我有一些圖像，我想計算Minkowski/box count dimension來确定圖像中的分形特征。下面是兩個示例圖像：
10.jpg：
24.jpg：
我使用以下代碼計算分形維數：import numpy as np
import scipy
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 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 = rgb2gray(scipy.misc.imread("24.jpg"))
print("Minkowski–Bouligand dimension (computed): ", fractal_dimension(I))
從我讀過的文獻來看，有人認為自然場景(如24.jpg)在本質上更具分形性，是以應該具有更大的分形維數值
它給我的結果與文獻所暗示的相反：10.jpg:1.259
24.jpg:1.073
我希望自然圖像的分形維數大于城市圖像的分形維數
我計算代碼中的值是否不正确？或者我隻是不正确地解釋結果？