Fractal dimension computing

fractal-dimension.py

# -----------------------------------------------------------------------------
# From https://en.wikipedia.org/wiki/Minkowski–Bouligand_dimension:
#
# In fractal geometry, the Minkowski–Bouligand dimension, also known as
# Minkowski dimension or box-counting dimension, is a way of determining the
# fractal dimension of a set S in a Euclidean space Rn, or more generally in a
# metric space (X, d).
# -----------------------------------------------------------------------------
import cv2

import numpy as np
import imageio

def fractal_dimension(Z, threshold=0.9):

    # 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])


    # 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 -coeffs[0]

def main_01():

    filename = 'Koch_curve2.png' #'sierpinski2.png' #'t02.jpg'
    originalImage = cv2.imread(filename)
    I = cv2.cvtColor(originalImage, cv2.COLOR_BGR2GRAY)/256.0


    # Koch curve should be 1.26
    EXPECTEDS = {
        'koch': 1.26,
        'sierpinski': 1.5849
    }

    Db = fractal_dimension(I, 0.9)
    print("Minkowski–Bouligand dimension (computed): ", Db)
    # print("Theoretical:        ", (np.log(3)/np.log(2)))

    return


if __name__ == "__main__":
    main_01()