.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/transform/plot_ransac.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_transform_plot_ransac.py: ========================================= Robust line model estimation using RANSAC ========================================= In this example we see how to robustly fit a line model to faulty data using the RANSAC (random sample consensus) algorithm. Firstly the data are generated by adding a gaussian noise to a linear function. Then, the outlier points are added to the data set. RANSAC iteratively estimates the parameters from the data set. At each iteration the following steps are performed: 1. Select ``min_samples`` random samples from the original data and check whether the set of data is valid (see ``is_data_valid`` option). 2. Estimate a model on the random subset (``model_cls.estimate(*data[random_subset]``) and check whether the estimated model is valid (see ``is_model_valid`` option). 3. Classify all the data points as either inliers or outliers by calculating the residuals using the estimated model (``model_cls.residuals(*data)``) - all data samples with residuals smaller than the ``residual_threshold`` are considered as inliers. 4. If the number of the inlier samples is greater than ever before, save the estimated model as the best model. In case the current estimated model has the same number of inliers, it is considered as the best model only if the sum of residuals is lower. These steps are performed either a maximum number of times or until one of the special stop criteria are met. The final model is estimated using all the inlier samples of the previously determined best model. .. GENERATED FROM PYTHON SOURCE LINES 34-82 .. code-block:: default import numpy as np from matplotlib import pyplot as plt from skimage.measure import LineModelND, ransac rng = np.random.default_rng() # generate coordinates of line x = np.arange(-200, 200) y = 0.2 * x + 20 data = np.column_stack([x, y]) # add gaussian noise to coordinates noise = rng.normal(size=data.shape) data += 0.5 * noise data[::2] += 5 * noise[::2] data[::4] += 20 * noise[::4] # add faulty data faulty = np.array(30 * [(180., -100)]) faulty += 10 * rng.normal(size=faulty.shape) data[:faulty.shape[0]] = faulty # fit line using all data model = LineModelND() model.estimate(data) # robustly fit line only using inlier data with RANSAC algorithm model_robust, inliers = ransac(data, LineModelND, min_samples=2, residual_threshold=1, max_trials=1000) outliers = (inliers == False) # generate coordinates of estimated models line_x = np.arange(-250, 250) line_y = model.predict_y(line_x) line_y_robust = model_robust.predict_y(line_x) fig, ax = plt.subplots() ax.plot(data[inliers, 0], data[inliers, 1], '.b', alpha=0.6, label='Inlier data') ax.plot(data[outliers, 0], data[outliers, 1], '.r', alpha=0.6, label='Outlier data') ax.plot(line_x, line_y, '-k', label='Line model from all data') ax.plot(line_x, line_y_robust, '-b', label='Robust line model') ax.legend(loc='lower left') plt.show() .. image-sg:: /auto_examples/transform/images/sphx_glr_plot_ransac_001.png :alt: plot ransac :srcset: /auto_examples/transform/images/sphx_glr_plot_ransac_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 83-84 Now, we generalize this example to 3D points. .. GENERATED FROM PYTHON SOURCE LINES 84-114 .. code-block:: default import numpy as np from matplotlib import pyplot as plt from skimage.measure import LineModelND, ransac # generate coordinates of line point = np.array([0, 0, 0], dtype='float') direction = np.array([1, 1, 1], dtype='float') / np.sqrt(3) xyz = point + 10 * np.arange(-100, 100)[..., np.newaxis] * direction # add gaussian noise to coordinates noise = rng.normal(size=xyz.shape) xyz += 0.5 * noise xyz[::2] += 20 * noise[::2] xyz[::4] += 100 * noise[::4] # robustly fit line only using inlier data with RANSAC algorithm model_robust, inliers = ransac(xyz, LineModelND, min_samples=2, residual_threshold=1, max_trials=1000) outliers = inliers == False fig = plt.figure() ax = fig.add_subplot(111, projection='3d') ax.scatter(xyz[inliers][:, 0], xyz[inliers][:, 1], xyz[inliers][:, 2], c='b', marker='o', label='Inlier data') ax.scatter(xyz[outliers][:, 0], xyz[outliers][:, 1], xyz[outliers][:, 2], c='r', marker='o', label='Outlier data') ax.legend(loc='lower left') plt.show() .. image-sg:: /auto_examples/transform/images/sphx_glr_plot_ransac_002.png :alt: plot ransac :srcset: /auto_examples/transform/images/sphx_glr_plot_ransac_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 0.549 seconds) .. _sphx_glr_download_auto_examples_transform_plot_ransac.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/v0.22.x?filepath=notebooks/auto_examples/transform/plot_ransac.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_ransac.py ` .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_ransac.ipynb ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_