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Change API for equalize_hist and cumulative_distribution.

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`equalize_hist`: "max_intensity" parameter no longer exists---img_as_float normalizes intensity range

`cumulative_distribution`: Return centers of bins instead of the edges.

Move `histogram` function from filter subpackage.

Add test of equalize_hist

Add example of histogram equalization.
This commit is contained in:
Tony S Yu
2011-12-22 10:16:32 -08:00
parent c87b1ad90e
commit 87c2353845
5 changed files with 159 additions and 55 deletions
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doc/examples/plot_equalize_hist.py
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"""
======================
Histogram Equalization
======================
This examples takes an image with low contrast and enhances its contrast using
histogram equalization. Histogram equalization enhances contrast by "spreading
out the most frequent intensity values" in an image [1]. The equalized image
has a roughly linear cumulative distribution function, as shown in this example.
.. [1] http://en.wikipedia.org/wiki/Histogram_equalization
"""
import matplotlib.pyplot as plt
from skimage import data
from skimage.util.dtype import dtype_range
from skimage import exposure
def plot_hist(img, bins=256, ax=None):
"""Plot histogram and cumulative histogram for image"""
ax = ax if ax is not None else plt.gca()
img_cdf, bins = exposure.cumulative_distribution(img, bins)
ax.hist(img.ravel(), bins=bins)
ax_right = ax.twinx()
ax_right.plot(bins, img_cdf, 'r')
xmin, xmax = dtype_range[img.dtype.type]
ax.set_xlim(xmin, xmax)
ax.set_ylabel('# pixels')
ax.set_xlabel('pixel intensiy')
ax_right.set_ylabel('fraction of total intensity')
img_orig = data.camera()
# squeeze image intensities to lower image contrast
img = img_orig / 5 + 100
img_eq = exposure.equalize_hist(img)
plt.subplot(2, 2, 1)
plt.imshow(img, cmap=plt.cm.gray, vmin=0, vmax=255)
plt.axis('off')
plt.subplot(2, 2, 2)
plot_hist(img)
plt.subplot(2, 2, 3)
plt.imshow(img_eq, cmap=plt.cm.gray, vmin=0, vmax=1)
plt.axis('off')
plt.subplot(2, 2, 4)
plot_hist(img_eq)
plt.subplots_adjust(left=0.05, hspace=0.25, wspace=0.3, top=0.95, bottom=0.1)
plt.show()
skimage/exposure/__init__.py
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@@ -1 +1 @@
from exposure import equalize_hist, cumulative_distribution
from exposure import histogram, equalize_hist, cumulative_distribution
skimage/exposure/exposure.py
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@@ -1,15 +1,63 @@
import numpy as np
__all__ = ['cumulative_distribution', 'equalize_hist']
import skimage
def cumulative_distribution(img, nbins=256):
__all__ = ['histogram', 'cumulative_distribution', 'equalize_hist']
def histogram(image, nbins, density=True):
"""Return histogram of image.
Unlike `numpy.histogram`, this function returns the centers of bins and
does not rebin integer arrays.
Parameters
----------
image : array
Input image.
nbins : int
Number of bins used to calculate histogram. This value is ignored for
integer arrays.
density : {True | False}
If True, values represent the probability density function.
If False, values represent the number of pixels in bins.
See numpy.histogram for details.
Returns
-------
hist : array
The values of the histogram.
bin_centers : array
The values at the center of the bins.
"""
if np.issubdtype(image.dtype, np.integer):
offset = 0
if np.min(image) < 0:
offset = np.min(image)
hist = np.bincount(image.ravel() - offset)
bin_centers = np.arange(len(hist)) + offset
# clip histogram to start with a non-zero bin
idx = np.nonzero(hist)[0][0]
return hist[idx:], bin_centers[idx:]
else:
if np.version.version >= '1.6':
hist, bin_edges = np.histogram(image.flat, nbins, density=density)
else:
