

.. _sphx_glr_auto_examples_segmentation_plot_extrema.py:


===============================
Extrema
===============================

We detect local maxima in a galaxy image. The image is corrupted by noise,
generating many local maxima. To keep only those maxima with sufficient
local contrast, we use h-maxima.



.. code-block:: python

    import numpy as np

    import matplotlib.pyplot as plt

    from skimage.measure import label
    from skimage import data
    from skimage import color
    from skimage.morphology import extrema
    from skimage import exposure


    color_image = data.hubble_deep_field()
    img = color.rgb2grey(color_image)

    # the rescaling is done only for visualization purpose.
    # the algorithms would work identically in an unscaled version of the
    # image. However, the parameter h needs to be adapted to the scale.
    img = exposure.rescale_intensity(img)

    # for visualization, we work on a crop of the image.
    x_0 = 70
    y_0 = 354
    width = 100
    height = 100








MAXIMA DETECTION



.. code-block:: python


    # Maxima in the galaxy image are detected by mathematical morphology.
    # There is no a priori constraint on the density.

    # We find all local maxima
    local_maxima = extrema.local_maxima(img)
    label_maxima = label(local_maxima)
    overlay = color.label2rgb(label_maxima, img, alpha=0.7, bg_label=0,
                              bg_color=None, colors=[(1, 0, 0)])

    # We observed in the previous image, that there are many local maxima
    # that are caused by the noise in the image.
    # For this, we find all local maxima with a height of h.
    # This height is the grey level value by which we need to descent
    # in order to reach a higher maximum and it can be seen as a local
    # contrast measurement.
    # The value of h scales with the dynamic range of the image, i.e.
    # if we multiply the image with a constant, we need to multiply
    # the value of h with the same constant in order to achieve the same result.
    h = 0.05
    h_maxima = extrema.h_maxima(img, h)
    label_h_maxima = label(h_maxima)
    overlay_h = color.label2rgb(label_h_maxima, img, alpha=0.7, bg_label=0,
                                bg_color=None, colors=[(1, 0, 0)])








GRAPHICAL OUTPUT



.. code-block:: python


    # a new figure with 3 subplots
    fig, ax = plt.subplots(1, 3, figsize=(15, 5))

    ax[0].imshow(img[y_0:(y_0 + height), x_0:(x_0 + width)], cmap='gray',
                 interpolation='none')
    ax[0].set_title('Original image')
    ax[0].axis('off')

    ax[1].imshow(overlay[y_0:(y_0 + height), x_0:(x_0 + width)],
                 interpolation='none')
    ax[1].set_title('Local Maxima')
    ax[1].axis('off')

    ax[2].imshow(overlay_h[y_0:(y_0 + height), x_0:(x_0 + width)],
                 interpolation='none')
    ax[2].set_title('h maxima for h = %.2f' % h)
    ax[2].axis('off')
    plt.show()



.. image:: /auto_examples/segmentation/images/sphx_glr_plot_extrema_001.png
    :align: center




**Total running time of the script:** ( 0 minutes  3.850 seconds)



.. container:: sphx-glr-footer


  .. container:: sphx-glr-download

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



  .. container:: sphx-glr-download

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

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

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