PEP8 fixes, License file added, tests added

* Added 7 tests (3 in TestSimpleImage, 4 as separate functions)
* Added ImageJ license file
* Updated Li code
  * threshold set from image instead of fixed at 0.5
  * subtract min to handle -ve images (as log is integral part of alg.)

skimage/filters/LICENSE.txt

@@ -0,0 +1,28 @@
+threshold_li based on imagej code:
+
+Copyright (c) 2009 - 2015, Board of Regents of the University of
+Wisconsin-Madison, Broad Institute of MIT and Harvard, and Max Planck
+Institute of Molecular Cell Biology and Genetics.
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without modification,
+are permitted provided that the following conditions are met:
+
+1. Redistributions of source code must retain the above copyright notice, this
+   list of conditions and the following disclaimer.
+
+2. Redistributions in binary form must reproduce the above copyright notice,
+   this list of conditions and the following disclaimer in the documentation
+   and/or other materials provided with the distribution.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
+LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+POSSIBILITY OF SUCH DAMAGE.

skimage/filters/tests/test_thresholding.py

@@ -5,6 +5,7 @@ import skimage
 from skimage import data
 from skimage.filters.thresholding import (threshold_adaptive,
                                           threshold_otsu,
+                                          threshold_li,
                                           threshold_yen,
                                           threshold_isodata)
 
@@ -28,6 +29,17 @@ class TestSimpleImage():
         image = np.float64(self.image)
         assert 2 <= threshold_otsu(image) < 3
 
+    def test_li(self):
+        assert int(threshold_li(self.image)) == 2
+
+    def test_li_negative_int(self):
+        image = self.image - 2
+        assert int(threshold_li(image)) == 0
+
+    def test_li_float_image(self):
+        image = np.float64(self.image)
+        assert 2 <= threshold_li(image) < 3
+
     def test_yen(self):
         assert threshold_yen(self.image) == 2
 
@@ -152,6 +164,29 @@ def test_otsu_astro_image():
     img = skimage.img_as_ubyte(data.astronaut())
     assert 109 < threshold_otsu(img) < 111
 
+def test_li_camera_image():
+    camera = skimage.img_as_ubyte(data.camera())
+    assert 63 < threshold_li(camera) < 65
+
+
+def test_li_coins_image():
+    coins = skimage.img_as_ubyte(data.coins())
+    assert 95 < threshold_li(coins) < 97
+
+
+def test_li_coins_image_as_float():
+    coins = skimage.img_as_float(data.coins())
+    assert 0.37 < threshold_li(coins) < 0.38
+
+
+def test_li_lena_image():
+    img = skimage.img_as_ubyte(data.lena())
+    assert 127 < threshold_li(img) < 129
+
+def test_li_astro_image():
+    img = skimage.img_as_ubyte(data.astronaut())
+    assert 66 < threshold_li(img) < 68
+
 def test_yen_camera_image():
     camera = skimage.img_as_ubyte(data.camera())
     assert 197 < threshold_yen(camera) < 199

skimage/filters/thresholding.py

@@ -1,8 +1,8 @@
 __all__ = ['threshold_adaptive',
            'threshold_otsu',
            'threshold_yen',
-           'threshold_isodata', 
-           'threshold_li',]
+           'threshold_isodata',
+           'threshold_li', ]
 
 import numpy as np
 import scipy.ndimage
@@ -306,7 +306,7 @@ def threshold_isodata(image, nbins=256, return_all=False):
 
 
 def threshold_li(image):
-    """Return threshold value based on Li's Minimum Cross Entropy method.
+    """Return threshold value based on adaptation of Li's Minimum Cross Entropy method.
 
     Parameters
     ----------
@@ -321,16 +321,17 @@ def threshold_li(image):
 
     References
     ----------
-    .. [1] Li C.H. and Lee C.K. (1993) "Minimum Cross Entropy Thresholding" 
+    .. [1] Li C.H. and Lee C.K. (1993) "Minimum Cross Entropy Thresholding"
            Pattern Recognition, 26(4): 617-625
-    .. [2] Li C.H. and Tam P.K.S. (1998) "An Iterative Algorithm for Minimum 
+    .. [2] Li C.H. and Tam P.K.S. (1998) "An Iterative Algorithm for Minimum
            Cross Entropy Thresholding"Pattern Recognition Letters, 18(8): 771-776
-    .. [3] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding 
-           Techniques and Quantitative Performance Evaluation" Journal of 
-           Electronic Imaging, 13(1): 146-165 
+    .. [3] Sezgin M. and Sankur B. (2004) "Survey over Image Thresholding
+           Techniques and Quantitative Performance Evaluation" Journal of
+           Electronic Imaging, 13(1): 146-165
            http://citeseer.ist.psu.edu/sezgin04survey.html
-    
-    Ported to skimage by J. Metz from ImageJ plugin by G.Landini
+    .. [4] ImageJ AutoThresholder code, http://fiji.sc/wiki/index.php/Auto_Threshold
+
+    Adapted for skimage by J. Metz from ImageJ plugin by G.Landini
 
     Examples
     --------
@@ -339,32 +340,37 @@ def threshold_li(image):
     >>> thresh = threshold_li(image)
     >>> binary = image <= thresh
     """
+    # Requires positive image ( log(mean))
+    offset = image.min()
+    # Can't use fixed tolerance for float image
+    imrange = image.max()-offset
+    image -= offset
 
-    tolerance=0.5
-    # Calculate the mean gray-level 
+    tolerance = 0.5 * imrange / 256.0
+    # Calculate the mean gray-level
     mean = image.mean()
-    
-    # Initial estimate 
+
+    # Initial estimate
     new_thresh = mean
-    old_thresh = new_thresh + 2*tolerance
+    old_thresh = new_thresh + 2 * tolerance
 
     # Stop the iterations when the difference between the
-    # new and old threshold values is less than the tolerance 
-    while abs( new_thresh - old_thresh ) > tolerance: 
+    # new and old threshold values is less than the tolerance
+    while abs(new_thresh - old_thresh) > tolerance:
         old_thresh = new_thresh
-        threshold = int(old_thresh + 0.5)   # range 
-        # Calculate the means of background and object pixels 
-        # Background 
-        mean_back = image[ image <= threshold ].mean()
-        # Object 
-        mean_obj = image[ image > threshold ].mean()
+        threshold = old_thresh + tolerance   # range
+        # Calculate the means of background and object pixels
+        # Background
+        mean_back = image[image <= threshold].mean()
+        # Object
+        mean_obj = image[image > threshold].mean()
 
         temp = (mean_back - mean_obj) / (np.log(mean_back) - np.log(mean_obj))
 
-        if temp < 0: # (temp < -2.220446049250313E-16)
-            new_thresh = int(temp - 0.5)
+        if temp < 0:
+            new_thresh = temp - tolerance
         else:
-            new_thresh = int(temp + 0.5)
-    
-    return threshold         
+            new_thresh = temp + tolerance
+
+    return threshold + offset