.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/applications/plot_rank_filters.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_applications_plot_rank_filters.py: ============ Rank filters ============ Rank filters are non-linear filters using local gray-level ordering to compute the filtered value. This ensemble of filters share a common base: the local gray-level histogram is computed on the neighborhood of a pixel (defined by a 2D structuring element). If the filtered value is taken as the middle value of the histogram, we get the classical median filter. Rank filters can be used for several purposes, such as: * image quality enhancement, e.g., image smoothing, sharpening * image pre-processing, e.g., noise reduction, contrast enhancement * feature extraction, e.g., border detection, isolated point detection * image post-processing, e.g., small object removal, object grouping, contour smoothing Some well-known filters (e.g., morphological dilation and morphological erosion) are specific cases of rank filters [1]_. In this example, we will see how to filter a gray-level image using some of the linear and non-linear filters available in skimage. We use the ``camera`` image from `skimage.data` for all comparisons. .. [1] Pierre Soille, On morphological operators based on rank filters, Pattern Recognition 35 (2002) 527-535, :DOI:`10.1016/S0031-3203(01)00047-4` .. GENERATED FROM PYTHON SOURCE LINES 36-57 .. code-block:: Python import numpy as np import matplotlib.pyplot as plt from skimage.util import img_as_ubyte from skimage import data from skimage.exposure import histogram noisy_image = img_as_ubyte(data.camera()) hist, hist_centers = histogram(noisy_image) fig, ax = plt.subplots(ncols=2, figsize=(10, 5)) ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_axis_off() ax[1].plot(hist_centers, hist, lw=2) ax[1].set_title('Gray-level histogram') fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_001.png :alt: Gray-level histogram :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_001.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 58-64 Noise removal ============= Some noise is added to the image: 1% of pixels are randomly set to 255, 1% are randomly set to 0. The **median** filter is applied to remove the noise. .. GENERATED FROM PYTHON SOURCE LINES 65-95 .. code-block:: Python from skimage.filters.rank import median from skimage.morphology import disk, ball rng = np.random.default_rng() noise = rng.random(noisy_image.shape) noisy_image = img_as_ubyte(data.camera()) noisy_image[noise > 0.99] = 255 noisy_image[noise < 0.01] = 0 fig, axes = plt.subplots(2, 2, figsize=(10, 10), sharex=True, sharey=True) ax = axes.ravel() ax[0].imshow(noisy_image, vmin=0, vmax=255, cmap=plt.cm.gray) ax[0].set_title('Noisy image') ax[1].imshow(median(noisy_image, disk(1)), vmin=0, vmax=255, cmap=plt.cm.gray) ax[1].set_title('Median $r=1$') ax[2].imshow(median(noisy_image, disk(5)), vmin=0, vmax=255, cmap=plt.cm.gray) ax[2].set_title('Median $r=5$') ax[3].imshow(median(noisy_image, disk(20)), vmin=0, vmax=255, cmap=plt.cm.gray) ax[3].set_title('Median $r=20$') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_002.png :alt: Noisy image, Median $r=1$, Median $r=5$, Median $r=20$ :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_002.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 96-113 The added noise is efficiently removed, as the image defaults are small (1-\ pixel wide), a small filter radius is sufficient. As the radius increases, objects with bigger sizes get filtered as well, such as the camera tripod. The median filter is often used for noise removal because it preserves borders. For example, consider noise which is located only on a few pixels in the entire image, as is the case with salt-and-pepper noise [2]_: the median filter will ignore the noisy pixels, for they will appear as outliers; thus, it will not change significantly the median of a group of local pixels, in contrast to what a moving average filter would do. .. [2] https://en.wikipedia.org/wiki/Salt-and-pepper_noise Image smoothing =============== The example hereunder shows how a local **mean** filter smooths the camera man image. .. GENERATED FROM PYTHON SOURCE LINES 114-132 .. code-block:: Python from skimage.filters.rank import mean loc_mean = mean(noisy_image, disk(10)) fig, ax = plt.subplots(ncols=2, figsize=(10, 5), sharex=True, sharey=True) ax[0].imshow(noisy_image, vmin=0, vmax=255, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(loc_mean, vmin=0, vmax=255, cmap=plt.cm.gray) ax[1].set_title('Local mean $r=10$') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_003.png :alt: Original, Local mean $r=10$ :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_003.