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Short tutorial on segmentation for the user guide +
example on the same subject used to generate the figures
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emmanuelle
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Longer examples and demonstrations
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----------------------------------
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"""
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===============================================================
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Comparing edge-based segmentation and region-based segmentation
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===============================================================
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In this example, we will see how to segment objects from a background.
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We use the ``coins`` image from ``skimage.data``. This image shows
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several coins outlined against a darker background. The segmentation of
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the coins cannot be done directly from the histogram of grey values,
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because the background shares enough grey levels with the coins that a
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thresholding segmentation is not sufficient. Simply thresholding the image
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leads either to missing significant parts of the coins, or to getting parts
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of the background together with the coins.
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We first try an edge-based segmentation. We use the Canny detector to
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delineate the contours of the coins. These contours are filled using
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mathematical morphology (``scipy.ndimage.binary_fill_holes``). Small spurious
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objects are easily removed by applying a threshold on the size of
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unconnected objects. However, this method is not very robust, since contours
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that are not perfectly closed are not filled correctly. This happens for one
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of the coins.
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We therefore try a second method, that is region-based. Here we use the
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watershed transform. An elevation map is provided by the Sobel gradient
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of the image. Markers of the background and the coins are determined from
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the extreme parts of the histogram of grey values.
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This second method works even better, and the coins can be segmented and
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labeled individually.
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"""
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import numpy as np
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from scipy import ndimage
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import matplotlib.pyplot as plt
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import skimage
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from skimage.filter import canny, sobel
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from skimage.morphology import watershed
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#------------------ Loading data --------------------------------
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from skimage import data
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coins = data.coins()
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#------------ Histogram of grey values ---------------------------
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histo = np.histogram(coins, bins=np.arange(0, 256))
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plt.figure(figsize=(8, 3))
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plt.subplot(121)
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plt.imshow(coins, cmap=plt.cm.gray, interpolation='nearest')
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plt.axis('off')
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plt.subplot(122)
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plt.plot(histo[1][:-1], histo[0], lw=2)
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plt.title('histogram of grey values')
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#------------------ Tentative thresholding --------------------------------
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plt.figure(figsize=(6, 3))
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plt.subplot(121)
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plt.imshow(coins > 100, cmap=plt.cm.gray, interpolation='nearest')
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plt.title('coins > 100')
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plt.axis('off')
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plt.subplot(122)
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plt.imshow(coins > 150, cmap=plt.cm.gray, interpolation='nearest')
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plt.title('coins > 150')
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plt.axis('off')
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plt.subplots_adjust(hspace=0.01, wspace=0.01, top=1, bottom=0, left=0,
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right=1)
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#------------------ Edge-based segmentation --------------------------------
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edges = canny(coins/255.)
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fill_coins = ndimage.binary_fill_holes(edges)
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label_objects, nb_labels = ndimage.label(fill_coins)
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sizes = np.bincount(label_objects.ravel())
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mask_sizes = sizes > 20
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mask_sizes[0] = 0
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coins_cleaned = mask_sizes[label_objects]
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plt.figure(figsize=(7, 3.))
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plt.subplot(131)
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plt.imshow(edges, cmap=plt.cm.gray, interpolation='nearest')
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plt.axis('off')
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plt.title('Canny detector')
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plt.subplot(132)
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plt.imshow(fill_coins, cmap=plt.cm.gray, interpolation='nearest')
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plt.axis('off')
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plt.title('Filling the holes')
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plt.subplot(133)
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plt.imshow(coins_cleaned, cmap=plt.cm.gray, interpolation='nearest')
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plt.axis('off')
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plt.title('Removing small objects')
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plt.subplots_adjust(hspace=0.01, wspace=0.01, top=1, bottom=0, left=0,
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right=1)
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#------------------ Region-based segmentation --------------------------------
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markers = np.zeros_like(coins)
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markers[coins < 30] = 1
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markers[coins > 150] = 2
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elevation_map = sobel(coins)
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segmentation = watershed(elevation_map, markers)
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plt.figure(figsize=(7, 3))
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plt.subplot(131)
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plt.imshow(markers, cmap=plt.cm.spectral, interpolation='nearest')
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plt.axis('off')
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plt.title('markers')
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plt.subplot(132)
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plt.imshow(elevation_map, cmap=plt.cm.jet, interpolation='nearest')
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plt.axis('off')
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plt.title('elevation_map')
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plt.subplot(133)
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plt.imshow(segmentation, cmap=plt.cm.gray, interpolation='nearest')
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plt.axis('off')
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plt.title('segmentation')
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plt.subplots_adjust(hspace=0.01, wspace=0.01, top=1, bottom=0, left=0,
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right=1)
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#------------------ Labeling the coins --------------------------------
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labeled_coins, _ = ndimage.label(segmentation - 1)
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plt.figure(figsize=(6, 4))
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plt.imshow(labeled_coins, cmap=plt.cm.spectral, interpolation='nearest')
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plt.axis('off')
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plt.show()
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@@ -5,4 +5,5 @@ User Guide
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:maxdepth: 1
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user_guide/data_types
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user_guide/segmentation
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user_guide/plugins
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Binary file not shown.
