From c87b1ad90ec1c24afdb85b019535c29218a8132e Mon Sep 17 00:00:00 2001
From: Tony S Yu <tsyu80@gmail.com>
Date: Mon, 12 Dec 2011 19:48:58 -0500
Subject: [PATCH 1/8] Add exposure module with histogram equalization function

---
 skimage/exposure/__init__.py |  1 +
 skimage/exposure/exposure.py | 65 ++++++++++++++++++++++++++++++++++++
 2 files changed, 66 insertions(+)
 create mode 100644 skimage/exposure/__init__.py
 create mode 100644 skimage/exposure/exposure.py

diff --git a/skimage/exposure/__init__.py b/skimage/exposure/__init__.py
new file mode 100644
index 00000000..51dcc5cf
--- /dev/null
+++ b/skimage/exposure/__init__.py
@@ -0,0 +1 @@
+from exposure import equalize_hist, cumulative_distribution
diff --git a/skimage/exposure/exposure.py b/skimage/exposure/exposure.py
new file mode 100644
index 00000000..1d328e3e
--- /dev/null
+++ b/skimage/exposure/exposure.py
@@ -0,0 +1,65 @@
+import numpy as np
+
+
+__all__ = ['cumulative_distribution', 'equalize_hist']
+
+
+def cumulative_distribution(img, nbins=256):
+    """Return cumulative distribution function (cdf) for the given image.
+
+    Parameters
+    ----------
+    img : array
+        Image array.
+    nbins : int
+        Number of bins for image histogram.
+
+    Returns
+    -------
+    img_cdf : array
+        Values of cumulative distribution function.
+    bin_edges : array
+        Bin edges for cdf. Length is ``len(img_cdf) + 1``.
+
+    References
+    ----------
+    .. [1] http://en.wikipedia.org/wiki/Cumulative_distribution_function
+
+    """
+    hist, bin_edges = np.histogram(img.flat, nbins, density=True)
+    img_cdf = hist.cumsum()
+    return img_cdf, bin_edges
+
+
+def equalize_hist(img, nbins=256, max_intensity=255):
+    """Return image after histogram equalization.
+
+    Parameters
+    ----------
+    img : array
+        Image array.
+    nbins : int
+        Number of bins for image histogram.
+    max_intensity : int
+        Maximum intensity of the returned image.
+
+    Returns
+    -------
+    out : array
+        Image array after histogram equalization.
+
+    Notes
+    -----
+    This function is adapted from [1] with the author's permission.
+
+    References
+    ----------
+    .. [1] http://www.janeriksolem.net/2009/06/histogram-equalization-with-python-and.html
+    .. [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)
+

From 87c2353845923241592ccd26c0fd553f5996a42c Mon Sep 17 00:00:00 2001
From: Tony S Yu <tsyu80@gmail.com>
Date: Tue, 13 Dec 2011 22:57:15 -0500
Subject: [PATCH 2/8] Change API for equalize_hist and cumulative_distribution.

`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.
---
 doc/examples/plot_equalize_hist.py      | 55 +++++++++++++++++
 skimage/exposure/__init__.py            |  2 +-
 skimage/exposure/exposure.py            | 81 +++++++++++++++++++------
 skimage/exposure/tests/test_exposure.py | 37 +++++++++++
 skimage/filter/thresholding.py          | 39 +-----------
 5 files changed, 159 insertions(+), 55 deletions(-)
 create mode 100644 doc/examples/plot_equalize_hist.py
 create mode 100644 skimage/exposure/tests/test_exposure.py

