_cross_entropy(image, threshold, bins=(-0.5, 0.5, 1.5, 2.5, 3.5, 4.5, 5.5, 6.5, 7.5, 8.5, 9.5, 10.5, 11.5, 12.5, 13.5, 14.5, 15.5, 16.5, 17.5, 18.5, 19.5, 20.5, 21.5, 22.5, 23.5, 24.5, 25.5, 26.5, 27.5, 28.5, 29.5, 30.5, 31.5, 32.5, 33.5, 34.5, 35.5, 36.5, 37.5, 38.5, 39.5, 40.5, 41.5, 42.5, 43.5, 44.5, 45.5, 46.5, 47.5, 48.5, 49.5, 50.5, 51.5, 52.5, 53.5, 54.5, 55.5, 56.5, 57.5, 58.5, 59.5, 60.5, 61.5, 62.5, 63.5, 64.5, 65.5, 66.5, 67.5, 68.5, 69.5, 70.5, 71.5, 72.5, 73.5, 74.5, 75.5, 76.5, 77.5, 78.5, 79.5, 80.5, 81.5, 82.5, 83.5, 84.5, 85.5, 86.5, 87.5, 88.5, 89.5, 90.5, 91.5, 92.5, 93.5, 94.5, 95.5, 96.5, 97.5, 98.5, 99.5, 100.5, 101.5, 102.5, 103.5, 104.5, 105.5, 106.5, 107.5, 108.5, 109.5, 110.5, 111.5, 112.5, 113.5, 114.5, 115.5, 116.5, 117.5, 118.5, 119.5, 120.5, 121.5, 122.5, 123.5, 124.5, 125.5, 126.5, 127.5, 128.5, 129.5, 130.5, 131.5, 132.5, 133.5, 134.5, 135.5, 136.5, 137.5, 138.5, 139.5, 140.5, 141.5, 142.5, 143.5, 144.5, 145.5, 146.5, 147.5, 148.5, 149.5, 150.5, 151.5, 152.5, 153.5, 154.5, 155.5, 156.5, 157.5, 158.5, 159.5, 160.5, 161.5, 162.5, 163.5, 164.5, 165.5, 166.5, 167.5, 168.5, 169.5, 170.5, 171.5, 172.5, 173.5, 174.5, 175.5, 176.5, 177.5, 178.5, 179.5, 180.5, 181.5, 182.5, 183.5, 184.5, 185.5, 186.5, 187.5, 188.5, 189.5, 190.5, 191.5, 192.5, 193.5, 194.5, 195.5, 196.5, 197.5, 198.5, 199.5, 200.5, 201.5, 202.5, 203.5, 204.5, 205.5, 206.5, 207.5, 208.5, 209.5, 210.5, 211.5, 212.5, 213.5, 214.5, 215.5, 216.5, 217.5, 218.5, 219.5, 220.5, 221.5, 222.5, 223.5, 224.5, 225.5, 226.5, 227.5, 228.5, 229.5, 230.5, 231.5, 232.5, 233.5, 234.5, 235.5, 236.5, 237.5, 238.5, 239.5, 240.5, 241.5, 242.5, 243.5, 244.5, 245.5, 246.5, 247.5, 248.5, 249.5, 250.5, 251.5, 252.5, 253.5, 254.5, 255.5))
See Li and Lee, 1993 ; this is the objective function threshold_li
minimizes. This function can be improved but this implementation most closely matches equation 8 in and equations 1-3 in .
The input array of values.
The value dividing the foreground and background in image
.
The number of bins or the bin edges. (Any valid value to the bins
argument of np.histogram
will work here.) For an exact calculation, each unique value should have its own bin. The default value for bins ensures exact handling of uint8 images: bins=256
results in aliasing problems due to bin width not being equal to 1.
The cross-entropy target value as defined in .
Compute cross-entropy between distributions above and below a threshold.
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