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 133-142 One may be interested in smoothing an image while preserving important borders (median filters already achieved this). Here, we use the **bilateral** filter that restricts the local neighborhood to pixels with gray levels similar to the central one. .. note:: A different implementation is available for color images in :func:`skimage.restoration.denoise_bilateral`. .. GENERATED FROM PYTHON SOURCE LINES 143-168 .. code-block:: Python from skimage.filters.rank import mean_bilateral noisy_image = img_as_ubyte(data.camera()) bilat = mean_bilateral(noisy_image.astype(np.uint16), disk(20), s0=10, s1=10) fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10), sharex='row', sharey='row') ax = axes.ravel() ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(bilat, cmap=plt.cm.gray) ax[1].set_title('Bilateral mean') ax[2].imshow(noisy_image[100:250, 350:450], cmap=plt.cm.gray) ax[3].imshow(bilat[100:250, 350:450], cmap=plt.cm.gray) for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_004.png :alt: Original, Bilateral mean :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_004.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 169-183 One can see that the large continuous part of the image (e.g. sky) is smoothed whereas other details are preserved. Contrast enhancement ==================== We compare here how the global histogram equalization is applied locally. The equalized image [3]_ has a roughly linear cumulative distribution function for each pixel neighborhood. The local version [4]_ of histogram equalization emphasizes every local gray-level variation. .. [3] https://en.wikipedia.org/wiki/Histogram_equalization .. [4] https://en.wikipedia.org/wiki/Adaptive_histogram_equalization .. GENERATED FROM PYTHON SOURCE LINES 183-221 .. code-block:: Python from skimage import exposure from skimage.filters import rank noisy_image = img_as_ubyte(data.camera()) # equalize globally and locally glob = exposure.equalize_hist(noisy_image) * 255 loc = rank.equalize(noisy_image, disk(20)) # extract histogram for each image hist = np.histogram(noisy_image, bins=np.arange(0, 256)) glob_hist = np.histogram(glob, bins=np.arange(0, 256)) loc_hist = np.histogram(loc, bins=np.arange(0, 256)) fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(12, 12)) ax = axes.ravel() ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_axis_off() ax[1].plot(hist[1][:-1], hist[0], lw=2) ax[1].set_title('Histogram of gray values') ax[2].imshow(glob, cmap=plt.cm.gray) ax[2].set_axis_off() ax[3].plot(glob_hist[1][:-1], glob_hist[0], lw=2) ax[3].set_title('Histogram of gray values') ax[4].imshow(loc, cmap=plt.cm.gray) ax[4].set_axis_off() ax[5].plot(loc_hist[1][:-1], loc_hist[0], lw=2) ax[5].set_title('Histogram of gray values') fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_005.png :alt: Histogram of gray values, Histogram of gray values, Histogram of gray values :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_005.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 222-228 Another way to maximize the number of gray-levels used for an image is to apply a local auto-leveling, i.e. the gray-value of a pixel is proportionally remapped between local minimum and local maximum. The following example shows how local auto-level enhances the camara man picture. .. GENERATED FROM PYTHON SOURCE LINES 228-248 .. code-block:: Python from skimage.filters.rank import autolevel noisy_image = img_as_ubyte(data.camera()) auto = autolevel(noisy_image.astype(np.uint16), disk(20)) fig, ax = plt.subplots(ncols=2, figsize=(10, 5), sharex=True, sharey=True) ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(auto, cmap=plt.cm.gray) ax[1].set_title('Local autolevel') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_006.png :alt: Original, Local autolevel :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_006.