diff --git a/doc/examples/plot_equalize_hist.py b/doc/examples/plot_equalize_hist.py
new file mode 100644
index 00000000..59b8defc
--- /dev/null
+++ b/doc/examples/plot_equalize_hist.py
@@ -0,0 +1,55 @@
+"""
+======================
+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()
+
diff --git a/skimage/exposure/__init__.py b/skimage/exposure/__init__.py
index 51dcc5cf..1c64aad4 100644
--- a/skimage/exposure/__init__.py
+++ b/skimage/exposure/__init__.py
@@ -1 +1 @@
-from exposure import equalize_hist, cumulative_distribution
+from exposure import histogram, equalize_hist, cumulative_distribution
diff --git a/skimage/exposure/exposure.py b/skimage/exposure/exposure.py
index 1d328e3e..06172597 100644
--- a/skimage/exposure/exposure.py
+++ b/skimage/exposure/exposure.py
@@ -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)
 
diff --git a/skimage/exposure/tests/test_exposure.py b/skimage/exposure/tests/test_exposure.py
new file mode 100644
index 00000000..b2d19b8a
--- /dev/null
+++ b/skimage/exposure/tests/test_exposure.py
@@ -0,0 +1,37 @@
+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()
+
diff --git a/skimage/filter/thresholding.py b/skimage/filter/thresholding.py
index 800e18b8..856bd78d 100644
--- a/skimage/filter/thresholding.py
+++ b/skimage/filter/thresholding.py
@@ -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
-

From d4ca519ca5d95a000b03c10e9ef11dabfd831388 Mon Sep 17 00:00:00 2001
From: Tony S Yu <tsyu80@gmail.com>
Date: Thu, 22 Dec 2011 10:48:28 -0800
Subject: [PATCH 3/8] Rename equalize_hist to equalize and minor cleanup

---
 doc/examples/plot_equalize_hist.py      | 21 ++++++++++-----------
 skimage/exposure/__init__.py            |  2 +-
 skimage/exposure/exposure.py            |  9 +++++----
 skimage/exposure/tests/test_exposure.py |  8 ++++----
 4 files changed, 20 insertions(+), 20 deletions(-)

diff --git a/doc/examples/plot_equalize_hist.py b/doc/examples/plot_equalize_hist.py
index 59b8defc..e2ff895e 100644
--- a/doc/examples/plot_equalize_hist.py
+++ b/doc/examples/plot_equalize_hist.py
@@ -5,7 +5,7 @@ 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
+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
@@ -18,25 +18,24 @@ from skimage.util.dtype import dtype_range
 from skimage import exposure
 
 
-def plot_hist(img, bins=256, ax=None):
+def plot_hist(img, bins=256):
     """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')
+    plt.hist(img.ravel(), bins=bins)
+    ax_cdf = plt.twinx()
+    ax_cdf.plot(bins, img_cdf, 'r')
     xmin, xmax = dtype_range[img.dtype.type]
-    ax.set_xlim(xmin, xmax)
+    plt.xlim(xmin, xmax)
 
-    ax.set_ylabel('# pixels')
-    ax.set_xlabel('pixel intensiy')
-    ax_right.set_ylabel('fraction of total intensity')
+    plt.ylabel('# pixels')
+    plt.xlabel('pixel intensiy')
+    ax_cdf.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)
+img_eq = exposure.equalize(img)
 
 plt.subplot(2, 2, 1)
 plt.imshow(img, cmap=plt.cm.gray, vmin=0, vmax=255)
diff --git a/skimage/exposure/__init__.py b/skimage/exposure/__init__.py
index 1c64aad4..ee5969ab 100644
--- a/skimage/exposure/__init__.py
+++ b/skimage/exposure/__init__.py
@@ -1 +1 @@
-from exposure import histogram, equalize_hist, cumulative_distribution
+from exposure import histogram, equalize, cumulative_distribution
diff --git a/skimage/exposure/exposure.py b/skimage/exposure/exposure.py
index 06172597..ca16c975 100644
--- a/skimage/exposure/exposure.py
+++ b/skimage/exposure/exposure.py
@@ -3,14 +3,15 @@ import numpy as np
 import skimage
 
 
-__all__ = ['histogram', 'cumulative_distribution', 'equalize_hist']
+__all__ = ['histogram', 'cumulative_distribution', 'equalize']
 
 
 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.
+    does not rebin integer arrays. For integer arrays, each integer value has
+    its own bin, which improves speed and intensity-resolution.
 