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Image Segmentation
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------------------
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Image segmentation is the task of labeling the pixels of objects of
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interest in an image.
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In this tutorial, we will see how to segment objects from a background.
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We use the ``coins`` image from ``skimage.data``. This image shows
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several coins outlined against a darker background. The segmentation of
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the coins cannot be done directly from the histogram of grey values,
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because the background shares enough grey levels with the coins that a
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thresholding segmentation is not sufficient.
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.. image:: ../../_images/plot_coins_segmentation_1.png
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:target: ../auto_examples/applications/plot_coins_segmentation.html
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:align: center
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::
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>>> import numpy as np
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>>> from skimage import data
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>>> coins = data.coins()
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>>> histo = np.histogram(coins, bins=np.arange(0, 256))
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Simply thresholding the image leads either to missing significant parts
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of the coins, or to getting parts of the background together with the
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coins. This is due to the inhomogeneous lighting of the image.
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.. image:: ../../_images/plot_coins_segmentation_2.png
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:target: ../auto_examples/applications/plot_coins_segmentation.html
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:align: center
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A first idea is to take advantage of the local contrast, that is, to
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use the gradients rather than the grey values.
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Edge-based segmentation
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~~~~~~~~~~~~~~~~~~~~~~~
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Let us first try to detect edges than enclose the coins. For edge
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detection, we use the `Canny detector
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<http://en.wikipedia.org/wiki/Canny_edge_detector>`_ of ``skimage.filter.canny``
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::
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>>> from skimage.filter import canny
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>>> edges = canny(coins/255.)
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As the background is very smooth, almost all edges are found at the
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boundary of the coins, or inside the coins.
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Now that we have contours that delineate the outer boundary of the coins,
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we fill the inner part of the coins using the
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``ndimage.binary_fill_holes`` function, that uses mathematical morphology
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to fill the holes.
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::
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>>> from scipy import ndimage
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>>> fill_coins = ndimage.binary_fill_holes(edges)
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.. image:: ../../_images/plot_coins_segmentation_3.png
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:target: ../auto_examples/applications/plot_coins_segmentation.html
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:align: center
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Most coins are well segmented out of the background. Small objects from
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the background can be easily removed using the ``ndimage.label``
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function, and removing objects smaller than a small threshold.
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::
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>>> label_objects, nb_labels = ndimage.label(fill_coins)
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>>> sizes = np.bincount(label_objects.ravel())
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>>> mask_sizes = sizes > 20
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>>> mask_sizes[0] = 0
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>>> coins_cleaned = mask_sizes[label_objects]
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However, the segmentation is not very satisfying, since one of the coins
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has not been segmented correctly at all. The reason is that the contour
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that we got from the Canny detector was not completely closed, therefore
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the filling function did not fill the inner part of the coin.
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Therefore, this segmentation method is not very robust: if we miss a
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single pixel of the contour of the object, we will not be able to fill
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it. Of course, we could try first to dilate the contours in order to
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close them. However, it is preferable to try a more robust method.
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Region-based segmentation
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~~~~~~~~~~~~~~~~~~~~~~~~~
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Let us first determine markers of the coins and the background. These
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markers are pixels that we can label unambiguously with one of the
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phases. Here, the markers are found at the two extreme parts of the
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histogram of grey values:
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::
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>>> markers = np.zeros_like(coins)
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>>> markers[coins < 30] = 1
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>>> markers[coins > 150] = 2
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We will use these markers in a watershed segmentation. The name watershed
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comes from an analogy with hydrology. The `watershed transform
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<http://en.wikipedia.org/wiki/Watershed_%28image_processing%29>`_ floods
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an image of elevation from markers, in order to determine the catchment
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basins of these markers. Watershed lines separate these catchment basins,
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and correspond to the segmentation that is looked for.
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The choice of the elevation map is critical for a good segmentation.
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Here, the amplitude of the gradient provides a good elevation map. We
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use the Sobel operator for computing the amplitude of the gradient::
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>>> from skimage.filter import sobel
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>>> elevation_map = sobel(coins)
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From the 3-D surface plot shown below, we see that high barriers separate
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well the coins from the background.
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.. image:: elevation_map.jpg
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:align: center
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Let us now compute the watershed transform::
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>>> from skimage.morphology import watershed
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>>> segmentation = watershed(elevation_map, markers)
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.. image:: ../../_images/plot_coins_segmentation_4.png
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:target: ../auto_examples/applications/plot_coins_segmentation.html
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:align: center
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With this method, the result is satisfying for all coins. Even if the
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markers for the background were not well distributed, the barriers in the
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elevation map were high enough for these markers to flood the entire
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background.
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We can now label all the coins one by one using ``ndimage.label``::
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>>> labeled_coins, _ = ndimage.label(segmentation - 1)
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.. image:: ../../_images/plot_coins_segmentation_5.png
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:target: ../auto_examples/applications/plot_coins_segmentation.html
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:align: center
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