mirror of
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emmanuelle
844858f01b
Modified comments in some gallery examples for compatibility with sphinx-gallery parsing. Also modified some links in the narrative doc since image file names have changed.
251 lines
8.7 KiB
Python
251 lines
8.7 KiB
Python
"""
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=======================
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Morphological Filtering
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=======================
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Morphological image processing is a collection of non-linear operations related
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to the shape or morphology of features in an image, such as boundaries,
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skeletons, etc. In any given technique, we probe an image with a small shape or
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template called a structuring element, which defines the region of interest or
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neighborhood around a pixel.
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In this document we outline the following basic morphological operations:
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1. Erosion
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2. Dilation
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3. Opening
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4. Closing
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5. White Tophat
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6. Black Tophat
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7. Skeletonize
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8. Convex Hull
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To get started, let's load an image using ``io.imread``. Note that morphology
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functions only work on gray-scale or binary images, so we set ``as_grey=True``.
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"""
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import os
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import matplotlib.pyplot as plt
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from skimage.data import data_dir
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from skimage.util import img_as_ubyte
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from skimage import io
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orig_phantom = img_as_ubyte(io.imread(os.path.join(data_dir, "phantom.png"),
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as_grey=True))
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fig, ax = plt.subplots()
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ax.imshow(orig_phantom, cmap=plt.cm.gray)
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######################################################################
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# Let's also define a convenience function for plotting comparisons:
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def plot_comparison(original, filtered, filter_name):
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fig, (ax1, ax2) = plt.subplots(ncols=2, figsize=(8, 4), sharex=True,
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sharey=True)
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ax1.imshow(original, cmap=plt.cm.gray)
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ax1.set_title('original')
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ax1.axis('off')
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ax1.set_adjustable('box-forced')
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ax2.imshow(filtered, cmap=plt.cm.gray)
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ax2.set_title(filter_name)
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ax2.axis('off')
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ax2.set_adjustable('box-forced')
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######################################################################
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# Erosion
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# =======
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#
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# Morphological ``erosion`` sets a pixel at (i, j) to the *minimum over all
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# pixels in the neighborhood centered at (i, j)*. The structuring element,
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# ``selem``, passed to ``erosion`` is a boolean array that describes this
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# neighborhood. Below, we use ``disk`` to create a circular structuring
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# element, which we use for most of the following examples.
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from skimage.morphology import erosion, dilation, opening, closing, white_tophat
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from skimage.morphology import black_tophat, skeletonize, convex_hull_image
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from skimage.morphology import disk
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selem = disk(6)
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eroded = erosion(orig_phantom, selem)
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plot_comparison(orig_phantom, eroded, 'erosion')
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######################################################################
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# Notice how the white boundary of the image disappears or gets eroded as we
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# increase the size of the disk. Also notice the increase in size of the two
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# black ellipses in the center and the disappearance of the 3 light grey
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# patches in the lower part of the image.
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#
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#Dilation
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#========
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#
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#Morphological ``dilation`` sets a pixel at (i, j) to the *maximum over all
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#pixels in the neighborhood centered at (i, j)*. Dilation enlarges bright
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#regions and shrinks dark regions.
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dilated = dilation(orig_phantom, selem)
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plot_comparison(orig_phantom, dilated, 'dilation')
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######################################################################
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# Notice how the white boundary of the image thickens, or gets dilated, as we
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#increase the size of the disk. Also notice the decrease in size of the two
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#black ellipses in the centre, and the thickening of the light grey circle
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#in the center and the 3 patches in the lower part of the image.
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#
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#Opening
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#=======
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#
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#Morphological ``opening`` on an image is defined as an *erosion followed by
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#a dilation*. Opening can remove small bright spots (i.e. "salt") and
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#connect small dark cracks.
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opened = opening(orig_phantom, selem)
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plot_comparison(orig_phantom, opened, 'opening')
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######################################################################
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#Since ``opening`` an image starts with an erosion operation, light regions
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#that are *smaller* than the structuring element are removed. The dilation
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#operation that follows ensures that light regions that are *larger* than
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#the structuring element retain their original size. Notice how the light
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#and dark shapes in the center their original thickness but the 3 lighter
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#patches in the bottom get completely eroded. The size dependence is
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#highlighted by the outer white ring: The parts of the ring thinner than the
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#structuring element were completely erased, while the thicker region at the
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#top retains its original thickness.
