Add new GLCM properties to graycoprops (scikit-image#7375)

* Add mean, variance, standard deviation, and entropy
* Explain that reference values where obtained by hand

Co-authored-by: Marianne Corvellec <[email protected]>

skimage/feature/tests/test_texture.py

@@ -176,6 +176,42 @@ def test_correlation(self):
         np.testing.assert_almost_equal(energy[0, 0], 0.71953255)
         np.testing.assert_almost_equal(energy[1, 0], 0.41176470)
 
+    def test_mean(self):
+        result = graycomatrix(
+            self.image, [1], [0, np.pi / 2], 4, normed=True, symmetric=True
+        )
+        mean = graycoprops(result, 'mean')[0, 0]
+
+        # Reference value was calculated by hand and is close to original source if precision 3 is used.
+        np.testing.assert_almost_equal(mean, 1.29166667)
+
+    def test_variance(self):
+        result = graycomatrix(
+            self.image, [1], [0, np.pi / 2], 4, normed=True, symmetric=True
+        )
+        variance = graycoprops(result, 'variance')[0, 0]
+
+        # Reference value was calculated by hand and is close to original source if precision 3 is used.
+        np.testing.assert_almost_equal(variance, 1.03993055)
+
+    def test_std(self):
+        result = graycomatrix(
+            self.image, [1], [0, np.pi / 2], 4, normed=True, symmetric=True
+        )
+        std = graycoprops(result, 'std')[0, 0]
+
+        # Reference value was calculated by hand and is close to original source if precision 3 is used.
+        np.testing.assert_almost_equal(std, 1.01976985)
+
+    def test_entropy(self):
+        result = graycomatrix(
+            self.image, [1], [0, np.pi / 2], 4, normed=True, symmetric=True
+        )
+        entropy = graycoprops(result, 'entropy')[0, 0]
+
+        # Reference value was calculated by hand and is close to original source if precision 3 is used.
+        np.testing.assert_almost_equal(entropy, 2.09472904)
+
     def test_uniform_properties(self):
         im = np.ones((4, 4), dtype=np.uint8)
         result = graycomatrix(
@@ -188,6 +224,10 @@ def test_uniform_properties(self):
             'energy',
             'correlation',
             'ASM',
+            'mean',
+            'variance',
+            'std',
+            'entropy',
         ]:
             graycoprops(result, prop)
 

skimage/feature/texture.py

@@ -180,6 +180,10 @@ def graycoprops(P, prop='contrast'):
     - 'correlation':
         .. math:: \\sum_{i,j=0}^{levels-1} P_{i,j}\\left[\\frac{(i-\\mu_i) \\
                   (j-\\mu_j)}{\\sqrt{(\\sigma_i^2)(\\sigma_j^2)}}\\right]
+    - 'mean': :math:`\\sum_{i=0}^{levels-1} i*P_{i}`
+    - 'variance': :math:`\\sum_{i=0}^{levels-1} P_{i}*(i-mean)^2`
+    - 'std': :math:`\\sqrt{variance}`
+    - 'entropy': :math:`\\sum_{i,j=0}^{levels-1} -P_{i,j}*log(P_{i,j})`
 
     Each GLCM is normalized to have a sum of 1 before the computation of
     texture properties.
@@ -196,7 +200,7 @@ def graycoprops(P, prop='contrast'):
         occurs at a distance d and at an angle theta from
         gray-level i.
     prop : {'contrast', 'dissimilarity', 'homogeneity', 'energy', \
-            'correlation', 'ASM'}, optional
+            'correlation', 'ASM', 'mean', 'variance', 'std', 'entropy'}, optional
         The property of the GLCM to compute. The default is 'contrast'.
 
     Returns
@@ -229,6 +233,12 @@ def graycoprops(P, prop='contrast'):
            [1.25      , 2.75      ]])
 
     """
+
+    def glcm_mean():
+        I = np.arange(num_level).reshape((num_level, 1, 1, 1))
+        mean = np.sum(I * P, axis=(0, 1))
+        return I, mean
+
     check_nD(P, 4, 'P')
 
     (num_level, num_level2, num_dist, num_angle) = P.shape
@@ -253,7 +263,7 @@ def graycoprops(P, prop='contrast'):
         weights = np.abs(I - J)
     elif prop == 'homogeneity':
         weights = 1.0 / (1.0 + (I - J) ** 2)
-    elif prop in ['ASM', 'energy', 'correlation']:
+    elif prop in ['ASM', 'energy', 'correlation', 'entropy', 'variance', 'mean', 'std']:
         pass
     else:
         raise ValueError(f'{prop} is an invalid property')
@@ -264,6 +274,19 @@ def graycoprops(P, prop='contrast'):
         results = np.sqrt(asm)
     elif prop == 'ASM':
         results = np.sum(P**2, axis=(0, 1))
+    elif prop == 'mean':
+        _, results = glcm_mean()
+    elif prop == 'variance':
+        I, mean = glcm_mean()
+        results = np.sum(P * ((I - mean) ** 2), axis=(0, 1))
+    elif prop == 'std':
+        I, mean = glcm_mean()
+        var = np.sum(P * ((I - mean) ** 2), axis=(0, 1))
+        results = np.sqrt(var)
+    elif prop == 'entropy':
+        ln = -np.log(P, where=(P != 0), out=np.zeros_like(P))
+        results = np.sum(P * ln, axis=(0, 1))
+
     elif prop == 'correlation':
         results = np.zeros((num_dist, num_angle), dtype=np.float64)
         I = np.array(range(num_level)).reshape((num_level, 1, 1, 1))