mirror of
https://github.com/wassname/scikit-image.git
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Improve description of long rank filter example
This commit is contained in:
Johannes Schönberger
@@ -1,12 +1,13 @@
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"""
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===============================================================
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============
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Rank filters
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===============================================================
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============
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Rank filters are non-linear filters using the local grey levels ordering to compute the filtered value.
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This ensemble of filters share a common base: the local grey-level histogram extraction computed on
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the neighborhood of a pixel (defined by a 2D structuring element).
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If the filtered value is taken as the middle value of the histogram, we get the classical median filter.
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Rank filters are non-linear filters using the local grey levels ordering to
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compute the filtered value. This ensemble of filters share a common base: the
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local grey-level histogram extraction computed on the neighborhood of a pixel
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(defined by a 2D structuring element). If the filtered value is taken as the
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middle value of the histogram, we get the classical median filter.
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Rank filters can be used for several purposes such as:
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@@ -22,15 +23,18 @@ Rank filters can be used for several purposes such as:
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* post-processing
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e.g. small object removal, object grouping, contour smoothing
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Some well known filters are specific cases of rank filters [1]_ e.g. morphological dilation, morphological erosion,
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median filters.
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Some well known filters are specific cases of rank filters [1]_ e.g.
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morphological dilation, morphological erosion, median filters.
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The different implementation availables in ``skimage`` are compared.
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The different implementation availables in `skimage` are compared.
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In this example, we will see how to filter a grey level image using some of the linear and non-linear filters
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availables in skimage. We use the ``camera`` image from ``skimage.data``.
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In this example, we will see how to filter a grey level image using some of the
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linear and non-linear filters availables in skimage. We use the `camera`
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image from `skimage.data`.
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.. [1] Pierre Soille, On morphological operators based on rank filters, Pattern
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Recognition 35 (2002) 527-535.
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.. [1] Pierre Soille, On morphological operators based on rank filters, Pattern Recognition 35 (2002) 527-535.
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"""
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import numpy as np
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@@ -50,16 +54,20 @@ plt.plot(hist[1][:-1], hist[0], lw=2)
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plt.title('histogram of grey values')
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"""
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.. image:: PLOT2RST.current_figure
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Noise removal
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==============
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=============
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some noise is added to the image, 1% of pixels are randomly set to 255, %1% are randomly set to 0.
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The **median** filter is applied to remove the noise.
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Some noise is added to the image, 1% of pixels are randomly set to 255, 1% are
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randomly set to 0. The **median** filter is applied to remove the noise.
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.. note::
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there are different implementations of median filter :
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`skimage.filter.median_filter` and `skimage.filter.rank.median`
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.. note:: there is different implementations of median filter : ``skimage.filter.median_filter``and
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`skimage.filter.rank.median``
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"""
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noise = np.random.random(ima.shape)
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@@ -91,16 +99,18 @@ plt.xlabel('median $r=20$')
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"""
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.. image:: PLOT2RST.current_figure
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The added noise is efficiently removed, as the image defaults are small (1 pixel wide), a small filter radius is
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sufficient. As the radius is increasing, objects with a bigger size are filtered too such as the camera tripod.
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Median filter is commonly used for noise removal because borders are preserved.
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The added noise is efficiently removed, as the image defaults are small (1 pixel
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wide), a small filter radius is sufficient. As the radius is increasing, objects
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with a bigger size are filtered as well, such as the camera tripod. The median
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filter is commonly used for noise removal because borders are preserved.
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Image smoothing
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================
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The example hereunder shows how a local **mean** smooth the cameraman image.
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The example hereunder shows how a local **mean** smoothes the camera man image.
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"""
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from skimage.filter.rank import mean
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fig = plt.figure(figsize=[10,7])
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@@ -114,13 +124,18 @@ plt.imshow(loc_mean,cmap=plt.cm.gray,vmin=0,vmax=255)
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plt.xlabel('local mean $r=10$')
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"""
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.. image:: PLOT2RST.current_figure
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One may be interested in smoothing an image while preserving important borders (median filters already achieved this),
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here we use the **bilateral** filter that restrict the local neighborhood to pixel having a grey level similar to the
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central one.
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One may be interested in smoothing an image while preserving important borders
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(median filters already achieved this), here we use the **bilateral** filter
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that restricts the local neighborhood to pixel having a grey level similar to
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the central one.
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.. note:: a different implementation is available for color images in ``skimage.filter.denoise_bilateral``.
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.. note::
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a different implementation is available for color images in
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`skimage.filter.denoise_bilateral`.
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"""
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@@ -145,9 +160,11 @@ plt.subplot(2,2,4)
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plt.imshow(bilat[200:350,350:450],cmap=plt.cm.gray)
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"""
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.. image:: PLOT2RST.current_figure
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One can see that the large continuous part of the image (e.g.sky) are smoothed whereas other details are preserved.
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One can see that the large continuous part of the image (e.g. sky) is smoothed
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whereas other details are preserved.
