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DOC: Remove peak detection tutorial.
The tutorial needs a lot of work and isn't a crucial part of this PR. Note: tutorial saved in a separate branch.
This commit is contained in:
Tony S Yu
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"""
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==============
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Peak detection
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==============
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Peak detection (a.k.a. spot detection or particle detection) is a common
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image analysis step. For example, it's used to detect tracer particles in a
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flow for particle image velocimetry (i.e. PIV) and to identify features in
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the Hough transform.
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To simplify plotting code, let's define a simple function that creates a new
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figure on each call, and removes tick labels.
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"""
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import matplotlib.pyplot as plt
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plt.rcParams['axes.titlesize'] = 10
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plt.rcParams['font.size'] = 10
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def imshow(image, **kwargs):
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plt.figure(figsize=(2.5, 2.5))
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plt.imshow(image, **kwargs)
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plt.axis('off')
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"""
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To explore different peak detection techniques, we use an image of circles with
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added noise:
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"""
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from skimage import data
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img = data.load('noisy_circles.jpg')
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imshow(img)
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"""
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.. image:: PLOT2RST.current_figure
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This image is noisy and has uneven background illumination. The peaks in the
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image, while readily identified by eye, can be tricky to find algorithmically.
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The first thing we need to do is remove the high-frequency noise; this can
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be done with a simple Gaussian filter.
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"""
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import scipy.ndimage as ndimg
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img_smooth = ndimg.gaussian_filter(img, 3)
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imshow(img_smooth)
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"""
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.. image:: PLOT2RST.current_figure
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Thresholding
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============
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One way to extract the background is to threshold the image.
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"""
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thresh_value = 100
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background = img_smooth.copy()
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background[img_smooth > thresh_value] = 0
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peaks = img_smooth - background
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"""
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Here, all pixels values below the threshold value are subtracted from the
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image. The resulting background image and the extracted peaks are shown below.
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"""
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imshow(background, vmin=0, vmax=255)
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plt.title("background image (thresholding)")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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imshow(peaks, vmin=0, vmax=255)
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plt.title("peaks (thresholding)")
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"""
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.. image:: PLOT2RST.current_figure
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Because of uneven illumination, peaks on the right bleed into each other.
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Increasing the threshold will fix this problem, but it will also cause some
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peaks on the left to go undetected.
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Morphological reconstruction
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============================
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Morphological reconstruction uses two images: a seed image and a mask image.
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Initially, all values of the reconstructed image start off pixel at the values
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of the seed image. A seed pixels of high intensity spread outwards until it
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hits the mask image (i.e. the mask value for a pixel is lower than the
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high-intensity value). Note that the mask is a gray-scale image that limits the
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maximum intensity at a pixel. This algorithm is clearer with pictures, which
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we generate below.
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One common case uses mask and seed images derived from the same image but
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shifted in intensity. Note: be careful when shifting images integer values,
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since this can lead to under/overflow of values. To prevent the uint8 image we
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started with from underflowing during subtraction, we first convert to float:
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"""
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from skimage import img_as_float
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img_r = img_as_float(img_smooth)
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import skimage.morphology as morph
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h = 0.1
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rec = morph.reconstruction(img_r-h, img_r)
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imshow(img_r, vmin=0, vmax=1)
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plt.title("original (smoothed) image")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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imshow(rec, vmin=0, vmax=1)
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plt.title("background image (reconstruction)")
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"""
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.. image:: PLOT2RST.current_figure
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This reconstructed image looks pretty much like the original, except that the
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peaks in the image are truncated. The reconstructed image can then be
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subtracted from the original image to reveal the peaks of the image.
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"""
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imshow(img_r-rec)
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plt.title("h-dome of image")
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"""
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.. image:: PLOT2RST.current_figure
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The result is known as the h-dome transformation [2]_, which extracts peaks of
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height `h` from the original image. To better understand what's going on,
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let's take a 1D slice along the middle of the image (cutting through peaks in
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the image).
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"""
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img_slice = img_r[99:100, :]
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rec_slice = morph.reconstruction(img_slice-h, img_slice)
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"""
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Plotting the reconstructed image (slice) next to the original image and the
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seed image shed light on the reconstruction process
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"""
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plt.figure(figsize=(4, 3))
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plt.plot(img_slice[0], 'k', label='original image')
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plt.plot(img_slice[0]-h, '0.5', label='seed image')
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plt.plot(rec_slice[0], 'r', label='reconstructed')
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plt.title("image slice")
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plt.xlabel('x')
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plt.ylabel('intensity')
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plt.legend()
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"""
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.. image:: PLOT2RST.current_figure
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Here, you see that morphological reconstruction dilates the seed image (i.e.
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the `h`-shifted image) until it intersects the mask (original image). Note that
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the peaks in the original image have very different intensity values (e.g. the
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peak at x=200 and x=100 differ by about 80). Subtracting the reconstructed
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image from the original image gives peaks of roughly equal intensity. Thus, the
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h-dome transformation is quiet effective at removing uneven, dark backgrounds
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from bright features. The inverse operation---the h-basin
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transformation---should be used when removing bright backgrounds from dark
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features.
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White tophat
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============
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"""
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selem = morph.disk(10)
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opening = morph.opening(img_smooth, selem)
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top_hat = img_smooth - opening
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imshow(opening, vmin=0, vmax=255)
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plt.title("Greyscale opening of image")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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imshow(top_hat)
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plt.title("Tophat with disk of r = 10")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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selem = morph.disk(5)
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top_hat = morph.white_tophat(img_smooth, selem)
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imshow(top_hat)
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plt.title("Tophat with disk of r = 5")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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selem = morph.square(20)
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opening = morph.opening(img_smooth, selem)
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# scikit's top hat filter uses uint8 and doesn't check for over(under)flow.
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mask = opening > img_smooth
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opening[mask] = img_smooth[mask]
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top_hat = img_smooth - opening
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imshow(opening, vmin=0, vmax=255)
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plt.title("Greyscale opening of image")
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"""
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.. image:: PLOT2RST.current_figure
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"""
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imshow(top_hat)
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plt.title("Tophat with square of w = 10")
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plt.show()
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"""
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.. image:: PLOT2RST.current_figure
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References
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==========
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.. [1] Crocker and Grier, Journal of Colloid and Interface Science (1996)
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.. [2] Vincent, L., IEEE Transactions on Image Processing (1993)
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"""
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