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# ----------------------------------------------------------------------------- | |
# 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 scipy.misc | |
import numpy as np | |
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] | |
I = scipy.misc.imread("sierpinski.png")/256.0 | |
print("Minkowski–Bouligand dimension (computed): ", fractal_dimension(I)) | |
print("Haussdorf dimension (theoretical): ", (np.log(3)/np.log(2))) |
Hi! I found this code very useful and I would like to cite it in my paper. Is there a correct way to cite this? Please help! I have to submit soon!
Glad the code is useful but I'm afraid there there's no proper way to cite a it. Maybe as a misc bibitem with the relevant url/author.
hello
sorry, can anyone tell me how to change the data that I want to get from the link to my laptop data?
I want to try to extract features of an iris
thanks, @jankaWIS
and sorry if I ask again is the 52 line is
images = [
'https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Peano_Sierpinski_carpet_4.svg/440px-Peano_Sierpinski_carpet_4.svg.png',
'https://upload.wikimedia.org/wikipedia/commons/thumb/b/b7/Sierpinski_carpet_3.svg/244px-Sierpinski_carpet_3.svg.png',
'https://upload.wikimedia.org/wikipedia/commons/f/f0/Flocke.PNG',
'https://upload.wikimedia.org/wikipedia/commons/thumb/3/3b/Quadratic_Koch_2.svg/2880px-Quadratic_Koch_2.svg.png',
'https://upload.wikimedia.org/wikipedia/commons/thumb/5/55/Quadratic_Koch.svg/300px-Quadratic_Koch.svg.png'
]
?
sorry I using the jupyter notebook so not to know about the number
Why are boxes of 2x2 excluded?
@akshahi17 check this answer https://stackoverflow.com/questions/15345790/scipy-misc-module-has-no-attribute-imread
the function has been deprecated so you can either downgrade (not recommended) or use what @rougier recommended (
imageio
) or what I'm using,imread
inmatplotlib.pyplot
.