statistical method for spatial correlation between images I am working on analyzing a data set and I was wondering what would be the most statistically valid method of demonstrating that there is a strong spatial correlation between images.  
I have a data set with about 50 pairs of images of cancerous tissue samples.  The first image in each pair shows the locations of gold nanoparticles, and the second image shows the locations of the blood vessels in the same tissue sample.  By looking at the images it is easy to see that the locations of the nanoparticles match up with the blood vessels, but I would like to prove this statistically in the paper.  This is an important point because it demonstrates that the nanoparticles bind specifically to the cancerous areas instead of the normal tissue.
I have been looking at different statistics such as a simple linear correlation or something like the answer to this question: Valid method to analyze spatial correlations in images? However, I haven't found anything that would work well for correlation between images.  

Edit from Ladislav Nado:
I fabricated two pictures from web...the size and resolution is equal.


 A: This is a problem that has been analyzed most extensively in the field of astronomy or cosmology with things like galaxy spatial correlation functions. The short answer is that you probably want to compute a 2D correlation function which can be computed efficiently with the Fast Fourier Transform (if needed). You might also want to Google terms like the Landy-Szalay estimator which allows treatment of masked-out areas and boundaries.   
It sounds like you also want to compute uncertainties or confidence intervals. This is a little trickier. In astronomy it has been estimated with Jack-knife techniques though I think it still lacks a rigorous foundation. Using Monte Carlo techniques is often useful for this as well but is also not entirely on a rigorous foundation either. 
A: You could manually trace the centerline or the walls of the blood vessels (or use machine learning to fill those areas. Then you could build a buffer fence around that area. As a second step, you could identify the particles on the image (either manually or by machine learning). Then you could calculate the statistics related to then number of nanoparticles inside the filled area of the buffer fence vs outside of it.
With fifty pairs of images, it might be faster and more accurate to draw the buffer fences and measure the number of particles in and out, manually.
A: Please see the R package SpatialPack. There you will find three different statistical approaches to address this problem
