def get_kapur_threshold(image, mask=None):
"""The Kapur, Sahoo, & Wong method of thresholding, adapted to log-space."""
cropped_image = np.array(image.flat) if mask is None else image[mask]
if np.product(cropped_image.shape) < 3:
return 0
if np.min(cropped_image) == np.max(cropped_image):
return cropped_image[0]
log_image = np.log2(smooth_with_noise(cropped_image, 8))
min_log_image = np.min(log_image)
max_log_image = np.max(log_image)
histogram = scipy.ndimage.histogram(log_image, min_log_image, max_log_image, 256)
histogram_values = min_log_image + (max_log_image - min_log_image) * np.array(range(256), float) / 255
# drop any zero bins
keep = histogram != 0
histogram = histogram[keep]
histogram_values = histogram_values[keep]
# check for corner cases
if np.product(histogram_values) == 1:
return 2 ** histogram_values[0]
# Normalize to probabilities
p = histogram.astype(float) / float(np.sum(histogram))
# Find the probabilities totals up to and above each possible threshold.
lo_sum = np.cumsum(p)
hi_sum = lo_sum[-1] - lo_sum
lo_e = np.cumsum(p * np.log2(p))
hi_e = lo_e[-1] - lo_e
# compute the entropies
lo_entropy = lo_e / lo_sum - np.log2(lo_sum)
hi_entropy = hi_e / hi_sum - np.log2(hi_sum)
sum_entropy = lo_entropy[:-1] + hi_entropy[:-1]
sum_entropy[np.logical_not(np.isfinite(sum_entropy))] = np.Inf
entry = np.argmin(sum_entropy)
return 2 ** ((histogram_values[entry] + histogram_values[entry + 1]) / 2)
def test_02_smooth_half(self):
out = cpms.smooth_with_noise(np.ones((100,100))*.5, 5)
# Roughly 1/2 (5000) should be above .5 and half below
# Over 1/2 should be within 1/32 of .5
self.assertTrue(out.ndim == 2)
self.assertTrue(out.shape[0] == 100)
self.assertTrue(out.shape[1] == 100)
self.assertTrue(abs(np.sum(out > .5)-5000) < 300) # unless we are 3sd unlucky
self.assertTrue(np.sum(np.abs(out-.5)< 1.0 / 32.0) > 4700) # unless we are > 3sd unlucky
def test_02_smooth_half(self):
out = cpms.smooth_with_noise(np.ones((100,100))*.5, 5)
# Roughly 1/2 (5000) should be above .5 and half below
# Over 1/2 should be within 1/32 of .5
self.assertTrue(out.ndim == 2)
self.assertTrue(out.shape[0] == 100)
self.assertTrue(out.shape[1] == 100)
self.assertTrue(abs(np.sum(out > .5)-5000) < 300) # unless we are 3sd unlucky
self.assertTrue(np.sum(np.abs(out-.5)< 1.0 / 32.0) > 4700) # unless we are > 3sd unlucky
def test_03_img_1201(self):
'''Regression test of img-1201'''
#
# Using internal knowledge: smooth_with_noise always seeds with 0
#
np.random.seed(0)
r = np.random.normal(size=(10, 20))
img = np.random.uniform(size=(10, 20))
for bits in range(8, 17):
result = cpms.smooth_with_noise(img, bits)
im = img.copy()
delta = 1.0 / float(2**bits)
im[im < delta] = delta
expected = np.exp2(
np.log2(im) + (np.log2(im + 2.0**-bits) - np.log2(im)) * r)
expected = np.clip(expected, 0, 1)
np.testing.assert_almost_equal(result, expected)
def test_03_img_1201(self):
'''Regression test of img-1201'''
#
# Using internal knowledge: smooth_with_noise always seeds with 0
#
np.random.seed(0)
r = np.random.normal(size=(10,20))
img = np.random.uniform(size=(10,20))
for bits in range(8,17):
result = cpms.smooth_with_noise(img, bits)
im = img.copy()
delta = 1.0 / float(2**bits)
im[im < delta] = delta
expected = np.exp2(np.log2(im) +
(np.log2(im + 2.0 ** -bits) - np.log2(im)) * r)
expected = np.clip(expected, 0, 1)
np.testing.assert_almost_equal(result, expected)
def get_kapur_threshold(image, mask=None):
"""The Kapur, Sahoo, & Wong method of thresholding, adapted to log-space."""
cropped_image = np.array(image.flat) if mask is None else image[mask]
if np.product(cropped_image.shape)<3:
return 0
if np.min(cropped_image) == np.max(cropped_image):
return cropped_image[0]
log_image = np.log2(smooth_with_noise(cropped_image, 8))
min_log_image = np.min(log_image)
max_log_image = np.max(log_image)
histogram = scipy.ndimage.histogram(log_image,
min_log_image,
max_log_image,
256)
histogram_values = (min_log_image + (max_log_image - min_log_image)*
np.array(range(256),float) / 255)
# drop any zero bins
keep = histogram != 0
histogram = histogram[keep]
histogram_values = histogram_values[keep]
# check for corner cases
if np.product(histogram_values)==1:
return 2**histogram_values[0]
# Normalize to probabilities
p = histogram.astype(float) / float(np.sum(histogram))
