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# -*- coding: utf-8 -*-
# Copyright (C) 2008-2012, Luis Pedro Coelho <luis@luispedro.org>
# vim: set ts=4 sts=4 sw=4 expandtab smartindent:
#
# Permission is hereby granted, free of charge, to any person obtaining a copy
# of this software and associated documentation files (the "Software"), to deal
# in the Software without restriction, including without limitation the rights
# to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
# copies of the Software, and to permit persons to whom the Software is
# furnished to do so, subject to the following conditions:
#
# The above copyright notice and this permission notice shall be included in
# all copies or substantial portions of the Software.
#
# THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
# IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
# FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
# AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
# LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
# OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
# THE SOFTWARE.
'''
Thresholding Module
===================
Thresholding functions:
:otsu(): Otsu method
:rc(): Riddler-Calvard's method
'''
from __future__ import division
import numpy as np
from .histogram import fullhistogram
__all__ = [
'otsu',
'rc',
]
def otsu(img, ignore_zeros=False):
"""
T = otsu(img, ignore_zeros=False)
Calculate a threshold according to the Otsu method.
Parameters
----------
img : an image as a numpy array.
This should be of an unsigned integer type.
ignore_zeros : Boolean
whether to ignore zero-valued pixels
(default: False)
Returns
-------
T : integer
the threshold
"""
# Calculated according to CVonline:
# http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MORSE/threshold.pdf
hist = fullhistogram(img)
hist = hist.astype(np.double)
if ignore_zeros:
hist[0] = 0
Ng = len(hist)
nB = np.cumsum(hist)
nO = nB[-1]-nB
mu_B = 0
mu_O = (np.arange(1, Ng)*hist[1:]).sum()/hist[1:].sum()
best = nB[0]*nO[0]*(mu_B-mu_O)*(mu_B-mu_O)
bestT = 0
for T in xrange(1, Ng):
if nB[T] == 0: continue
if nO[T] == 0: break
mu_B = (mu_B*nB[T-1] + T*hist[T]) / nB[T]
mu_O = (mu_O*nO[T-1] - T*hist[T]) / nO[T]
sigma_between = nB[T]*nO[T]*(mu_B-mu_O)*(mu_B-mu_O)
if sigma_between > best:
best = sigma_between
bestT = T
return bestT
def rc(img, ignore_zeros=False):
"""
T = rc(img, ignore_zeros=False)
Calculate a threshold according to the Riddler-Calvard method.
Parameters
----------
img : ndarray
Image of any type
ignore_zeros : boolean, optional
Whether to ignore zero valued pixels (default: False)
Returns
-------
T : float
threshold
"""
hist = fullhistogram(img)
if ignore_zeros:
if hist[0] == img.size:
return 0
hist[0] = 0
N = hist.size
# Precompute most of what we need:
first_moment = np.cumsum(np.arange(N) * hist)
cumsum = np.cumsum(hist)
r_first_moment = np.flipud(np.cumsum(np.flipud(np.arange(N) * hist)))
r_cumsum = np.flipud(np.cumsum(np.flipud(hist)))
maxt = N-1
while hist[maxt] == 0:
maxt -= 1
res = maxt
t = 0
while t < min(maxt, res):
if cumsum[t] and r_cumsum[t+1]:
res = (first_moment[t]/cumsum[t] + r_first_moment[t+1]/r_cumsum[t+1])/2
t += 1
return res
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