.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/edges/plot_ridge_filter.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_auto_examples_edges_plot_ridge_filter.py>`
        to download the full example code or to run this example in your browser via Binder

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_edges_plot_ridge_filter.py:


===============
Ridge operators
===============

Ridge filters can be used to detect ridge-like structures, such as neurites
[1]_, tubes [2]_, vessels [3]_, wrinkles [4]_ or rivers.

Different ridge filters may be suited for detecting different structures,
e.g., depending on contrast or noise level.

The present class of ridge filters relies on the eigenvalues of
the Hessian matrix of image intensities to detect ridge structures where the
intensity changes perpendicular but not along the structure.

References
----------

.. [1] Meijering, E., Jacob, M., Sarria, J. C., Steiner, P., Hirling, H.,
       Unser, M. (2004). Design and validation of a tool for neurite tracing
       and analysis in fluorescence microscopy images. Cytometry Part A, 58(2),
       167-176.
       :DOI:`10.1002/cyto.a.20022`

.. [2] Sato, Y., Nakajima, S., Shiraga, N., Atsumi, H., Yoshida, S.,
       Koller, T., ..., Kikinis, R. (1998). Three-dimensional multi-scale line
       filter for segmentation and visualization of curvilinear structures in
       medical images. Medical image analysis, 2(2), 143-168.
       :DOI:`10.1016/S1361-8415(98)80009-1`

.. [3] Frangi, A. F., Niessen, W. J., Vincken, K. L., & Viergever, M. A. (1998,
       October). Multiscale vessel enhancement filtering. In International
       Conference on Medical Image Computing and Computer-Assisted Intervention
       (pp. 130-137). Springer Berlin Heidelberg.
       :DOI:`10.1007/BFb0056195`

.. [4] Ng, C. C., Yap, M. H., Costen, N., & Li, B. (2014, November). Automatic
       wrinkle detection using hybrid Hessian filter. In Asian Conference on
       Computer Vision (pp. 609-622). Springer International Publishing.
       :DOI:`10.1007/978-3-319-16811-1_40`

.. GENERATED FROM PYTHON SOURCE LINES 42-87



.. image-sg:: /auto_examples/edges/images/sphx_glr_plot_ridge_filter_001.png
   :alt: original, meijering σ = [1], meijering σ = [1, 2, 3, 4], sato σ = [1], sato σ = [1, 2, 3, 4], frangi σ = [1], frangi σ = [1, 2, 3, 4], hessian σ = [1], hessian σ = [1, 2, 3, 4]
   :srcset: /auto_examples/edges/images/sphx_glr_plot_ridge_filter_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    from skimage import data
    from skimage import color
    from skimage.filters import meijering, sato, frangi, hessian
    import matplotlib.pyplot as plt


    def original(image, **kwargs):
        """Return the original image, ignoring any kwargs."""
        return image


    image = color.rgb2gray(data.retina())[300:700, 700:900]
    cmap = plt.cm.gray

    plt.rcParams["axes.titlesize"] = "medium"
    axes = plt.figure(figsize=(10, 4)).subplots(2, 9)
    for i, black_ridges in enumerate([True, False]):
        for j, (func, sigmas) in enumerate(
            [
                (original, None),
                (meijering, [1]),
                (meijering, range(1, 5)),
                (sato, [1]),
                (sato, range(1, 5)),
                (frangi, [1]),
                (frangi, range(1, 5)),
                (hessian, [1]),
                (hessian, range(1, 5)),
            ]
        ):
            result = func(image, black_ridges=black_ridges, sigmas=sigmas)
            axes[i, j].imshow(result, cmap=cmap)
            if i == 0:
                title = func.__name__
                if sigmas:
                    title += f"\n\N{GREEK SMALL LETTER SIGMA} = {list(sigmas)}"
                axes[i, j].set_title(title)
            if j == 0:
                axes[i, j].set_ylabel(f'{black_ridges = }')
            axes[i, j].set_xticks([])
            axes[i, j].set_yticks([])

    plt.tight_layout()
    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 2.277 seconds)


.. _sphx_glr_download_auto_examples_edges_plot_ridge_filter.py:

.. only:: html

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

    .. container:: binder-badge

      .. image:: images/binder_badge_logo.svg
        :target: https://mybinder.org/v2/gh/scikit-image/scikit-image/v0.23.2?filepath=notebooks/auto_examples/edges/plot_ridge_filter.ipynb
        :alt: Launch binder
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

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

    .. container:: sphx-glr-download sphx-glr-download-python

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


.. only:: html

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

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