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Contrast enhancement
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@@ -155,8 +172,9 @@ Contrast enhancement
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We compare here how the global histogram equalization is applied locally.
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The equalized image [2]_ has a roughly linear cumulative distribution function for each pixel neighborhood.
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The local version [3]_ of the histogram equalization emphasized every local graylevel variations.
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The equalized image [2]_ has a roughly linear cumulative distribution function
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for each pixel neighborhood. The local version [3]_ of the histogram
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equalization emphasizes every local graylevel variations.
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.. [2] http://en.wikipedia.org/wiki/Histogram_equalization
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.. [3] http://en.wikipedia.org/wiki/Adaptive_histogram_equalization
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@@ -195,14 +213,19 @@ plt.axis('off')
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plt.subplot(326)
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plt.plot(loc_hist[1][:-1], loc_hist[0], lw=2)
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plt.title('histogram of grey values')
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"""
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.. image:: PLOT2RST.current_figure
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an other way to maximize the number of grey level used for an image is to apply a local autoleveling,
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i.e. here a pixel grey level is proportionally remapped between local minimum and local maximum.
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another way to maximize the number of grey levels used for an image is to apply
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a local autoleveling, i.e. here a pixel grey level is proportionally remapped
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between local minimum and local maximum.
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The following example shows how local autolevel enhances the camara man picture.
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The following example show how local autolevel enhance the camaraman picture.
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"""
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from skimage.filter.rank import autolevel
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ima = data.camera()
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@@ -218,16 +241,20 @@ plt.xlabel('original')
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plt.subplot(1,2,2)
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plt.imshow(auto,cmap=plt.cm.gray)
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plt.xlabel('local autolevel')
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"""
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.. image:: PLOT2RST.current_figure
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This filter is very sensitive to local outlayers, see the little white spot in the sky left part. This is due
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to a local maximum which is very high comparing to the rest of the neighborhood. One can moderate this
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using the percentile version of the autolevel filter which uses to given percentiles (one inferior, one superior)
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in place of local minimum and maximum. The example bellow illustrate how the percentile parameters influence the
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local autolevel result.
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This filter is very sensitive to local outlayers, see the little white spot in
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the sky left part. This is due to a local maximum which is very high comparing
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to the rest of the neighborhood. One can moderate this using the percentile
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version of the autolevel filter which uses given percentiles (one inferior,
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one superior) in place of local minimum and maximum. The example below
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illustrates how the percentile parameters influence the local autolevel result.
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"""
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from skimage.filter.rank import percentile_autolevel
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image = data.camera()
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@@ -255,10 +282,12 @@ for ax in axes:
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ax.axis('off')
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"""
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.. image:: PLOT2RST.current_figure
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Morphological contrast enhancement filter replaces the central pixel by local maximum
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if the original grey level value if closest to local maximum, by the minimum local otherwise.
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The morphological contrast enhancement filter replaces the central pixel by the
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local maximum if the original pixel value is closest to local maximum, otherwise
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by the minimum local.
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"""
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@@ -282,10 +311,11 @@ plt.subplot(2,2,4)
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plt.imshow(enh[200:350,350:450],cmap=plt.cm.gray)
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"""
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.. image:: PLOT2RST.current_figure
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The percentile version of the local morphological contrast enhancement, uses percentile *p0* and *p1* instead of local
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minimum and local maximum.
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The percentile version of the local morphological contrast enhancement uses
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percentile *p0* and *p1* instead of the local minimum and maximum.
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"""
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@@ -309,21 +339,29 @@ plt.subplot(2,2,4)
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plt.imshow(penh[200:350,350:450],cmap=plt.cm.gray)
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"""
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.. image:: PLOT2RST.current_figure
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Image threshold
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===============
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The Otsu's threshold [1]_ method can be applied locally using local greylevel distribution.
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In the example below, for each pixel, an "optimal" threshold is determined by maximizing
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the variance between two classes of pixels of the local neighborhood defined by a structuring element.
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The example compares the local threshold with the global threshold `skimage.filter.threshold_otsu``.
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The Otsu's threshold [1]_ method can be applied locally using the local
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greylevel distribution. In the example below, for each pixel, an "optimal"
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threshold is determined by maximizing the variance between two classes of pixels
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of the local neighborhood defined by a structuring element.
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.. note: local threshold is much slower than global one.
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The example compares the local threshold with the global threshold
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`skimage.filter.threshold_otsu`.
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.. note::
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Local thresholding is much slower than global one. There exists a function
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for global Otsu thresholding: `skimage.filter.threshold_otsu`.
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.. [1] http://en.wikipedia.org/wiki/Otsu's_method
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"""
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from skimage.filter.rank import otsu
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from skimage.filter import threshold_otsu
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@@ -357,10 +395,13 @@ plt.imshow(glob_otsu,cmap=plt.cm.gray)
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plt.xlabel('global Otsu ($t=%d$)'%t_glob_otsu)
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"""
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.. image:: PLOT2RST.current_figure
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The following example, shows on a synthetic image how local Otsu's threshold handle a global level shift.
