.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/plot_splinebox_vs_scipy_coin.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_splinebox_vs_scipy_coin.py: Comparison splinebox and scipy: contour approximation ----------------------------------------------------- This example compares splinebox and scipy when trying to approximate a contour/shape with a closed spline with a fixe number of control points. .. GENERATED FROM PYTHON SOURCE LINES 8-15 .. code-block:: Python import matplotlib.pyplot as plt import numpy as np import scipy import skimage import splinebox .. GENERATED FROM PYTHON SOURCE LINES 16-17 Let's load the astronaut example image from skimage and crop out a single coins using slicing. .. GENERATED FROM PYTHON SOURCE LINES 17-21 .. code-block:: Python img = skimage.data.coins()[90:150, 240:300] plt.imshow(img, cmap="gray") plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_001.png :alt: plot splinebox vs scipy coin :srcset: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 22-23 Next, we will segment the coin using Otsu's method and fix some holes in the mask. .. GENERATED FROM PYTHON SOURCE LINES 23-29 .. code-block:: Python thresh = skimage.filters.threshold_otsu(img) mask = img > thresh mask = skimage.morphology.remove_small_holes(mask) plt.imshow(mask, cmap="gray") plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_002.png :alt: plot splinebox vs scipy coin :srcset: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 30-33 We can find the contour of the coin using find contours. The return value is a list of contours. Since our binary image only has one contour we select the first element of the list. .. GENERATED FROM PYTHON SOURCE LINES 33-39 .. code-block:: Python contours = skimage.measure.find_contours(mask) contour = contours[0] plt.imshow(mask, cmap="gray", alpha=0.5) plt.plot(contour[:, 1], contour[:, 0]) plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_003.png :alt: plot splinebox vs scipy coin :srcset: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 40-42 For closed contours, the last point is identical to the first one, so we will chop it off. .. GENERATED FROM PYTHON SOURCE LINES 42-44 .. code-block:: Python contour = contour[:-1] .. GENERATED FROM PYTHON SOURCE LINES 45-48 Our goal is to fit a cubic B-spline with M control points to the contour. We will first use splinbox to acchive this and then use scipy. .. GENERATED FROM PYTHON SOURCE LINES 48-64 .. code-block:: Python M = 9 spline = splinebox.Spline(M=M, basis_function=splinebox.B3(), closed=True) spline.fit(contour) ts = np.linspace(0, M, 100) splinebox_vals = spline.eval(ts) splinebox_control_points = spline.control_points plt.imshow(mask, cmap="gray", alpha=0.5) # plt.scatter(contours[0][:, 1], contours[0][:, 0], label="contour") plt.plot(splinebox_vals[:, 1], splinebox_vals[:, 0], label="splinebox") plt.scatter(splinebox_control_points[:, 1], splinebox_control_points[:, 0]) plt.legend() plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_004.png :alt: plot splinebox vs scipy coin :srcset: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 65-66 Let see how this compares to scipy... .. GENERATED FROM PYTHON SOURCE LINES 66-71 .. code-block:: Python # Number of data points N = len(contour) k = 3 .. GENERATED FROM PYTHON SOURCE LINES 72-75 To get a spline with a specific number of control points in scipy we have to precalculate the parameters values `t` for the knots and the parameter values `u` for the data points. It is important that we account for the periodicity and padding of the knots. .. GENERATED FROM PYTHON SOURCE LINES 75-78 .. code-block:: Python t = np.arange(-k, M + k + 1) u = np.linspace(0, M, N + 1)[:-1] .. GENERATED FROM PYTHON SOURCE LINES 79-83 When constructinc the spline using `splprep` we have to specify the oder of the basis spline, the `u` and `t` we just computed, and the periodicity. Since we don't want to smooth our fit but instead regularize it by fixing the number of control points we need to set `s=0` and `task=-1`. .. GENERATED FROM PYTHON SOURCE LINES 83-94 .. code-block:: Python tck, u = scipy.interpolate.splprep(contour.T, k=k, u=u, t=t, task=-1, s=0, per=N) ts = np.linspace(0, M, 100) scipy_vals = scipy.interpolate.splev(ts, tck) scipy_control_points = tck[1] plt.imshow(mask, cmap="gray", alpha=0.5) # plt.scatter(contours[0][:, 1], contours[0][:, 0], label="contour") plt.plot(scipy_vals[1], scipy_vals[0], label="scipy") plt.scatter(scipy_control_points[1], scipy_control_points[0]) plt.legend() plt.show() .. image-sg:: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_005.png :alt: plot splinebox vs scipy coin :srcset: /auto_examples/images/sphx_glr_plot_splinebox_vs_scipy_coin_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.437 seconds) .. _sphx_glr_download_auto_examples_plot_splinebox_vs_scipy_coin.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_splinebox_vs_scipy_coin.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_splinebox_vs_scipy_coin.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: plot_splinebox_vs_scipy_coin.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_