.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/features_detection/plot_shape_index.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` 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_features_detection_plot_shape_index.py: =========== Shape Index =========== The shape index is a single valued measure of local curvature, derived from the eigen values of the Hessian, defined by Koenderink & van Doorn [1]_. It can be used to find structures based on their apparent local shape. The shape index maps to values from -1 to 1, representing different kind of shapes (see the documentation for details). In this example, a random image with spots is generated, which should be detected. A shape index of 1 represents 'spherical caps', the shape of the spots we want to detect. The leftmost plot shows the generated image, the center shows a 3D render of the image, taking intensity values as height of a 3D surface, and the right one shows the shape index (s). As visible, the shape index readily amplifies the local shape of noise as well, but is insusceptible to global phenomena (e.g. uneven illumination). The blue and green marks are points which deviate no more than 0.05 from the desired shape. To attenuate noise in the signal, the green marks are taken from the shape index (s) after another Gaussian blur pass (yielding s'). Note how spots interjoined too closely are *not* detected, as they do not posses the desired shape. .. [1] Koenderink, J. J. & van Doorn, A. J., "Surface shape and curvature scales", Image and Vision Computing, 1992, 10, 557-564. :DOI:`10.1016/0262-8856(92)90076-F` .. GENERATED FROM PYTHON SOURCE LINES 41-145 .. image-sg:: /auto_examples/features_detection/images/sphx_glr_plot_shape_index_001.png :alt: Input image, 3D visualization, Shape index, $\sigma=1$ :srcset: /auto_examples/features_detection/images/sphx_glr_plot_shape_index_001.png :class: sphx-glr-single-img .. code-block:: Python import numpy as np import matplotlib.pyplot as plt from scipy import ndimage as ndi from skimage.feature import shape_index from skimage.draw import disk def create_test_image(image_size=256, spot_count=30, spot_radius=5, cloud_noise_size=4): """ Generate a test image with random noise, uneven illumination and spots. """ rng = np.random.default_rng() image = rng.normal(loc=0.25, scale=0.25, size=(image_size, image_size)) for _ in range(spot_count): rr, cc = disk( (rng.integers(image.shape[0]), rng.integers(image.shape[1])), spot_radius, shape=image.shape, ) image[rr, cc] = 1 image *= rng.normal(loc=1.0, scale=0.1, size=image.shape) image *= ndi.zoom( rng.normal(loc=1.0, scale=0.5, size=(cloud_noise_size, cloud_noise_size)), image_size / cloud_noise_size, ) return ndi.gaussian_filter(image, sigma=2.0) # First create the test image and its shape index image = create_test_image() s = shape_index(image) # In this example we want to detect 'spherical caps', # so we threshold the shape index map to # find points which are 'spherical caps' (~1) target = 1 delta = 0.05 point_y, point_x = np.where(np.abs(s - target) < delta) point_z = image[point_y, point_x] # The shape index map relentlessly produces the shape, even that of noise. # In order to reduce the impact of noise, we apply a Gaussian filter to it, # and show the results once in s_smooth = ndi.gaussian_filter(s, sigma=0.5) point_y_s, point_x_s = np.where(np.abs(s_smooth - target) < delta) point_z_s = image[point_y_s, point_x_s] fig = plt.figure(figsize=(12, 4)) ax1 = fig.add_subplot(1, 3, 1) ax1.imshow(image, cmap=plt.cm.gray) ax1.axis('off') ax1.set_title('Input image') scatter_settings = dict(alpha=0.75, s=10, linewidths=0) ax1.scatter(point_x, point_y, color='blue', **scatter_settings) ax1.scatter(point_x_s, point_y_s, color='green', **scatter_settings) ax2 = fig.add_subplot(1, 3, 2, projection='3d', sharex=ax1, sharey=ax1) x, y = np.meshgrid(np.arange(0, image.shape[0], 1), np.arange(0, image.shape[1], 1)) ax2.plot_surface(x, y, image, linewidth=0, alpha=0.5) ax2.scatter( point_x, point_y, point_z, color='blue', label='$|s - 1|<0.05$', **scatter_settings ) ax2.scatter( point_x_s, point_y_s, point_z_s, color='green', label='$|s\' - 1|<0.05$', **scatter_settings, ) ax2.legend(loc='lower left') ax2.axis('off') ax2.set_title('3D visualization') ax3 = fig.add_subplot(1, 3, 3, sharex=ax1, sharey=ax1) ax3.imshow(s, cmap=plt.cm.gray) ax3.axis('off') ax3.set_title(r'Shape index, $\sigma=1$') fig.tight_layout() plt.show() .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 1.071 seconds) .. _sphx_glr_download_auto_examples_features_detection_plot_shape_index.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/features_detection/plot_shape_index.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_shape_index.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_shape_index.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_