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 249-254 This filter is very sensitive to local outliers. One can moderate this using the percentile version of the auto-level filter which uses given percentiles (one inferior, one superior) in place of local minimum and maximum. The example below illustrates how the percentile parameters influence the local auto-level result. .. GENERATED FROM PYTHON SOURCE LINES 254-293 .. code-block:: Python from skimage.filters.rank import autolevel_percentile image = data.camera() footprint = disk(20) loc_autolevel = autolevel(image, footprint=footprint) loc_perc_autolevel0 = autolevel_percentile(image, footprint=footprint, p0=0.01, p1=0.99) loc_perc_autolevel1 = autolevel_percentile(image, footprint=footprint, p0=0.05, p1=0.95) loc_perc_autolevel2 = autolevel_percentile(image, footprint=footprint, p0=0.1, p1=0.9) loc_perc_autolevel3 = autolevel_percentile(image, footprint=footprint, p0=0.15, p1=0.85) fig, axes = plt.subplots(nrows=3, ncols=2, figsize=(10, 10), sharex=True, sharey=True) ax = axes.ravel() title_list = [ 'Original', 'auto_level', 'auto-level 1%', 'auto-level 5%', 'auto-level 10%', 'auto-level 15%', ] image_list = [ image, loc_autolevel, loc_perc_autolevel0, loc_perc_autolevel1, loc_perc_autolevel2, loc_perc_autolevel3, ] for i in range(0, len(image_list)): ax[i].imshow(image_list[i], cmap=plt.cm.gray, vmin=0, vmax=255) ax[i].set_title(title_list[i]) ax[i].set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_007.png :alt: Original, auto_level, auto-level 1%, auto-level 5%, auto-level 10%, auto-level 15% :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_007.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 294-297 The morphological contrast enhancement filter replaces the central pixel by the local maximum if the original pixel value is closest to local maximum, otherwise by the minimum local. .. GENERATED FROM PYTHON SOURCE LINES 297-322 .. code-block:: Python from skimage.filters.rank import enhance_contrast noisy_image = img_as_ubyte(data.camera()) enh = enhance_contrast(noisy_image, disk(5)) fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10), sharex='row', sharey='row') ax = axes.ravel() ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(enh, cmap=plt.cm.gray) ax[1].set_title('Local morphological contrast enhancement') ax[2].imshow(noisy_image[100:250, 350:450], cmap=plt.cm.gray) ax[3].imshow(enh[100:250, 350:450], cmap=plt.cm.gray) for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_008.png :alt: Original, Local morphological contrast enhancement :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_008.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 323-325 The percentile version of the local morphological contrast enhancement uses percentile *p0* and *p1* instead of the local minimum and maximum. .. GENERATED FROM PYTHON SOURCE LINES 325-350 .. code-block:: Python from skimage.filters.rank import enhance_contrast_percentile noisy_image = img_as_ubyte(data.camera()) penh = enhance_contrast_percentile(noisy_image, disk(5), p0=0.1, p1=0.9) fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10), sharex='row', sharey='row') ax = axes.ravel() ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(penh, cmap=plt.cm.gray) ax[1].set_title('Local percentile morphological\n contrast enhancement') ax[2].imshow(noisy_image[100:250, 350:450], cmap=plt.cm.gray) ax[3].imshow(penh[100:250, 350:450], cmap=plt.cm.gray) for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_009.png :alt: Original, Local percentile morphological contrast enhancement :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_009.