Validate Blur Model¶
We must ensure that the estimated parameters are indeed a good fit for the measured data. This is done by comparing line profiles across the sharp edge between the measured radiograph and the predicted radiograph from the blur model. The output of the blur model given parameters of source blur, detector blur, and transmission function is computed using the function
pysaber.get_trans_fit(). The fit must be evaluated for every sharp-edge radiograph that is input topysaber.estimate_blur().Verify the agreement between the measured radiograph and the blur model prediction. Carefully zoom into the region containing the sharp edge and verify if the predicted blur matches with the blur in the measured radiograph. Also, verify the agreement between the measured radiograph values and blur model prediction in regions further away from the sharp edge. The predicted radiograph that is output by the blur model contains additional padding. Hence, it is necessary to account for this padding when comparing with the measured radiograph.
If the fit is not tight, consider reducing the value of the input argument
threshof the functionpysaber.estimate_blur()to obtain a better fit. Reducing the convergence threshold,thresh, can improve the agreement between the measured radiograph and the blur model prediction, but will inevitably result in longer run times. A good fit indicates that the blur model is able to accurately model the X-ray source and detector blurs.Example python scripts for line profile comparisons between the blur model prediction and measured radiograph are shown below. To obtain the data that is required to run this script, download and unzip the zip file at the link
data. To run the script as is within the current working directory, the files in the zip file must be placed within a folder calleddata.
import numpy as np
from PIL import Image #To read images in TIFF format
from pysaber import get_trans_fit #To get blurred radiograph as predicted by the blur model
import matplotlib.pyplot as plt #To display images
pix_wid = 0.675 #Width of each pixel in micrometers
#Read a horizontal edge radiograph for which accuracy of fit must be analyzed
rad = Image.open('data/horz_edge_25mm.tif') #Read radiograph
rad = np.asarray(rad) #Convert to numpy array
bright = Image.open('data/horz_bright.tif') #Read bright field
bright = np.asarray(bright) #Convert to numpy array
dark = Image.open('data/horz_dark.tif') #Read dark field
dark = np.asarray(dark) #Convert to numpy array
nrad = (rad-dark)/(bright-dark) #Normalize radiograph
sod = 24751.89 #Source to object distance (SOD) of radiograph
sdd = 71003.08 #Source to detector distance (SDD) of radiograph
#Parameters of X-ray source blur
src_params = {'source_FWHM_x_axis':2.69,
'source_FWHM_y_axis':3.01,
'norm_power':1.0,
'cutoff_FWHM_multiplier':10}
#Parameters of detector blur
det_params = {'detector_FWHM_1':1.85,
'detector_FWHM_2':126.5,
'detector_weight_1':0.916,
'norm_power':1.0,
'cutoff_FWHM_1_multiplier':10,
'cutoff_FWHM_2_multiplier':10}
#Transmission function parameters
trans_params = [0.015,0.98]
#Get the blurred radiograph as predicted by the blur model
pred_nrad,_ = get_trans_fit(nrad,sod,sdd-sod,pix_wid,src_params,det_params,trans_params,edge='straight',pad=[3,3])
#Show a line plot comparing the measured radiograph and the predicted blurred radiograph
sz = nrad.shape
coords = np.arange(-(sz[0]//2),sz[0]//2,1)*pix_wid
mid = (pred_nrad.shape[0]//2,pred_nrad.shape[1]//2)
plt.plot(coords,nrad[:,sz[1]//2])
#Due to padding, pred_nrad is three times the size of nrad in each dimension
#For proper alignment in the presence of padding, both nrad and pred_nrad are center aligned
#Center alignment is used since an equal amount of padding is applied at both ends of each axis
plt.plot(coords,pred_nrad[mid[0]-(sz[0]//2):mid[0]+(sz[0]//2),mid[1]])
plt.xlabel('micrometers')
plt.legend(['Measured','Prediction'])
plt.show()
import numpy as np
from PIL import Image #To read images in TIFF format
from pysaber import get_trans_fit #To get blurred radiograph as predicted by the blur model
import matplotlib.pyplot as plt #To display images
pix_wid = 0.675 #Width of each pixel in micrometers
#Read a vertical edge radiograph for which accuracy of fit must be analyzed
rad = Image.open('data/vert_edge_25mm.tif') #Read radiograph
rad = np.asarray(rad) #Convert to numpy array
bright = Image.open('data/vert_bright.tif') #Read bright field
bright = np.asarray(bright) #Convert to numpy array
dark = Image.open('data/vert_dark.tif') #Read dark field
dark = np.asarray(dark) #Convert to numpy array
nrad = (rad-dark)/(bright-dark) #Normalize radiograph
sod = 24753.05 #Source to object distance (SOD) of radiograph
sdd = 71010.86 #Source to detector distance (SDD) of radiograph
#Parameters of X-ray source blur
src_params = {'source_FWHM_x_axis':2.69,
'source_FWHM_y_axis':3.01,
'norm_power':1.0,
'cutoff_FWHM_multiplier':10}
#Parameters of detector blur
det_params = {'detector_FWHM_1':1.85,
'detector_FWHM_2':126.5,
'detector_weight_1':0.916,
'norm_power':1.0,
'cutoff_FWHM_1_multiplier':10,
'cutoff_FWHM_2_multiplier':10}
#Transmission function parameters
trans_params = [0.015,0.98]
#Get the blurred radiograph as predicted by the blur model
pred_nrad,_ = get_trans_fit(nrad,sod,sdd-sod,pix_wid,src_params,det_params,trans_params,edge='straight',pad=[3,3])
#Show a line plot comparing the measured radiograph and the predicted blurred radiograph
sz = nrad.shape
coords = np.arange(-(sz[1]//2),sz[1]//2,1)*pix_wid
mid = (pred_nrad.shape[0]//2,pred_nrad.shape[1]//2)
plt.plot(coords,nrad[sz[0]//2,:])
#Due to padding, pred_nrad is three times the size of nrad in each dimension
#For proper alignment in the presence of padding, both nrad and pred_nrad are center aligned
#Center alignment is used since an equal amount of padding is applied at both ends of each axis
plt.plot(coords,pred_nrad[mid[0],mid[1]-(sz[1]//2):mid[1]+(sz[1]//2)])
plt.xlabel('micrometers')
plt.legend(['Measured','Prediction'])
plt.show()