hist, bin_edges = np.histogram(image.flat, nbins, normed=density)
bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.
return hist, bin_centers
def cumulative_distribution(image, nbins=256):
"""Return cumulative distribution function (cdf) for the given image.
Parameters
----------
img : array
image : array
Image array.
nbins : int
Number of bins for image histogram.
@@ -18,34 +66,33 @@ def cumulative_distribution(img, nbins=256):
-------
img_cdf : array
Values of cumulative distribution function.
bin_edges : array
Bin edges for cdf. Length is ``len(img_cdf) + 1``.
bin_centers : array
Centers of bins.
References
----------
.. [1] http://en.wikipedia.org/wiki/Cumulative_distribution_function
"""
hist, bin_edges = np.histogram(img.flat, nbins, density=True)
hist, bin_centers = histogram(image, nbins)
img_cdf = hist.cumsum()
return img_cdf, bin_edges
img_cdf = img_cdf / float(img_cdf[-1])
return img_cdf, bin_centers
def equalize_hist(img, nbins=256, max_intensity=255):
def equalize_hist(image, nbins=256):
"""Return image after histogram equalization.
Parameters
----------
img : array
image : array
Image array.
nbins : int
Number of bins for image histogram.
max_intensity : int
Maximum intensity of the returned image.
Returns
-------
out : array
out : float array
Image array after histogram equalization.
Notes
@@ -58,8 +105,8 @@ def equalize_hist(img, nbins=256, max_intensity=255):
.. [2] http://en.wikipedia.org/wiki/Histogram_equalization
"""
cdf, bin_edges = cumulative_distribution(img, nbins)
cdf = max_intensity * cdf / cdf[-1]
out = np.interp(img.flat, bin_edges[:-1], cdf)
return out.reshape(img.shape)
image = skimage.img_as_float(image)
cdf, bin_centers = cumulative_distribution(image, nbins)
out = np.interp(image.flat, bin_centers, cdf)
return out.reshape(image.shape)
skimage/exposure/tests/test_exposure.py
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import numpy as np
import skimage
from skimage import data
from skimage import exposure
# squeeze image intensities to lower image contrast
test_img = data.camera() / 5 + 100
def test_equalize_hist_ubyte():
img_eq = exposure.equalize_hist(test_img)
cdf, bin_edges = exposure.cumulative_distribution(img_eq)
check_cdf_slope(cdf)
def test_equalize_hist_float():
img = skimage.img_as_float(test_img)
img_eq = exposure.equalize_hist(img)
cdf, bin_edges = exposure.cumulative_distribution(img_eq)
check_cdf_slope(cdf)
def check_cdf_slope(cdf):
"""Slope of cdf which should equal 1 for an equalized histogram."""
norm_intensity = np.linspace(0, 1, len(cdf))
slope, intercept = np.polyfit(norm_intensity, cdf, 1)
assert 0.9 < slope < 1.1
if __name__ == '__main__':
from numpy import testing
testing.run_module_suite()
skimage/filter/thresholding.py
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@@ -1,5 +1,7 @@
import numpy as np
from skimage.exposure import histogram
__all__ = ['threshold_otsu']
@@ -50,40 +52,3 @@ def threshold_otsu(image, nbins=256):
threshold = bin_centers[:-1][idx]
return threshold
def histogram(image, nbins):
"""Return histogram of image.
Unlike `numpy.histogram`, this function returns the centers of bins and
does not rebin integer arrays.
Parameters
----------
image : array
Input image.
nbins : int
Number of bins used to calculate histogram. This value is ignored for
integer arrays.
Returns
-------
hist : array
The values of the histogram.
bin_centers : array
The values at the center of the bins.
"""
if np.issubdtype(image.dtype, np.integer):
offset = 0
if np.min(image) < 0:
offset = np.min(image)
hist = np.bincount(image.ravel() - offset)
bin_centers = np.arange(len(hist)) + offset
# clip histogram to return only non-zero bins
idx = np.nonzero(hist)[0][0]
return hist[idx:], bin_centers[idx:]
else:
hist, bin_edges = np.histogram(image, bins=nbins)
bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.
return hist, bin_centers