This post describes a few different methods to quantify how "close" two different 2D images/datasets are to each other.
We define a 2D datasets in this case to be:
z1(x,y) and z2(x,y)
This could be an image in a 2d plane or some other 2d dataset. Obviously, first just look at the images and now one would want to quantify their degree of identicalness.
1. Slope of M1 vs M2
Unzip the 2d array of image and plot them in the array (make sure to unzip the same way).
Check for:
(a) R2 should be close to 1
(b) The slope should be close to 1
(c) The offset should be close to 0
Make sure the errors are correctly defined for each of the three fits and they can be rather independent of each other.
2. Difference plot
Plot the difference of the two images on an image to find if there are any blind spots/something funny. If not, also unzip the 2d array and plot it as a series to look for weird outliers and check if each point is within the series. If yes, look and check them why is the difference so high.
3. Plot the ratio of unzipped 2d->1D arrays of the two measurements as a series. This should be as close to 1 as possible. Look for particular outlier and identify the reasons. If necessary, also make a box plot but don't just look for mean and SD!
CODE:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Jun 8 10:42:08 2018
@author: pranjal.bordia
"""
import pandas as pd
import seaborn as sns
import numpy as np
from scipy import stats
from scipy.optimize import curve_fit
def f(x, A, B): # this is your 'straight line' y=f(x)
return A*x + B
x = np.arange(0, 2, 0.1)
y = np.arange(0, 2 , 0.1)
xx, yy = np.meshgrid(x, y)
z1 = (xx**2 + yy**2) + 0.6*np.random.rand(20,20)
z2 = (xx**2 + yy**2) + 0.6*np.random.rand(20,20)
#### Metric one, Slope
z1array = z1.ravel()
z2array = z2.ravel()
def r2(x, y):
return stats.pearsonr(x, y)[0] ** 2
g = sns.jointplot(z1array, z2array, kind="reg", stat_func=r2,scatter_kws={'s':10},ci=95)
xlabel('Measurement 1')
ylabel('Measurement 2')
A,B = curve_fit(f, z1array, z2array)[0]
g.fig.text(0.15,0.65,' Slope = '+str(round(A,5))+'\nIntercept='+str(round(B,5)))
tight_layout()
savefig('M1M2Slope.png',dpi=600)
### Metric 2, Difference Plot
z3 = z2 - z1
figure()
sns.heatmap(z3,cmap='coolwarm',vmin=-2.6,vmax = 2.6)
xlabel('X')
xlabel('Y')
savefig('2DDiffPlot.png',dpi=300)
z3array = z3.ravel()
figure()
plot(z3array)
xlabel('Some point')
ylabel('Difference in two measurements')
savefig('2DDiffPlotSeries.png',dpi=300)
### Metric 2, Ratio Plot
z3ratio = array(z1array)/array(z2array)
figure()
plot(z3ratio,'o',ms=4)
xlabel('Some point')
ylabel('Ratio in two measurements')
savefig('2DRatioPlotSeries.png',dpi=300)
1. Slope of M1 vs M2
Unzip the 2d array of image and plot them in the array (make sure to unzip the same way).
Check for:
(a) R2 should be close to 1
(b) The slope should be close to 1
(c) The offset should be close to 0
Make sure the errors are correctly defined for each of the three fits and they can be rather independent of each other.
2. Difference plot
Plot the difference of the two images on an image to find if there are any blind spots/something funny. If not, also unzip the 2d array and plot it as a series to look for weird outliers and check if each point is within the series. If yes, look and check them why is the difference so high.
3. Plot the ratio of unzipped 2d->1D arrays of the two measurements as a series. This should be as close to 1 as possible. Look for particular outlier and identify the reasons. If necessary, also make a box plot but don't just look for mean and SD!
CODE:
#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Fri Jun 8 10:42:08 2018
@author: pranjal.bordia
"""
import pandas as pd
import seaborn as sns
import numpy as np
from scipy import stats
from scipy.optimize import curve_fit
def f(x, A, B): # this is your 'straight line' y=f(x)
return A*x + B
x = np.arange(0, 2, 0.1)
y = np.arange(0, 2 , 0.1)
xx, yy = np.meshgrid(x, y)
z1 = (xx**2 + yy**2) + 0.6*np.random.rand(20,20)
z2 = (xx**2 + yy**2) + 0.6*np.random.rand(20,20)
#### Metric one, Slope
z1array = z1.ravel()
z2array = z2.ravel()
def r2(x, y):
return stats.pearsonr(x, y)[0] ** 2
g = sns.jointplot(z1array, z2array, kind="reg", stat_func=r2,scatter_kws={'s':10},ci=95)
xlabel('Measurement 1')
ylabel('Measurement 2')
A,B = curve_fit(f, z1array, z2array)[0]
g.fig.text(0.15,0.65,' Slope = '+str(round(A,5))+'\nIntercept='+str(round(B,5)))
tight_layout()
savefig('M1M2Slope.png',dpi=600)
### Metric 2, Difference Plot
z3 = z2 - z1
figure()
sns.heatmap(z3,cmap='coolwarm',vmin=-2.6,vmax = 2.6)
xlabel('X')
xlabel('Y')
savefig('2DDiffPlot.png',dpi=300)
z3array = z3.ravel()
figure()
plot(z3array)
xlabel('Some point')
ylabel('Difference in two measurements')
savefig('2DDiffPlotSeries.png',dpi=300)
### Metric 2, Ratio Plot
z3ratio = array(z1array)/array(z2array)
figure()
plot(z3ratio,'o',ms=4)
xlabel('Some point')
ylabel('Ratio in two measurements')
savefig('2DRatioPlotSeries.png',dpi=300)
Comments
Post a Comment