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 351-366 Image threshold =============== The Otsu threshold method [5]_ can be applied locally using the local gray-\ level distribution. In the example below, for each pixel, an "optimal" threshold is determined by maximizing the variance between two classes of pixels of the local neighborhood defined by a structuring element. These algorithms can be used on both 2D and 3D images. The example compares local thresholding with global thresholding, which is provided by :func:`skimage.filters.threshold_otsu`. Note that the former is much slower than the latter. .. [5] https://en.wikipedia.org/wiki/Otsu's_method .. GENERATED FROM PYTHON SOURCE LINES 367-405 .. code-block:: Python from skimage.filters.rank import otsu from skimage.filters import threshold_otsu from skimage import exposure p8 = data.page() radius = 10 footprint = disk(radius) # t_loc_otsu is an image t_loc_otsu = otsu(p8, footprint) loc_otsu = p8 >= t_loc_otsu # t_glob_otsu is a scalar t_glob_otsu = threshold_otsu(p8) glob_otsu = p8 >= t_glob_otsu fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12, 12), sharex=True, sharey=True) ax = axes.ravel() fig.colorbar(ax[0].imshow(p8, cmap=plt.cm.gray), ax=ax[0]) ax[0].set_title('Original') fig.colorbar(ax[1].imshow(t_loc_otsu, cmap=plt.cm.gray), ax=ax[1]) ax[1].set_title(f'Local Otsu ($r={radius}$)') ax[2].imshow(p8 >= t_loc_otsu, cmap=plt.cm.gray) ax[2].set_title('Original >= local Otsu') ax[3].imshow(glob_otsu, cmap=plt.cm.gray) ax[3].set_title(f'Global Otsu ($t={t_glob_otsu}$)') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_010.png :alt: Original, Local Otsu ($r=10$), Original >= local Otsu, Global Otsu ($t=157$) :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_010.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 406-407 The example below performs the same comparison, using a 3D image this time. .. GENERATED FROM PYTHON SOURCE LINES 407-443 .. code-block:: Python brain = exposure.rescale_intensity(data.brain().astype(float)) radius = 5 neighborhood = ball(radius) # t_loc_otsu is an image t_loc_otsu = rank.otsu(brain, neighborhood) loc_otsu = brain >= t_loc_otsu # t_glob_otsu is a scalar t_glob_otsu = threshold_otsu(brain) glob_otsu = brain >= t_glob_otsu fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12, 12), sharex=True, sharey=True) ax = axes.ravel() slice_index = 3 fig.colorbar(ax[0].imshow(brain[slice_index], cmap=plt.cm.gray), ax=ax[0]) ax[0].set_title('Original') fig.colorbar(ax[1].imshow(t_loc_otsu[slice_index], cmap=plt.cm.gray), ax=ax[1]) ax[1].set_title(f'Local Otsu ($r={radius}$)') ax[2].imshow(brain[slice_index] >= t_loc_otsu[slice_index], cmap=plt.cm.gray) ax[2].set_title('Original >= local Otsu') ax[3].imshow(glob_otsu[slice_index], cmap=plt.cm.gray) ax[3].set_title(f'Global Otsu ($t={t_glob_otsu}$)') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_011.png :alt: Original, Local Otsu ($r=5$), Original >= local Otsu, Global Otsu ($t=0.287109375$) :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_011.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none /opt/hostedtoolcache/Python/3.12.3/x64/lib/python3.12/site-packages/skimage/filters/rank/generic.py:353: UserWarning: Possible precision loss converting image of type float64 to uint8 as required by rank filters. Convert manually using skimage.util.img_as_ubyte to silence this warning. .. GENERATED FROM PYTHON SOURCE LINES 444-446 The following example shows how local Otsu thresholding handles a global level shift applied to a synthetic image. .. GENERATED FROM PYTHON SOURCE LINES 446-468 .. code-block:: Python n = 100 theta = np.linspace(0, 10 * np.pi, n) x = np.sin(theta) m = (np.tile(x, (n, 1)) * np.linspace(0.1, 1, n) * 128 + 128).astype(np.uint8) radius = 10 t = rank.otsu(m, disk(radius)) fig, ax = plt.subplots(ncols=2, figsize=(10, 5), sharex=True, sharey=True) ax[0].imshow(m, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(m >= t, cmap=plt.cm.gray) ax[1].set_title(f'Local Otsu ($r={radius}$)') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_012.png :alt: Original, Local Otsu ($r=10$) :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_012.