max_entropy_threshold.py

import numpy as np


def max_entropy_threshold(histogram):
    """
    Implements Kapur-Sahoo-Wong (Maximum Entropy) thresholding method
    Kapur J.N., Sahoo P.K., and Wong A.K.C. (1985) "A New Method for Gray-Level Picture Thresholding Using the Entropy
    of the Histogram", Graphical Models and Image Processing, 29(3): 273-285
    M. Emre Celebi
    06.15.2007
    Ported to ImageJ plugin by G.Landini from E Celebi's fourier_0.8 routines
    2016-04-28: Adapted for Python 2.7 by Robert Metchev from Java source of MaxEntropy() in the Autothresholder plugin
    http://rsb.info.nih.gov/ij/plugins/download/AutoThresholder.java
    Licensed under GNU GPLv3
    :param histogram: Sequence representing the histogram of the image
    :return threshold: Resulting maximum entropy threshold
    """

    # calculate CDF (cumulative density function)
    cdf = histogram.astype(np.float).cumsum()

    # find histogram's nonzero area
    valid_idx = np.nonzero(histogram)[0]
    first_bin = valid_idx[0]
    last_bin = valid_idx[-1]

    # initialize search for maximum
    max_ent, threshold = 0, 0

    for it in range(first_bin, last_bin + 1):
        # Background (dark)
        hist_range = histogram[:it + 1]
        hist_range = hist_range[hist_range != 0] / cdf[it]  # normalize within selected range & remove all 0 elements
        tot_ent = -np.sum(hist_range * np.log(hist_range))  # background entropy

        # Foreground/Object (bright)
        hist_range = histogram[it + 1:]
        # normalize within selected range & remove all 0 elements
        hist_range = hist_range[hist_range != 0] / (cdf[last_bin] - cdf[it])
        tot_ent -= np.sum(hist_range * np.log(hist_range))  # accumulate object entropy

        # find max
        if tot_ent > max_ent:
            max_ent, threshold = tot_ent, it

    return threshold