     Parameters
     ----------
@@ -80,7 +81,7 @@ def cumulative_distribution(image, nbins=256):
     return img_cdf, bin_centers
 
 
-def equalize_hist(image, nbins=256):
+def equalize(image, nbins=256):
     """Return image after histogram equalization.
 
     Parameters
@@ -97,7 +98,7 @@ def equalize_hist(image, nbins=256):
 
     Notes
     -----
-    This function is adapted from [1] with the author's permission.
+    This function is adapted from [1]_ with the author's permission.
 
     References
     ----------
diff --git a/skimage/exposure/tests/test_exposure.py b/skimage/exposure/tests/test_exposure.py
index b2d19b8a..22339de7 100644
--- a/skimage/exposure/tests/test_exposure.py
+++ b/skimage/exposure/tests/test_exposure.py
@@ -9,16 +9,16 @@ from skimage import exposure
 test_img = data.camera() / 5 + 100
 
 
-def test_equalize_hist_ubyte():
-    img_eq = exposure.equalize_hist(test_img)
+def test_equalize_ubyte():
+    img_eq = exposure.equalize(test_img)
 
     cdf, bin_edges = exposure.cumulative_distribution(img_eq)
     check_cdf_slope(cdf)
 
 
-def test_equalize_hist_float():
+def test_equalize_float():
     img = skimage.img_as_float(test_img)
-    img_eq = exposure.equalize_hist(img)
+    img_eq = exposure.equalize(img)
 
     cdf, bin_edges = exposure.cumulative_distribution(img_eq)
     check_cdf_slope(cdf)

From 62d3b5590b0e5d45d1128bc60daa1a9eb39ee1eb Mon Sep 17 00:00:00 2001
From: Tony S Yu <tsyu80@gmail.com>
Date: Thu, 22 Dec 2011 10:58:02 -0800
Subject: [PATCH 4/8] Remove `density` parameter in `histogram`

The `density` (or `normed`) parameter was set in the original implementation of `equalize`, but it is unnecessary since `cumulative_distribution` renormalizes values. The only other function in scikits-image that calls `histogram` (`filter.threshold_otsu`) is not affected by renormalization.
---
 skimage/exposure/exposure.py | 13 ++-----------
 1 file changed, 2 insertions(+), 11 deletions(-)

diff --git a/skimage/exposure/exposure.py b/skimage/exposure/exposure.py
index ca16c975..d120b386 100644
--- a/skimage/exposure/exposure.py
+++ b/skimage/exposure/exposure.py
@@ -6,7 +6,7 @@ import skimage
 __all__ = ['histogram', 'cumulative_distribution', 'equalize']
 
 
-def histogram(image, nbins, density=True):
+def histogram(image, nbins=256):
     """Return histogram of image.
 
     Unlike `numpy.histogram`, this function returns the centers of bins and
@@ -20,10 +20,6 @@ def histogram(image, nbins, density=True):
     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
     -------
@@ -43,12 +39,7 @@ def histogram(image, nbins, density=True):
         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)
-
+        hist, bin_edges = np.histogram(image.flat, nbins)
         bin_centers = (bin_edges[:-1] + bin_edges[1:]) / 2.
         return hist, bin_centers
 

From 60f146c780a65df0ba1429f09be8cba7c22c27d9 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Mon, 26 Dec 2011 01:53:37 -0800
Subject: [PATCH 5/8] DOC: Update contributors.

---
 CONTRIBUTORS.txt | 6 ++++--
 1 file changed, 4 insertions(+), 2 deletions(-)

diff --git a/CONTRIBUTORS.txt b/CONTRIBUTORS.txt
index 007f267a..bb17033a 100644
--- a/CONTRIBUTORS.txt
+++ b/CONTRIBUTORS.txt
@@ -26,9 +26,11 @@
 - Tony Yu
   Reading of paletted images; build, bug and doc fixes.
   Code to generate skimage logo.
+  Otsu thresholding, histogram equalisation, and more.
 
