Plotting two different image histograms as a single 2D histogram plot

Question

I'm looking to plot the histogram of one uint16 image on the x axis and the histogram of another uint16 image on the y axis, such that I get a colormap of the relationship between them as a 2D plot.

I have tried to form two seperate histograms and then construct the 2D array in a loop however this is failing.

first = np.histogram(img1, bins = 1000)
first = first[0]


second = np.histogram(img2, bins = 1000)
second = second[0]


empty_array = np.zeros((1000,1000), dtype = np.float64)

for i in range(1000):
    for j in range(1000):
        empty_array[i,j] = first[j] + second[1000-j]

Answer 1

If you're trying to study the histogram of two variables and how they relate to each other in a single function, consider reading about multi-variate normal distributions. This would apply to studying distributions of pixels in a image for sure. https://juanitorduz.github.io/multivariate_normal/

It looks like this is what you were trying to do?:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns; sns.set(color_codes=True)
sns.set_context("notebook")
sns.set_style("darkgrid")


# %% Construct normal distribution data
n = 100
hist1 = np.random.normal(0,1,n)
hist2 = np.random.normal(0,1,n)

# %% Plot distributions on their own axis
sns.jointplot(x=hist1, y=hist2, kind="kde", space=0)

A different process than the KDE plot that actually finds the multi-variate PDF that defines your data then plots the PDF. This time hist2 has a different distribution than hist1 which makes the spread on the contour plot different:

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import seaborn as sns; sns.set(color_codes=True)
sns.set_context("notebook")
sns.set_style("darkgrid")
from scipy.stats import multivariate_normal as mvn

# %% Create test data for multivariate PDF
n = 1000
hist1 = np.random.normal(0,1,n)
hist2 = np.random.normal(0,2,n)

# %% Calculate mean and covariance of data
mean = [hist1.mean(), hist2.mean()]
cov_mat = np.cov( np.array([hist1, hist2]) )

# %% Create multivariate function with calculated means and covariance
mv_norm_f = mvn(mean=mean, cov=cov_mat)

# %% Setup ranges of variables for PDF function
range = np.linspace(-1,1,n)
x, y = np.meshgrid(range, range, indexing='xy')
xy = np.empty(x.shape + (2,))
xy[:, :, 0] = x
xy[:, :, 1] = y
print(x.shape)
print(xy.shape)

# %% Call PDF function on ranges of variables
z = mv_norm_f.pdf( xy )

# %% Shaded contour plot the PDF
plt.figure()

plt.contourf(x, y, z)

plt.xlabel("X")
plt.ylabel("Y")
plt.colorbar()
plt.grid('on')
plt.show()

Answer 2

This is a solution using seaborn, as already suggested by @kilozulu. I would not use data that is already binned to generate this plot, because you are losing the association of data points between the two images. Rather, feed in the pixel intentities directly:

import seaborn as sns
import numpy as np
import matplotlib.pyplot as plt

#dummy images
img1 = np.random.normal(0,10,(100,100))
img2 = np.random.normal(0,10,(100,100))

# make jointplot with linearised images:
sns.jointplot(img1.ravel(), img2.ravel(), kind='kde')