.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/optical_flow_methods_convergence.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_optical_flow_methods_convergence.py: Optical flow methods convergence ================================ In this example we test the convergence of the optical flow methods available in pysteps using idealized motion fields. To test the convergence, using an example precipitation field we will: - Read precipitation field from a file - Morph the precipitation field using a given motion field (linear or rotor) to generate a sequence of moving precipitation patterns. - Using the available optical flow methods, retrieve the motion field from the precipitation time sequence (synthetic precipitation observations). Let's first load the libraries that we will use. .. GENERATED FROM PYTHON SOURCE LINES 20-33 .. code-block:: Python from datetime import datetime import time import matplotlib.pyplot as plt import numpy as np from matplotlib.pyplot import get_cmap from scipy.ndimage import uniform_filter import pysteps as stp from pysteps import motion, io, rcparams from pysteps.motion.vet import morph from pysteps.visualization import plot_precip_field, quiver .. GENERATED FROM PYTHON SOURCE LINES 34-40 Load the reference precipitation data ------------------------------------- First, we will import a radar composite from the archive. You need the pysteps-data archive downloaded and the pystepsrc file configured with the data_source paths pointing to data folders. .. GENERATED FROM PYTHON SOURCE LINES 40-46 .. code-block:: Python # Selected case date = datetime.strptime("201505151630", "%Y%m%d%H%M") data_source = rcparams.data_sources["mch"] .. GENERATED FROM PYTHON SOURCE LINES 47-49 Load the data from the archive ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 49-72 .. code-block:: Python root_path = data_source["root_path"] path_fmt = data_source["path_fmt"] fn_pattern = data_source["fn_pattern"] fn_ext = data_source["fn_ext"] importer_name = data_source["importer"] importer_kwargs = data_source["importer_kwargs"] # Find the reference field in the archive fns = io.archive.find_by_date( date, root_path, path_fmt, fn_pattern, fn_ext, timestep=5, num_prev_files=0 ) # Read the reference radar composite importer = io.get_method(importer_name, "importer") reference_field, quality, metadata = io.read_timeseries( fns, importer, **importer_kwargs ) del quality # Not used reference_field = np.squeeze(reference_field) # Remove time dimension .. GENERATED FROM PYTHON SOURCE LINES 73-75 Preprocess the data ~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 75-97 .. code-block:: Python # Convert to mm/h reference_field, metadata = stp.utils.to_rainrate(reference_field, metadata) # Mask invalid values reference_field = np.ma.masked_invalid(reference_field) # Plot the reference precipitation plot_precip_field(reference_field, title="Reference field") plt.show() # Log-transform the data [dBR] reference_field, metadata = stp.utils.dB_transform( reference_field, metadata, threshold=0.1, zerovalue=-15.0 ) print("Precip. pattern shape: " + str(reference_field.shape)) # This suppress nan conversion warnings in plot functions reference_field.data[reference_field.mask] = np.nan .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_001.png :alt: Reference field :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_001.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Precip. pattern shape: (640, 710) .. GENERATED FROM PYTHON SOURCE LINES 98-107 Synthetic precipitation observations ------------------------------------ Now we need to create a series of precipitation fields by applying the ideal motion field to the reference precipitation field "n" times. To evaluate the accuracy of the computed_motion vectors, we will use a relative RMSE measure. Relative MSE = <(expected_motion - computed_motion)^2> / .. GENERATED FROM PYTHON SOURCE LINES 107-120 .. code-block:: Python # Relative RMSE = Rel_RMSE = sqrt(Relative MSE) # # - Rel_RMSE = 0%: no error # - Rel_RMSE = 100%: The retrieved motion field has an average error equal in # magnitude to the motion field. # # Relative RMSE is computed over a region surrounding the precipitation # field, were there is enough information to retrieve the motion field. # The "precipitation region" includes the precipitation pattern plus a margin of # approximately 20 grid points. .. GENERATED FROM PYTHON SOURCE LINES 121-122 Let's create a function to construct different motion fields. .. GENERATED FROM PYTHON SOURCE LINES 122-173 .. code-block:: Python def create_motion_field(input_precip, motion_type): """ Create idealized motion fields to be applied to the reference image. Parameters ---------- input_precip: numpy array (lat, lon) motion_type: str The supported motion fields are: - linear_x: (u=2, v=0) - linear_y: (u=0, v=2) - rotor: rotor field Returns ------- ideal_motion : numpy array (u, v) """ # Create an imaginary grid on the image and create a motion field to be # applied to the image. ny, nx = input_precip.shape x_pos = np.arange(nx) y_pos = np.arange(ny) x, y = np.meshgrid(x_pos, y_pos, indexing="ij") ideal_motion = np.zeros((2, nx, ny)) if motion_type == "linear_x": ideal_motion[0, :] = 2 # Motion along x elif motion_type == "linear_y": ideal_motion[1, :] = 2 # Motion along y elif motion_type == "rotor": x_mean = x.mean() y_mean = y.mean() norm = np.sqrt(x * x + y * y) mask = norm != 0 ideal_motion[0, mask] = 2 * (y - y_mean)[mask] / norm[mask] ideal_motion[1, mask] = -2 * (x - x_mean)[mask] / norm[mask] else: raise ValueError("motion_type not supported.") # We need to swap the axes because the optical flow methods expect # (lat, lon) or (y,x) indexing convention. ideal_motion = ideal_motion.swapaxes(1, 2) return ideal_motion .. GENERATED FROM PYTHON SOURCE LINES 174-176 Let's create another function that construct the temporal series of precipitation observations. .. GENERATED FROM PYTHON SOURCE LINES 176-322 .. code-block:: Python def create_observations(input_precip, motion_type, num_times=9): """ Create synthetic precipitation observations by displacing the input field using an ideal motion field. Parameters ---------- input_precip: numpy array (lat, lon) Input precipitation field. motion_type: str The supported motion fields are: - linear_x: (u=2, v=0) - linear_y: (u=0, v=2) - rotor: rotor field num_times: int, optional Length of the observations sequence. Returns ------- synthetic_observations: numpy array Sequence of observations """ ideal_motion = create_motion_field(input_precip, motion_type) # The morph function expects (lon, lat) or (x, y) dimensions. # Hence, we need to swap the lat,lon axes. # NOTE: The motion field passed to the morph function can't have any NaNs. # Otherwise, it can result in a segmentation fault. morphed_field, mask = morph( input_precip.swapaxes(0, 1), ideal_motion.swapaxes(1, 2) ) mask = np.array(mask, dtype=bool) synthetic_observations = np.ma.MaskedArray(morphed_field, mask=mask) synthetic_observations = synthetic_observations[np.newaxis, :] for t in range(1, num_times): morphed_field, mask = morph( synthetic_observations[t - 1], ideal_motion.swapaxes(1, 2) ) mask = np.array(mask, dtype=bool) morphed_field = np.ma.MaskedArray( morphed_field[np.newaxis, :], mask=mask[np.newaxis, :] ) synthetic_observations = np.ma.concatenate( [synthetic_observations, morphed_field], axis=0 ) # Swap back to (lat, lon) synthetic_observations = synthetic_observations.swapaxes(1, 2) synthetic_observations = np.ma.masked_invalid(synthetic_observations) synthetic_observations.data[np.ma.getmaskarray(synthetic_observations)] = 0 return ideal_motion, synthetic_observations def plot_optflow_method_convergence(input_precip, optflow_method_name, motion_type): """ Test the convergence to the actual solution of the optical flow method used. Parameters ---------- input_precip: numpy array (lat, lon) Input precipitation field. optflow_method_name: str Optical flow method name motion_type: str The supported motion fields are: - linear_x: (u=2, v=0) - linear_y: (u=0, v=2) - rotor: rotor field """ if optflow_method_name.lower() != "darts": num_times = 2 else: num_times = 9 ideal_motion, precip_obs = create_observations( input_precip, motion_type, num_times=num_times ) oflow_method = motion.get_method(optflow_method_name) elapsed_time = time.perf_counter() computed_motion = oflow_method(precip_obs, verbose=False) print( f"{optflow_method_name} computation time: " f"{(time.perf_counter() - elapsed_time):.1f} [s]" ) precip_obs, _ = stp.utils.dB_transform(precip_obs, inverse=True) precip_data = precip_obs.max(axis=0) precip_data.data[precip_data.mask] = 0 precip_mask = (uniform_filter(precip_data, size=20) > 0.1) & ~precip_obs.mask.any( axis=0 ) cmap = get_cmap("jet").copy() cmap.set_under("grey", alpha=0.25) cmap.set_over("none") # Compare retrieved motion field with the ideal one plt.figure(figsize=(9, 4)) plt.subplot(1, 2, 1) ax = plot_precip_field(precip_obs[0], title="Reference motion") quiver(ideal_motion, step=25, ax=ax) plt.subplot(1, 2, 2) ax = plot_precip_field(precip_obs[0], title="Retrieved motion") quiver(computed_motion, step=25, ax=ax) # To evaluate the accuracy of the computed_motion vectors, we will use # a relative RMSE measure. # Relative MSE = < (expected_motion - computed_motion)^2 > / # Relative RMSE = sqrt(Relative MSE) mse = ((ideal_motion - computed_motion)[:, precip_mask] ** 2).mean() rel_mse = mse / (ideal_motion[:, precip_mask] ** 2).mean() plt.suptitle( f"{optflow_method_name} " f"Relative RMSE: {np.sqrt(rel_mse) * 100:.2f}%" ) plt.show() .. GENERATED FROM PYTHON SOURCE LINES 323-328 Lucas-Kanade ------------ Constant motion x-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 328-330 .. code-block:: Python plot_optflow_method_convergence(reference_field, "LucasKanade", "linear_x") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_002.png :alt: LucasKanade Relative RMSE: 1.52%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_002.