def fsim(org_img: np.ndarray, pred_img: np.ndarray):
"""
Feature-based similarity index, based on phase congruency (PC) and image gradient magnitude (GM)
There are different ways to implement PC, the authors of the original FSIM paper use the method
defined by Kovesi (1999). The Python phasepack project fortunately provides an implementation
of the approach.
There are also alternatives to implement GM, the FSIM authors suggest to use the Scharr
operation which is implemented in OpenCV.
"""
_assert_image_shapes_equal(org_img, pred_img, "FSIM")
T1 = 0.85 # a constant based on the dynamic range PC
T2 = 160 # a constant based on the dynamic range GM
alpha = beta = 1 # parameters used to adjust the relative importance of PC and GM features
fsim_list = []
for i in range(org_img.shape[2]):
# Calculate the PC for original and predicted images
pc1_2dim = pc(org_img[:, :, i],
nscale=4,
minWaveLength=6,
mult=2,
sigmaOnf=0.5978)
pc2_2dim = pc(pred_img[:, :, i],
nscale=4,
minWaveLength=6,
mult=2,
sigmaOnf=0.5978)
# pc1_2dim and pc2_2dim are tuples with the length 7, we only need the 4th element which is the PC.
# The PC itself is a list with the size of 6 (number of orientation). Therefore, we need to
# calculate the sum of all these 6 arrays.
pc1_2dim_sum = np.zeros((org_img.shape[0], org_img.shape[1]),
dtype=np.float64)
pc2_2dim_sum = np.zeros((pred_img.shape[0], pred_img.shape[1]),
dtype=np.float64)
for orientation in range(6):
pc1_2dim_sum += pc1_2dim[4][orientation]
pc2_2dim_sum += pc2_2dim[4][orientation]
# Calculate GM for original and predicted images based on Scharr operator
gm1 = _gradient_magnitude(org_img[:, :, i], cv2.CV_16U)
gm2 = _gradient_magnitude(pred_img[:, :, i], cv2.CV_16U)
# Calculate similarity measure for PC1 and PC2
S_pc = _similarity_measure(pc1_2dim_sum, pc2_2dim_sum, T1)
# Calculate similarity measure for GM1 and GM2
S_g = _similarity_measure(gm1, gm2, T2)
S_l = (S_pc**alpha) * (S_g**beta)
numerator = np.sum(S_l * np.maximum(pc1_2dim_sum, pc2_2dim_sum))
denominator = np.sum(np.maximum(pc1_2dim_sum, pc2_2dim_sum))
fsim_list.append(numerator / denominator)
return np.mean(fsim_list)
def fsim_metric(org_img: np.ndarray, pred_img: np.ndarray, T1=0.85, T2=160) -> float: """ Feature-based similarity index, based on phase congruency (PC) and image gradient magnitude (GM) There are different ways to implement PC, the authors of the original FSIM paper use the method defined by Kovesi (1999). The Python phasepack project fortunately provides an implementation of the approach. There are also alternatives to implement GM, the FSIM authors suggest to use the Scharr operation which is implemented in OpenCV. Note that FSIM is defined in the original papers for grayscale as well as for RGB images. Our use cases are mostly multi-band images e.g. RGB + NIR. To accommodate for this fact, we compute FSIM for each individual band and then take the average. Note also that T1 and T2 are constants depending on the dynamic range of PC/GM values. In theory this parameters would benefit from fine-tuning based on the used data, we use the values found in the original paper as defaults. Args: org_img -- numpy array containing the original image pred_img -- predicted image T1 -- constant based on the dynamic range of PC values T2 -- constant based on the dynamic range of GM values """ #_assert_image_shapes_equal(org_img, pred_img, "FSIM") alpha = beta = 1 # parameters used to adjust the relative importance of PC and GM features fsim_list = [] for i in range(org_img.shape[2]): # Calculate the PC for original and predicted images pc1_2dim = pc(org_img[:, :, i], nscale=4, minWaveLength=6, mult=2, sigmaOnf=0.5978) pc2_2dim = pc(pred_img[:, :, i], nscale=4, minWaveLength=6, mult=2, sigmaOnf=0.5978) # pc1_2dim and pc2_2dim are tuples with the length 7, we only need the 4th element which is the PC. # The PC itself is a list with the size of 6 (number of orientation). Therefore, we need to # calculate the sum of all these 6 arrays. pc1_2dim_sum = np.zeros((org_img.shape[0], org_img.shape[1]), dtype=np.float64) pc2_2dim_sum = np.zeros((pred_img.shape[0], pred_img.shape[1]), dtype=np.float64) for orientation in range(6): pc1_2dim_sum += pc1_2dim[4][orientation] pc2_2dim_sum += pc2_2dim[4][orientation] # Calculate GM for original and predicted images based on Scharr operator gm1 = _gradient_magnitude(org_img[:, :, i], cv2.CV_16U) gm2 = _gradient_magnitude(pred_img[:, :, i], cv2.CV_16U) # Calculate similarity measure for PC1 and PC2 S_pc = _similarity_measure(pc1_2dim_sum, pc2_2dim_sum, T1) # Calculate similarity measure for GM1 and GM2 S_g = _similarity_measure(gm1, gm2, T2) S_l = (S_pc ** alpha) * (S_g ** beta) numerator = np.sum(S_l * np.maximum(pc1_2dim_sum, pc2_2dim_sum)) denominator = np.sum(np.maximum(pc1_2dim_sum, pc2_2dim_sum)) fsim_list.append(numerator / denominator) return np.mean(fsim_list)