.. note::
    :class: sphx-glr-download-link-note

    Click :ref:`here <sphx_glr_download_intro_scipy_auto_examples_solutions_plot_image_blur.py>` to download the full example code
.. rst-class:: sphx-glr-example-title

.. _sphx_glr_intro_scipy_auto_examples_solutions_plot_image_blur.py:


=======================================================
Simple image blur by convolution with a Gaussian kernel
=======================================================

Blur an an image (:download:`../../../../data/elephant.png`) using a
Gaussian kernel.

Convolution is easy to perform with FFT: convolving two signals boils
down to multiplying their FFTs (and performing an inverse FFT).




.. code-block:: python


    import numpy as np
    from scipy import fftpack
    import matplotlib.pyplot as plt







The original image
####################################################################



.. code-block:: python


    # read image
    img = plt.imread('../../../../data/elephant.png')
    plt.figure()
    plt.imshow(img)




.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_image_blur_001.png
    :class: sphx-glr-single-img




Prepare an Gaussian convolution kernel
####################################################################



.. code-block:: python


    # First a 1-D  Gaussian
    t = np.linspace(-10, 10, 30)
    bump = np.exp(-0.1*t**2)
    bump /= np.trapz(bump) # normalize the integral to 1

    # make a 2-D kernel out of it
    kernel = bump[:, np.newaxis] * bump[np.newaxis, :]







Implement convolution via FFT
####################################################################



.. code-block:: python


    # Padded fourier transform, with the same shape as the image
    # We use :func:`scipy.signal.fftpack.fft2` to have a 2D FFT
    kernel_ft = fftpack.fft2(kernel, shape=img.shape[:2], axes=(0, 1))

    # convolve
    img_ft = fftpack.fft2(img, axes=(0, 1))
    # the 'newaxis' is to match to color direction
    img2_ft = kernel_ft[:, :, np.newaxis] * img_ft
    img2 = fftpack.ifft2(img2_ft, axes=(0, 1)).real

    # clip values to range
    img2 = np.clip(img2, 0, 1)

    # plot output
    plt.figure()
    plt.imshow(img2)




.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_image_blur_002.png
    :class: sphx-glr-single-img




Further exercise (only if you are familiar with this stuff):

A "wrapped border" appears in the upper left and top edges of the
image. This is because the padding is not done correctly, and does
not take the kernel size into account (so the convolution "flows out
of bounds of the image").  Try to remove this artifact.


A function to do it: :func:`scipy.signal.fftconvolve`
####################################################################

 The above exercise was only for didactic reasons: there exists a
 function in scipy that will do this for us, and probably do a better
 job: :func:`scipy.signal.fftconvolve`



.. code-block:: python


    from scipy import signal
    # mode='same' is there to enforce the same output shape as input arrays
    # (ie avoid border effects)
    img3 = signal.fftconvolve(img, kernel[:, :, np.newaxis], mode='same')
    plt.figure()
    plt.imshow(img3)




.. image:: /intro/scipy/auto_examples/solutions/images/sphx_glr_plot_image_blur_003.png
    :class: sphx-glr-single-img




Note that we still have a decay to zero at the border of the image.
Using :func:`scipy.ndimage.gaussian_filter` would get rid of this
artifact



.. code-block:: python



    plt.show()







**Total running time of the script:** ( 0 minutes  0.064 seconds)


.. _sphx_glr_download_intro_scipy_auto_examples_solutions_plot_image_blur.py:


.. only :: html

 .. container:: sphx-glr-footer
    :class: sphx-glr-footer-example



  .. container:: sphx-glr-download

     :download:`Download Python source code: plot_image_blur.py <plot_image_blur.py>`



  .. container:: sphx-glr-download

     :download:`Download Jupyter notebook: plot_image_blur.ipynb <plot_image_blur.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.readthedocs.io>`_