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 469-477 Image morphology ================ Local maximum and local minimum are the base operators for gray-level morphology. Here is an example of the classical morphological gray-level filters: opening, closing and morphological gradient. .. GENERATED FROM PYTHON SOURCE LINES 477-507 .. code-block:: Python from skimage.filters.rank import maximum, minimum, gradient noisy_image = img_as_ubyte(data.camera()) opening = maximum(minimum(noisy_image, disk(5)), disk(5)) closing = minimum(maximum(noisy_image, disk(5)), disk(5)) grad = gradient(noisy_image, disk(5)) # display results fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(10, 10), sharex=True, sharey=True) ax = axes.ravel() ax[0].imshow(noisy_image, cmap=plt.cm.gray) ax[0].set_title('Original') ax[1].imshow(closing, cmap=plt.cm.gray) ax[1].set_title('Gray-level closing') ax[2].imshow(opening, cmap=plt.cm.gray) ax[2].set_title('Gray-level opening') ax[3].imshow(grad, cmap=plt.cm.gray) ax[3].set_title('Morphological gradient') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_013.png :alt: Original, Gray-level closing, Gray-level opening, Morphological gradient :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_013.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 508-524 Feature extraction =================== Local histograms can be exploited to compute local entropy, which is related to the local image complexity. Entropy is computed using base 2 logarithm, i.e., the filter returns the minimum number of bits needed to encode local gray-level distribution. :func:`skimage.filters.rank.entropy` returns the local entropy on a given structuring element. The following example applies this filter on 8- and 16-bit images. .. note:: To better use the available image bit, the function returns 10x entropy for 8-bit images and 1000x entropy for 16-bit images. .. GENERATED FROM PYTHON SOURCE LINES 525-547 .. code-block:: Python from skimage import data from skimage.filters.rank import entropy from skimage.morphology import disk import numpy as np import matplotlib.pyplot as plt image = data.camera() fig, ax = plt.subplots(ncols=2, figsize=(12, 6), sharex=True, sharey=True) fig.colorbar(ax[0].imshow(image, cmap=plt.cm.gray), ax=ax[0]) ax[0].set_title('Image') fig.colorbar(ax[1].imshow(entropy(image, disk(5)), cmap=plt.cm.gray), ax=ax[1]) ax[1].set_title('Entropy') for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_014.png :alt: Image, Entropy :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_014.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 548-558 Implementation ============== The central part of the `skimage.filters.rank` filters is built on a sliding window that updates the local gray-level histogram. This approach limits the algorithm complexity to O(n) where n is the number of image pixels. The complexity is also limited with respect to the structuring element size. In the following, we compare the performance of different implementations available in `skimage`. .. GENERATED FROM PYTHON SOURCE LINES 559-600 .. code-block:: Python from time import time from scipy.ndimage import percentile_filter from skimage.morphology import dilation from skimage.filters.rank import median, maximum def exec_and_timeit(func): """Decorator that returns both function results and execution time.""" def wrapper(*arg): t1 = time() res = func(*arg) t2 = time() ms = (t2 - t1) * 1000.0 return (res, ms) return wrapper @exec_and_timeit def cr_med(image, footprint): return median(image=image, footprint=footprint) @exec_and_timeit def cr_max(image, footprint): return maximum(image=image, footprint=footprint) @exec_and_timeit def cm_dil(image, footprint): return dilation(image=image, footprint=footprint) @exec_and_timeit def ndi_med(image, n): return percentile_filter(image, 50, size=n * 2 - 1) .. GENERATED FROM PYTHON SOURCE LINES 601-607 Comparison between * `skimage.filters.rank.maximum` * `skimage.morphology.dilation` on increasing structuring element size: .. GENERATED FROM PYTHON SOURCE LINES 607-629 .. code-block:: Python a = data.camera() rec = [] e_range = range(1, 20, 2) for r in e_range: elem = disk(r + 1) rc, ms_rc = cr_max(a, elem) rcm, ms_rcm = cm_dil(a, elem) rec.append((ms_rc, ms_rcm)) rec = np.asarray(rec) fig, ax = plt.subplots(figsize=(10, 10), sharey=True) ax.set_title('Performance with respect to element size') ax.set_ylabel('Time (ms)') ax.set_xlabel('Element radius') ax.plot(e_range, rec) ax.legend(['filters.rank.maximum', 'morphology.dilate']) fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_015.png :alt: Performance with respect to element size :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_015.