shape as input.

  Notes

  The multidimensional filter is implemented as a sequence of 1-D convolution filters. The intermediate arrays are stored in the same data type as the output. Therefore, for output types with a limited precision, the results may be imprecise because intermediate results may be stored with insufficient precision.

  The Gaussian kernel will have size `2*radius + 1` along each axis. If radius is None, the default `radius = round(truncate * sigma)` will be used.

  Array API Standard Support

  `gaussian_filter` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ⛔
  JAX | ⚠️ no JIT | ⛔
  Dask | ⚠️ computes graph | n/a

  > See Support for the array API standard for more information.

  Examples

      >>> from scipy.ndimage import gaussian_filter
      >>> import numpy as np
      >>> a = np.arange(50, step=2).reshape((5,5))
      >>> a
      array([[ 0,  2,  4,  6,  8],
             [10, 12, 14, 16, 18],
             [20, 22, 24, 26, 28],
             [30, 32, 34, 36, 38],
             [40, 42, 44, 46, 48]])
      >>> gaussian_filter(a, sigma=1)
      array([[ 4,  6,  8,  9, 11],
             [10, 12, 14, 15, 17],
             [20, 22, 24, 25, 27],
             [29, 31, 33, 34, 36],
             [35, 37, 39, 40, 42]])

      >>> from scipy import datasets
      >>> import matplotlib.pyplot as plt
      >>> fig = plt.figure()
      >>> plt.gray()  # show the filtered result in grayscale
      >>> ax1 = fig.add_subplot(121)  # left side
      >>> ax2 = fig.add_subplot(122)  # right side
      >>> ascent = datasets.ascent()
      >>> result = gaussian_filter(ascent, sigma=5)
      >>> ax1.imshow(ascent)
      >>> ax2.imshow(result)
      >>> plt.show()