.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_peptides.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. .. rst-class:: sphx-glr-example-title .. _sphx_glr_auto_examples_plot_peptides.py: Measure the curvature of a peptide ================================== In this example, we measure the curvature of a peptide in an AFM image. Image credit: Yiwei Zheng, `LBNI `_, `EPFL `_ .. GENERATED FROM PYTHON SOURCE LINES 9-19 .. code-block:: Python import matplotlib.pyplot as plt import numpy as np import scipy import skan import skimage import splinebox import tifffile .. GENERATED FROM PYTHON SOURCE LINES 21-23 1. Load and Inspect the Data ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 23-28 .. code-block:: Python img = tifffile.imread("peptides.tif") plt.imshow(img, cmap="afmhot") plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_001.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 29-31 2. Segmentation and Skeletonization ----------------------------------- .. GENERATED FROM PYTHON SOURCE LINES 31-41 .. code-block:: Python thresh = skimage.filters.threshold_otsu(img) mask = img > thresh skeleton = skimage.morphology.skeletonize(mask) label_img = skimage.measure.label(skeleton) label_biggest = np.argmax(np.bincount(label_img.flatten())[1:]) + 1 skeleton = label_img == label_biggest plt.imshow(skeleton) plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_002.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 42-44 3. Select longest path ---------------------- .. GENERATED FROM PYTHON SOURCE LINES 44-57 .. code-block:: Python graph, coords = skan.csr.skeleton_to_csgraph(skeleton) coords = np.stack(coords, axis=-1) dist_matrix, predecessors = scipy.sparse.csgraph.shortest_path(graph, return_predecessors=True) stop_index, start_index = np.unravel_index(np.argmax(dist_matrix), dist_matrix.shape) i = start_index skeleton_points = [] while i != stop_index: skeleton_points.append(coords[i]) i = predecessors[stop_index, i] skeleton_points = np.array(skeleton_points) .. GENERATED FROM PYTHON SOURCE LINES 58-60 4. Fit Spline ------------- .. GENERATED FROM PYTHON SOURCE LINES 60-75 .. code-block:: Python M = 20 basis_function = splinebox.basis_functions.B3() initial_spline = splinebox.spline_curves.Spline(M=M, basis_function=basis_function, closed=False) initial_spline.fit(skeleton_points) t = np.linspace(0, M - 1, M * 100) initial_vals = initial_spline.eval(t) initial_knots = initial_spline.knots plt.imshow(img, cmap="afmhot") plt.plot(initial_vals[:, 1], initial_vals[:, 0]) plt.scatter(initial_knots[:, 1], initial_knots[:, 0]) plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_003.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 76-78 5. Refine Spline ---------------- .. GENERATED FROM PYTHON SOURCE LINES 78-112 .. code-block:: Python def loss_function(control_points, alpha): spline.control_points = control_points.reshape((-1, 2)) coords = spline.eval(t) pixel_values = scipy.ndimage.map_coordinates(img, coords.T) image_energy = np.mean(pixel_values) internal_energy = np.mean(spline.eval(t, derivative=2) ** 2) energy = -1 * image_energy + alpha * internal_energy return energy initial_control_points = initial_spline.control_points spline = initial_spline.copy() scipy.optimize.minimize( loss_function, initial_control_points.flatten(), args=(0.3,), method="Powell", tol=0.01, ) vals = spline.eval(t) knots = spline.knots plt.figure() plt.imshow(img, cmap="afmhot") plt.plot(initial_vals[:, 1], initial_vals[:, 0], label="initial spline", alpha=0.3) plt.scatter(initial_knots[:, 1], initial_knots[:, 0], alpha=0.3) plt.plot(vals[:, 1], vals[:, 0], label="refined spline") plt.scatter(knots[:, 1], knots[:, 0]) plt.legend() plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_004.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 113-115 6. Curvature Comb ----------------- .. GENERATED FROM PYTHON SOURCE LINES 115-137 .. code-block:: Python total_length = spline.arc_length() lengths = np.linspace(0, total_length, 200) t = spline.arc_length_to_parameter(lengths) vals = spline.eval(t) curvature = spline.curvature(t) normals = spline.normal(t) comb = vals + 500 * curvature[:, np.newaxis] * normals plt.figure() plt.imshow(img, cmap="afmhot") plt.plot(comb[:, 1], comb[:, 0], label="Curvature comb", color="yellowgreen") for p in range(0, len(t), 3): plt.plot([vals[p, 1], comb[p, 1]], [vals[p, 0], comb[p, 0]], color="yellowgreen") plt.plot(vals[:, 1], vals[:, 0], label="spline") plt.xlim((0, img.shape[1])) plt.ylim((img.shape[0], 0)) plt.legend() plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_005.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 138-140 7. Plot Curvature vs. Length ---------------------------- .. GENERATED FROM PYTHON SOURCE LINES 140-147 .. code-block:: Python plt.figure() plt.axhline(0, linestyle="--", color="black", alpha=0.5) plt.plot(lengths, curvature) plt.xlabel("length [px]") plt.ylabel("curvature") plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_peptides_006.png :alt: plot peptides :srcset: /auto_examples/images/sphx_glr_plot_peptides_006.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 3.658 seconds) .. _sphx_glr_download_auto_examples_plot_peptides.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_peptides.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_peptides.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_peptides.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_