import numpy as np
[docs]
def compute_gradient_features(im_label, im_intensity,
num_hist_bins=10, rprops=None):
"""Calculates gradient features from an intensity image.
Parameters
----------
im_label : array_like
A labeled mask image wherein intensity of a pixel is the ID of the
object it belongs to. Non-zero values are considered to be foreground
objects.
im_intensity : array_like
Intensity image
num_hist_bins: int, optional
Number of bins used to computed the gradient histogram of an object.
Histogram is used to energy and entropy features. Default is 10.
rprops : output of skimage.measure.regionprops, optional
rprops = skimage.measure.regionprops( im_label ). If rprops is not
passed then it will be computed inside which will increase the
computation time.
Returns
-------
fdata: pandas.DataFrame
A pandas dataframe containing the gradient features listed below for
each object/label.
Notes
-----
List of gradient features computed by this function:
Gradient.Mag.Mean : float
Mean of gradient data.
Gradient.Mag.Std : float
Standard deviation of gradient data.
Gradient.Mag.Skewness : float
Skewness of gradient data. Value is 0 when all values are equal.
Gradient.Mag.Kurtosis : float
Kurtosis of gradient data. Value is -3 when all values are equal.
Gradient.Mag.HistEnergy : float
Energy of the gradient magnitude histogram of object pixels
Gradient.Mag.HistEnergy : float
Entropy of the gradient magnitude histogram of object pixels.
Gradient.Canny.Sum : float
Sum of canny filtered gradient data.
Gradient.Canny.Mean : float
Mean of canny filtered gradient data.
References
----------
.. [#] Daniel Zwillinger and Stephen Kokoska. "CRC standard probability
and statistics tables and formulae," Crc Press, 1999.
"""
import pandas as pd
import scipy.stats
from skimage.feature import canny
from skimage.measure import regionprops
# List of feature names
feature_list = [
'Gradient.Mag.Mean',
'Gradient.Mag.Std',
'Gradient.Mag.Skewness',
'Gradient.Mag.Kurtosis',
'Gradient.Mag.HistEntropy',
'Gradient.Mag.HistEnergy',
'Gradient.Canny.Sum',
'Gradient.Canny.Mean',
]
# compute object properties if not provided
if rprops is None:
rprops = regionprops(im_label)
# create pandas data frame containing the features for each object
numFeatures = len(feature_list)
numLabels = len(rprops)
fdata = pd.DataFrame(np.zeros((numLabels, numFeatures)),
columns=feature_list)
Gx, Gy = np.gradient(im_intensity)
diffG = np.sqrt(Gx**2 + Gy**2)
cannyG = canny(im_intensity)
for i in range(numLabels):
if rprops[i] is None:
continue
# get gradients of object pixels
pixelGradients = np.sort(
diffG[rprops[i].coords[:, 0], rprops[i].coords[:, 1]],
)
# compute mean
fdata.at[i, 'Gradient.Mag.Mean'] = np.mean(pixelGradients)
# compute standard deviation
fdata.at[i, 'Gradient.Mag.Std'] = np.std(pixelGradients)
# compute skewness
fdata.at[i, 'Gradient.Mag.Skewness'] = scipy.stats.skew(pixelGradients)
# compute kurtosis
fdata.at[i, 'Gradient.Mag.Kurtosis'] = \
scipy.stats.kurtosis(pixelGradients)
# compute intensity histogram
hist, bins = np.histogram(pixelGradients, bins=num_hist_bins)
prob = hist / np.sum(hist, dtype=np.float32)
# compute entropy
fdata.at[i, 'Gradient.Mag.HistEntropy'] = scipy.stats.entropy(prob)
# compute energy
fdata.at[i, 'Gradient.Mag.HistEnergy'] = np.sum(prob**2)
bw_canny = cannyG[rprops[i].coords[:, 0], rprops[i].coords[:, 1]]
canny_sum = np.sum(bw_canny).astype('float')
fdata.at[i, 'Gradient.Canny.Sum'] = canny_sum
fdata.at[i, 'Gradient.Canny.Mean'] = canny_sum / len(pixelGradients)
return fdata