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none LucasKanade computation time: 1.2 [s] .. GENERATED FROM PYTHON SOURCE LINES 331-333 Constant motion y-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 333-335 .. code-block:: Python plot_optflow_method_convergence(reference_field, "LucasKanade", "linear_y") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_003.png :alt: LucasKanade Relative RMSE: 1.47%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_003.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none LucasKanade computation time: 1.1 [s] .. GENERATED FROM PYTHON SOURCE LINES 336-338 Rotational motion ~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 338-340 .. code-block:: Python plot_optflow_method_convergence(reference_field, "LucasKanade", "rotor") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_004.png :alt: LucasKanade Relative RMSE: 9.57%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_004.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none LucasKanade computation time: 1.2 [s] .. GENERATED FROM PYTHON SOURCE LINES 341-346 Variational Echo Tracking (VET) ------------------------------- Constant motion x-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 346-348 .. code-block:: Python plot_optflow_method_convergence(reference_field, "VET", "linear_x") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_005.png :alt: VET Relative RMSE: 0.00%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_005.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none VET computation time: 2.0 [s] .. GENERATED FROM PYTHON SOURCE LINES 349-351 Constant motion y-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 351-353 .. code-block:: Python plot_optflow_method_convergence(reference_field, "VET", "linear_y") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_006.png :alt: VET Relative RMSE: 0.00%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_006.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none VET computation time: 1.9 [s] .. GENERATED FROM PYTHON SOURCE LINES 354-356 Rotational motion ~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 356-358 .. code-block:: Python plot_optflow_method_convergence(reference_field, "VET", "rotor") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_007.png :alt: VET Relative RMSE: 3.73%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_007.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none VET computation time: 14.5 [s] .. GENERATED FROM PYTHON SOURCE LINES 359-364 DARTS ----- Constant motion x-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 364-366 .. code-block:: Python plot_optflow_method_convergence(reference_field, "DARTS", "linear_x") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_008.png :alt: DARTS Relative RMSE: 22.97%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_008.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none DARTS computation time: 1.2 [s] .. GENERATED FROM PYTHON SOURCE LINES 367-369 Constant motion y-direction ~~~~~~~~~~~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 369-371 .. code-block:: Python plot_optflow_method_convergence(reference_field, "DARTS", "linear_y") .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_009.png :alt: DARTS Relative RMSE: 20.32%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_009.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none DARTS computation time: 1.2 [s] .. GENERATED FROM PYTHON SOURCE LINES 372-374 Rotational motion ~~~~~~~~~~~~~~~~~ .. GENERATED FROM PYTHON SOURCE LINES 374-377 .. code-block:: Python plot_optflow_method_convergence(reference_field, "DARTS", "rotor") # sphinx_gallery_thumbnail_number = 5 .. image-sg:: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_010.png :alt: DARTS Relative RMSE: 53.43%, Reference motion, Retrieved motion :srcset: /auto_examples/images/sphx_glr_optical_flow_methods_convergence_010.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none DARTS computation time: 1.2 [s] .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 28.305 seconds) .. _sphx_glr_download_auto_examples_optical_flow_methods_convergence.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: optical_flow_methods_convergence.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: optical_flow_methods_convergence.py ` .. container:: sphx-glr-download sphx-glr-download-zip :download:`Download zipped: optical_flow_methods_convergence.zip ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_