# Find the probabilities totals up to and above each possible threshold.
lo_sum = np.cumsum(p);
hi_sum = lo_sum[-1] - lo_sum;
lo_e = np.cumsum(p * np.log2(p));
hi_e = lo_e[-1] - lo_e;
# compute the entropies
lo_entropy = lo_e / lo_sum - np.log2(lo_sum);
hi_entropy = hi_e / hi_sum - np.log2(hi_sum);
sum_entropy = lo_entropy[:-1] + hi_entropy[:-1];
sum_entropy[np.logical_not(np.isfinite(sum_entropy))] = np.Inf
entry = np.argmin(sum_entropy);
return 2**((histogram_values[entry] + histogram_values[entry+1]) / 2);
def sum_of_entropies(image, mask, binary_image):
"""Bin the foreground and background pixels and compute the entropy
of the distribution of points among the bins
"""
mask = mask.copy()
mask[np.isnan(image)] = False
if not np.any(mask):
return 0
#
# Clamp the dynamic range of the foreground
#
minval = np.max(image[mask]) / 256
if minval == 0:
return 0
clamped_image = image.copy()
clamped_image[clamped_image < minval] = minval
#
# Smooth image with -8 bits of noise
#
image = smooth_with_noise(clamped_image, 8)
im_min = np.min(image)
im_max = np.max(image)
#
# Figure out the bounds for the histogram
#
upper = np.log2(im_max)
lower = np.log2(im_min)
if upper == lower:
# All values are the same, answer is log2 of # of pixels
return math.log(np.sum(mask), 2)
#
# Create log-transformed lists of points in the foreground and background
#
fg = image[binary_image & mask]
bg = image[(~binary_image) & mask]
if len(fg) == 0 or len(bg) == 0:
return 0
log_fg = np.log2(fg)
log_bg = np.log2(bg)
#
# Make these into histograms
hfg = numpy_histogram(log_fg, 256, range=(lower, upper))[0]
hbg = numpy_histogram(log_bg, 256, range=(lower, upper))[0]
#hfg = scipy.ndimage.histogram(log_fg,lower,upper,256)
#hbg = scipy.ndimage.histogram(log_bg,lower,upper,256)
#
# Drop empty bins
#
hfg = hfg[hfg > 0]
hbg = hbg[hbg > 0]
if np.product(hfg.shape) == 0:
hfg = np.ones((1, ), int)
if np.product(hbg.shape) == 0:
hbg = np.ones((1, ), int)
#
# Normalize
#
hfg = hfg.astype(float) / float(np.sum(hfg))
hbg = hbg.astype(float) / float(np.sum(hbg))
#
# Compute sum of entropies
#
return np.sum(hfg * np.log2(hfg)) + np.sum(hbg * np.log2(hbg))
def test_01_smooth_zero(self):
"""Make sure smooth doesn't crash on all zeros"""
out = cpms.smooth_with_noise(np.zeros((3, 3)), 5)
self.assertTrue(np.all(out >= 0))
self.assertTrue(np.all(out <= 1))
def sum_of_entropies(image, mask, threshold):
"""Bin the foreground and background pixels and compute the entropy
of the distribution of points among the bins
"""
mask=mask.copy()
mask[np.isnan(image)] = False
if not np.any(mask):
return 0
#
# Clamp the dynamic range of the foreground
#
minval = np.max(image[mask])/256
if minval == 0:
return 0
clamped_image = image.copy()
clamped_image[clamped_image < minval] = minval
#
# Smooth image with -8 bits of noise
#
image = smooth_with_noise(clamped_image, 8)
im_min = np.min(image)
im_max = np.max(image)
#
# Figure out the bounds for the histogram
#
upper = np.log2(im_max)
lower = np.log2(im_min)
if upper == lower:
# All values are the same, answer is log2 of # of pixels
return math.log(np.sum(mask),2)
#
# Create log-transformed lists of points in the foreground and background
#
fg = image[np.logical_and(mask, image >= threshold)]
bg = image[np.logical_and(mask, image < threshold)]
if len(fg) == 0 or len(bg) == 0:
return 0
log_fg = np.log2(fg)
log_bg = np.log2(bg)
#
# Make these into histograms
hfg = numpy_histogram(log_fg, 256, range=(lower,upper))[0]
hbg = numpy_histogram(log_bg, 256, range=(lower,upper))[0]
#hfg = scipy.ndimage.histogram(log_fg,lower,upper,256)
#hbg = scipy.ndimage.histogram(log_bg,lower,upper,256)
#
# Drop empty bins
#
hfg = hfg[hfg>0]
hbg = hbg[hbg>0]
if np.product(hfg.shape) == 0:
hfg = np.ones((1,),int)
if np.product(hbg.shape) == 0:
hbg = np.ones((1,),int)
#
# Normalize
#
hfg = hfg.astype(float) / float(np.sum(hfg))
hbg = hbg.astype(float) / float(np.sum(hbg))
#
# Compute sum of entropies
#
return np.sum(hfg * np.log2(hfg)) + np.sum(hbg*np.log2(hbg))
def test_01_smooth_zero(self):
"""Make sure smooth doesn't crash on all zeros"""
out = cpms.smooth_with_noise(np.zeros((3,3)), 5)
self.assertTrue(np.all(out >=0))
self.assertTrue(np.all(out <=1))