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"""
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The following example shows how local Otsu's threshold handles a global level
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shift applied to a synthetic image .
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"""
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n = 100
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theta = np.linspace(0,10*np.pi,n)
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@@ -377,18 +418,23 @@ plt.subplot(1,2,2)
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plt.imshow(m>=t,interpolation='nearest')
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plt.xlabel('local Otsu ($radius=%d$)'%radius)
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"""
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.. image:: PLOT2RST.current_figure
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Image morphology
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================
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Local maximum and local minimum are the base operators for grey level morphology.
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Local maximum and local minimum are the base operators for grey level
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morphology.
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.. note:: ``skimage.dilate`` and ``skimage.erode`` are equivalent filters (see below for comparison).
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.. note::
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Here is an example of classical morphological grey level filters : opening, closing and morphological gradient.
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`skimage.dilate` and `skimage.erode` are equivalent filters (see below for
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comparison).
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Here is an example of the classical morphological grey level filters: opening,
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closing and morphological gradient.
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"""
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@@ -416,25 +462,27 @@ plt.imshow(grad,cmap=plt.cm.gray)
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plt.xlabel('morphological gradient')
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"""
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.. image:: PLOT2RST.current_figure
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Feature extraction
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===================
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Local histogram can be exploited to compute local entropy, which is related to the local image complexity.
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Entropy is computed using base 2 logarithm i.e. the filter returns the minimum number of bits needed to encode local
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greylevel distribution.
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Local histogram can be exploited to compute local entropy, which is related to
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the local image complexity. Entropy is computed using base 2 logarithm i.e. the
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filter returns the minimum number of bits needed to encode local greylevel
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distribution.
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``skimage.rank.entropy`` returns local entropy on a given structuring element.
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`skimage.rank.entropy` returns local entropy on a given structuring element.
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The following example shows this filter applied on 8- and 16- bit images.
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.. note:: to better use the available image bit, the function returns 10x entropy for 8-bit images and 1000x entropy
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for 16-bit images.
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.. note::
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to better use the available image bit, the function returns 10x entropy for
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8-bit images and 1000x entropy for 16-bit images.
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"""
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from skimage import data
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from skimage.filter.rank import entropy
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from skimage.morphology import disk
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@@ -472,16 +520,19 @@ plt.xlabel('entropy*1000')
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plt.colorbar()
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"""
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.. image:: PLOT2RST.current_figure
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Implementation
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================
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The central part of the ``skimage.rank`` filters is build on a sliding window that update local grey level histogram.
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This approach limits the algorithm complexity to O(n) where n is the number of image pixels. The complexity is also
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limited with respect to the structuring element size.
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The central part of the `skimage.rank` filters is build on a sliding window that
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update local grey level histogram. This approach limits the algorithm complexity
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to O(n) where n is the number of image pixels. The complexity is also limited
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with respect to the structuring element size.
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"""
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from time import time
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from scipy.ndimage.filters import percentile_filter
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@@ -490,9 +541,7 @@ from skimage.filter import median_filter
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from skimage.filter.rank import median,maximum
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def exec_and_timeit(func):
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""" Decorator that returns both function results and execution time
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(result, ms)
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"""
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"""Decorator that returns both function results and execution time."""
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def wrapper(*arg):
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t1 = time()
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res = func(*arg)
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@@ -523,12 +572,14 @@ def ndi_med(image,n):
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return percentile_filter(image,50,size=n*2-1)
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"""
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Comparison between
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* ``rank.maximum``
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* ``cmorph.dilate``
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* `rank.maximum`
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* `cmorph.dilate`
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on increasing structuring element size
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"""
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a = data.camera()
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@@ -551,9 +602,11 @@ plt.plot(e_range,rec)
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plt.legend(['crank.maximum','cmorph.dilate'])
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"""
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and increasing image size
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.. image:: PLOT2RST.current_figure
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"""
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r = 9
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@@ -578,17 +631,18 @@ plt.legend(['crank.maximum','cmorph.dilate'])
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"""
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.. image:: PLOT2RST.current_figure
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Comparison between:
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* ``rank.median``
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* ``ctmf.median_filter``
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* ``ndimage.percentile``
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* `rank.median`
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* `ctmf.median_filter`
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* `ndimage.percentile`
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on increasing structuring element size
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"""
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"""
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a = data.camera()
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@@ -609,12 +663,14 @@ plt.plot(e_range,rec)
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plt.legend(['rank.median','ctmf.median_filter','ndimage.percentile'])
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plt.ylabel('time (ms)')
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plt.xlabel('element radius')
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"""
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.. image:: PLOT2RST.current_figure
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comparison of outcome of the three methods
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"""
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plt.figure()
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plt.imshow(np.hstack((rc,rctmf,rndi)))
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plt.xlabel('rank.median vs ctmf.median_filter vs ndimage.percentile')
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@@ -649,6 +705,7 @@ plt.xlabel('image size')
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"""
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.. image:: PLOT2RST.current_figure
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"""
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plt.show()
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