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 630-631 and increasing image size: .. GENERATED FROM PYTHON SOURCE LINES 631-654 .. code-block:: Python r = 9 elem = disk(r + 1) rec = [] s_range = range(100, 1000, 100) for s in s_range: a = (rng.random((s, s)) * 256).astype(np.uint8) (rc, ms_rc) = cr_max(a, elem) (rcm, ms_rcm) = cm_dil(a, elem) rec.append((ms_rc, ms_rcm)) rec = np.asarray(rec) fig, ax = plt.subplots() ax.set_title('Performance with respect to image size') ax.set_ylabel('Time (ms)') ax.set_xlabel('Image size') ax.plot(s_range, rec) ax.legend(['filters.rank.maximum', 'morphology.dilate']) fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_016.png :alt: Performance with respect to image size :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_016.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 655-661 Comparison between: * `skimage.filters.rank.median` * `scipy.ndimage.percentile_filter` on increasing structuring element size: .. GENERATED FROM PYTHON SOURCE LINES 661-681 .. code-block:: Python a = data.camera() rec = [] e_range = range(2, 30, 4) for r in e_range: elem = disk(r + 1) rc, ms_rc = cr_med(a, elem) rndi, ms_ndi = ndi_med(a, r) rec.append((ms_rc, ms_ndi)) rec = np.asarray(rec) fig, ax = plt.subplots() ax.set_title('Performance with respect to element size') ax.plot(e_range, rec) ax.legend(['filters.rank.median', 'scipy.ndimage.percentile']) ax.set_ylabel('Time (ms)') ax.set_xlabel('Element radius') .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_017.png :alt: Performance with respect to element size :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_017.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-script-out .. code-block:: none Text(0.5, 23.52222222222222, 'Element radius') .. GENERATED FROM PYTHON SOURCE LINES 682-683 Comparison of outcome of the two methods: .. GENERATED FROM PYTHON SOURCE LINES 683-697 .. code-block:: Python fig, ax = plt.subplots(ncols=2, figsize=(10, 5), sharex=True, sharey=True) ax[0].set_title('filters.rank.median') ax[0].imshow(rc, cmap=plt.cm.gray) ax[1].set_title('scipy.ndimage.percentile') ax[1].imshow(rndi, cmap=plt.cm.gray) for a in ax: a.set_axis_off() fig.tight_layout() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_018.png :alt: filters.rank.median, scipy.ndimage.percentile :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_018.png :class: sphx-glr-single-img .. GENERATED FROM PYTHON SOURCE LINES 698-699 on increasing image size: .. GENERATED FROM PYTHON SOURCE LINES 699-723 .. code-block:: Python r = 9 elem = disk(r + 1) rec = [] s_range = [100, 200, 500, 1000] for s in s_range: a = (rng.random((s, s)) * 256).astype(np.uint8) (rc, ms_rc) = cr_med(a, elem) rndi, ms_ndi = ndi_med(a, r) rec.append((ms_rc, ms_ndi)) rec = np.asarray(rec) fig, ax = plt.subplots() ax.set_title('Performance with respect to image size') ax.plot(s_range, rec) ax.legend(['filters.rank.median', 'scipy.ndimage.percentile']) ax.set_ylabel('Time (ms)') ax.set_xlabel('Image size') fig.tight_layout() plt.show() .. image-sg:: /auto_examples/applications/images/sphx_glr_plot_rank_filters_019.png :alt: Performance with respect to image size :srcset: /auto_examples/applications/images/sphx_glr_plot_rank_filters_019.png :class: sphx-glr-single-img .. rst-class:: sphx-glr-timing **Total running time of the script:** (0 minutes 41.378 seconds) .. _sphx_glr_download_auto_examples_applications_plot_rank_filters.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/v0.24.0?filepath=notebooks/auto_examples/applications/plot_rank_filters.ipynb :alt: Launch binder :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_rank_filters.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_rank_filters.py ` .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_