Kittler-Illingworth Thresholding

kittler.py

import numpy as np

def Kittler(im, out):
    """
    The reimplementation of Kittler-Illingworth Thresholding algorithm by Bob Pepin
    Works on 8-bit images only
    Original Matlab code: https://www.mathworks.com/matlabcentral/fileexchange/45685-kittler-illingworth-thresholding
    Paper: Kittler, J. & Illingworth, J. Minimum error thresholding. Pattern Recognit. 19, 41–47 (1986).
    """
    h,g = np.histogram(im.ravel(),256,[0,256])
    h = h.astype(np.float)
    g = g.astype(np.float)
    g = g[:-1]
    c = np.cumsum(h)
    m = np.cumsum(h * g)
    s = np.cumsum(h * g**2)
    sigma_f = np.sqrt(s/c - (m/c)**2)
    cb = c[-1] - c
    mb = m[-1] - m
    sb = s[-1] - s
    sigma_b = np.sqrt(sb/cb - (mb/cb)**2)
    p =  c / c[-1]
    v = p * np.log(sigma_f) + (1-p)*np.log(sigma_b) - p*np.log(p) - (1-p)*np.log(1-p)
    v[~np.isfinite(v)] = np.inf
    idx = np.argmin(v)
    t = g[idx]
    out[:,:] = 0
    out[im >= t] = 255

Can you please let know what to pass in the "out" argument to the function?

An empty array of the same size and type as im. So, you can call it like:

img = <your grayscale input image as integer 2D array>
img_thresholded = np.empty_like(img)
Kittler(img, img_thresholded)