rpnifs/python_rpnifs/fractdim.py

import sys
import numpy as np
import scipy
import scipy.misc

def rgb2gray(rgb):
    r, g, b = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2]
    gray = 0.2989 * r + 0.5870 * g + 0.1140 * b
    return gray

def rgba2gray(rgba):
    r, g, b, a = rgb[:,:,0], rgb[:,:,1], rgb[:,:,2], rgb[:,:,3]
    gray = (0.2989 * r + 0.5870 * g + 0.1140 * b) * (a/255)
    return gray

def fractal_dimension(Z, threshold=None):
    ''' @return Minkowski–Bouligand dimension (computed) '''
    # Only for 2d image
    assert(len(Z.shape) == 2)

    # From https://github.com/rougier/numpy-100 (#87)
    def boxcount(Z, k):
        S = np.add.reduceat(
            np.add.reduceat(Z, np.arange(0, Z.shape[0], k), axis=0),
                               np.arange(0, Z.shape[1], k), axis=1)

        # We count non-empty (0) and non-full boxes (k*k)
        return len(np.where((S > 0) & (S < k*k))[0])

    if threshold is None:
        threshold = np.mean(Z)
        if threshold < 0.2:
            threshold = 0.2

    # Transform Z into a binary array
    Z = (Z < threshold)

    # Minimal dimension of image
    p = min(Z.shape)

    # Greatest power of 2 less than or equal to p
    n = 2**np.floor(np.log(p)/np.log(2))

    # Extract the exponent
    n = int(np.log(n)/np.log(2))

    # Build successive box sizes (from 2**n down to 2**1)
    sizes = 2**np.arange(n, 1, -1)

    # Actual box counting with decreasing size
    counts = []
    for size in sizes:
        counts.append(boxcount(Z, size))

    # Fit the successive log(sizes) with log (counts)
    coeffs = np.polyfit(np.log(sizes), np.log(counts), 1)
    return 0 if np.isnan(-coeffs[0]) else -coeffs[0]