What algorithm should be used for finding spatial correlation between images?

Question

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 points in different images.

My data set has 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 well 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 more sophisticated like the Moran's I statistic. However, I haven't found anything that would work well for correlation between images.

Answer 1

I think the correlation might work for you. For a gray image, you can vectorize them and use xcorr or corrcoef functions to get the correlations. For RGB image, if you would like all the details from three channels, you may need to work on the MuPAD Notebook Interface, in which plot::Raster translates the RGB values into a 2D mesh of rectangles. Then you can implement the correlations.

Another possible quantification of the GNP binding is to apply blood vessel segmentation, and use the result as a mask, then calculate the recall/precision (false positive vs false negative) as a indication of the GNP ability to bind blood vessels.

Answer 2

I would measure the distance between each gold particle and the nearest blood vessel. Average these minimal distances across all particles - this is your statistic. This can be done for all 50 pairs, and then the 50 numbers can be averaged again. The resulting scalar represents the average distance of a gold particle from the nearest blood-vessel across your entire data.

How do you know if it's significant? In order to generate the null distribution, shuffle the images so each gold particle image will be paired with a randomly chosen blood vessels image. Measure the statistic again. Repeat this ~10000 times. The percent of iterations with equal or lesser mean distance than the actual, unshuffled distance, is your p-value (include the original permutation in the sample to ensure correct coverage probability).