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#
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#Closing
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#=======
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#
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#Morphological ``closing`` on an image is defined as a *dilation followed by
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#an erosion*. Closing can remove small dark spots (i.e. "pepper") and
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#connect small bright cracks.
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#
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#To illustrate this more clearly, let's add a small crack to the white
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#border:
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phantom = orig_phantom.copy()
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phantom[10:30, 200:210] = 0
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closed = closing(phantom, selem)
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plot_comparison(phantom, closed, 'closing')
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######################################################################
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# Since ``closing`` an image starts with an dilation operation, dark regions
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# that are *smaller* than the structuring element are removed. The dilation
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# operation that follows ensures that dark regions that are *larger* than the
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# structuring element retain their original size. Notice how the white
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# ellipses at the bottom get connected because of dilation, but other dark
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# region retain their original sizes. Also notice how the crack we added is
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# mostly removed.
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#
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# White tophat
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# ============
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#
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# The ``white_tophat`` of an image is defined as the *image minus its
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# morphological opening*. This operation returns the bright spots of the
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# image that are smaller than the structuring element.
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#
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# To make things interesting, we'll add bright and dark spots to the image:
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phantom = orig_phantom.copy()
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phantom[340:350, 200:210] = 255
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phantom[100:110, 200:210] = 0
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w_tophat = white_tophat(phantom, selem)
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plot_comparison(phantom, w_tophat, 'white tophat')
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######################################################################
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# As you can see, the 10-pixel wide white square is highlighted since it is
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# smaller than the structuring element. Also, the thin, white edges around
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# most of the ellipse are retained because they're smaller than the
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# structuring element, but the thicker region at the top disappears.
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#
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# Black tophat
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# ============
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#
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# The ``black_tophat`` of an image is defined as its morphological **closing
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# minus the original image**. This operation returns the *dark spots of the
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# image that are smaller than the structuring element*.
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b_tophat = black_tophat(phantom, selem)
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plot_comparison(phantom, b_tophat, 'black tophat')
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######################################################################
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#As you can see, the 10-pixel wide black square is highlighted since
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#it is smaller than the structuring element.
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#
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#**Duality**
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#
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#As you should have noticed, many of these operations are simply the reverse
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#of another operation. This duality can be summarized as follows:
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#
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# 1. Erosion <-> Dilation
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#
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# 2. Opening <-> Closing
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#
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# 3. White tophat <-> Black tophat
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#
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#Skeletonize
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#===========
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#
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#Thinning is used to reduce each connected component in a binary image to a
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#*single-pixel wide skeleton*. It is important to note that this is
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#performed on binary images only.
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horse = io.imread(os.path.join(data_dir, "horse.png"), as_grey=True)
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sk = skeletonize(horse == 0)
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plot_comparison(horse, sk, 'skeletonize')
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######################################################################
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#
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# As the name suggests, this technique is used to thin the image to 1-pixel
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# wide skeleton by applying thinning successively.
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#
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# Convex hull
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# ===========
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#
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# The ``convex_hull_image`` is the *set of pixels included in the smallest
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# convex polygon that surround all white pixels in the input image*. Again
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# note that this is also performed on binary images.
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hull1 = convex_hull_image(horse == 0)
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plot_comparison(horse, hull1, 'convex hull')
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######################################################################
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# As the figure illustrates, ``convex_hull_image`` gives the smallest polygon
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# which covers the white or True completely in the image.
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#
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# If we add a small grain to the image, we can see how the convex hull adapts
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# to enclose that grain:
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import numpy as np
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horse_mask = horse == 0
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horse_mask[45:50, 75:80] = 1
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hull2 = convex_hull_image(horse_mask)
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plot_comparison(horse_mask, hull2, 'convex hull')
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######################################################################
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#
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# Additional Resources
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# ====================
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#
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# 1. `MathWorks tutorial on morphological processing
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# <http://www.mathworks.com/help/images/morphology-fundamentals-dilation-and-
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# erosion.html>`_
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#
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# 2. `Auckland university's tutorial on Morphological Image
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# Processing <http://www.cs.auckland.ac.nz/courses/compsci773s1c/lectures
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# /ImageProcessing-html/topic4.htm>`_
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#
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# 3. http://en.wikipedia.org/wiki/Mathematical_morphology
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