 - Zachary Pincus
-  Tracing of low cost paths, FreeImage I/O plugin, iso-contours
+  Tracing of low cost paths, FreeImage I/O plugin, iso-contours,
+  and more.
 
 - Almar Klein
   Binary heap class for graph algorithms
@@ -45,7 +47,7 @@
 
 - Emmanuelle Guillart
   Total variation noise filtering, integration of CellProfiler's
-  mathematical morphology tools.
+  mathematical morphology tools, tutorials, and more.
 
 - Maël Primet
   Total variation noise filtering

From d74295c7f1cf98af31abaa2fc4033b5269923ae1 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Mon, 26 Dec 2011 01:53:59 -0800
Subject: [PATCH 6/8] DOC: Explain why bincount is used to histogram integer
 arrays.

---
 skimage/exposure/exposure.py | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/skimage/exposure/exposure.py b/skimage/exposure/exposure.py
index d120b386..42a60dbf 100644
--- a/skimage/exposure/exposure.py
+++ b/skimage/exposure/exposure.py
@@ -28,6 +28,8 @@ def histogram(image, nbins=256):
     bin_centers : array
         The values at the center of the bins.
     """
+
+    # For integer types, histogramming with bincount is more efficient.
     if np.issubdtype(image.dtype, np.integer):
         offset = 0
         if np.min(image) < 0:

From 19fa34f269c71c571f82363c286b376f7b106dfd Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Mon, 26 Dec 2011 01:55:00 -0800
Subject: [PATCH 7/8] DOC: Rename equalize example to match function name.

---
 doc/examples/{plot_equalize_hist.py => plot_equalize.py} | 0
 1 file changed, 0 insertions(+), 0 deletions(-)
 rename doc/examples/{plot_equalize_hist.py => plot_equalize.py} (100%)

diff --git a/doc/examples/plot_equalize_hist.py b/doc/examples/plot_equalize.py
similarity index 100%
rename from doc/examples/plot_equalize_hist.py
rename to doc/examples/plot_equalize.py

From 4e054fce7c5c6e2f4aa7df847cd0541e64897eb9 Mon Sep 17 00:00:00 2001
From: Stefan van der Walt <stefan@sun.ac.za>
Date: Mon, 26 Dec 2011 02:01:08 -0800
Subject: [PATCH 8/8] DOC: Move around plot statements so that all axes are
 labeled.

---
 doc/examples/plot_equalize.py | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/doc/examples/plot_equalize.py b/doc/examples/plot_equalize.py
index e2ff895e..9cb30dd7 100644
--- a/doc/examples/plot_equalize.py
+++ b/doc/examples/plot_equalize.py
@@ -22,15 +22,15 @@ def plot_hist(img, bins=256):
     """Plot histogram and cumulative histogram for image"""
     img_cdf, bins = exposure.cumulative_distribution(img, bins)
     plt.hist(img.ravel(), bins=bins)
+    plt.ylabel('Number of pixels')
+    plt.xlabel('Pixel intensiy')
+
     ax_cdf = plt.twinx()
     ax_cdf.plot(bins, img_cdf, 'r')
     xmin, xmax = dtype_range[img.dtype.type]
     plt.xlim(xmin, xmax)
 
-    plt.ylabel('# pixels')
-    plt.xlabel('pixel intensiy')
-    ax_cdf.set_ylabel('fraction of total intensity')
-
+    ax_cdf.set_ylabel('Fraction of total intensity')
 
 img_orig = data.camera()
 # squeeze image intensities to lower image contrast
@@ -39,12 +39,14 @@ img_eq = exposure.equalize(img)
 
 plt.subplot(2, 2, 1)
 plt.imshow(img, cmap=plt.cm.gray, vmin=0, vmax=255)
+plt.title('Low contrast input image')
 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.title('After\nhistogram equalization')
 plt.axis('off')
 plt.subplot(2, 2, 4)
 plot_hist(img_eq)