heatmapimage processingmachine learningpythonsimilarities
I have two images/heatmaps (2d matrix) of identical size. I need to statistically compare the similarity between the two. With 'similarity', I mean that high and low values of one image appear in similar areas in the other image.
Does anyone have an idea on how to do this? (I am using Python.)
Most simplest way how to solve this in two images is extract the values from both rasters and do correlation. I am not sure if this solution will fit to your spacific case. In what "format" do you have the images? (greyscale, RGB, size, resolution...). Please give more specific details.
Two rasters in R for demonstration:
Values for picture A:
x <- c(1.0,1.0,1.0,1.0,0.5,0.5,0.0,0.0,0.5,0.5,
2.0,2.0,1.5,1.5,1.0,1.0,0.5,1.0,1.0,1.0,
2.5,2.0,2.0,2.0,2.0,1.0,1.0,1.5,2.0,2.0,
2.5,3.0,3.0,3.0,2.5,2.0,2.0,2.0,2.5,2.5,
2.5,3.5,4.0,3.5,2.5,2.0,2.5,3.0,3.0,3.5,
2.5,3.5,3.5,2.5,2.0,2.5,3.0,3.5,4.0,3.5,
2.5,3.5,3.5,3.0,3.5,4.0,4.0,4.0,3.5,2.5,
2.5,3.5,4.0,4.0,3.5,3.5,3.0,3.0,2.5,2.0,
2.5,3.5,3.5,3.0,2.5,2.5,2.0,2.0,2.0,1.5,
2.0,3.0,2.5,2.0,2.0,1.5,1.5,1.5,1.0,1.0)
Values for picture B:
y <- c(rep(1, times = 10),
rep(2, times = 6), 1, rep(2, times = 3),
rep(2, times = 10),
rep(3, times = 4), rep(2, times = 4), 3,3,
3,4,4,3,2,rep(3, times = 4), 4,
3,4,rep(3, times = 5), rep(4, times = 3),
3,4,3,3,3,4,4,4,3,3,
3, rep(4, times = 4), rep(3, times=4), 2,
3,3,4,3,3,3,rep(2, times = 4),
2,3,3,3,rep(2, times = 6))
Creation of arrays -> conversion of arrays into rasters
x_array<-array(x, dim=c(10,10))
y_array<-array(y, dim=c(10,10))
x_raster<-raster(x_array)
y_raster<-raster(y_array)
Setting color palette and plotting...
colors_x <- c("#fff7f3","#fde0dd","#fcc5c0","#fa9fb5","#f768a1","#dd3497",
"#ae017e","#7a0177","#49006a")
colors_y <- c("#fff7f3","#fcc5c0","#f768a1","#ae017e")
par(mfrow=c(1,2))
plot(x_raster, col = colors_x)
plot(y_raster, col = colors_y)
...and here is the correlation
cor(x,y)
Pearson's product-moment correlation
data: x and y
t = 21.7031, df = 98, p-value < 2.2e-16
alternative hypothesis: true correlation is not equal to 0
95 percent confidence interval:
0.8686333 0.9385211
sample estimates:
cor
0.9098219
Maybe there is more specialized solution to this but I think that this solution is pretty robust, simple and straightforward.
Link worth of interest: (for ImageJ)
http://imagej.nih.gov/ij/plugins/intracell/index.html
Ya, pretty much agree with everyone here. The first thing you're going to want to do is transform to a perceptually uniform color space; for me, either HSL or LAB have worked the best, depending on the application.
From there, creating a color histogram for each image and comparing the histograms is probably the best way to go. Here's an interesting post on different methods for doing this: http://www.pyimagesearch.com/2014/07/14/3-ways-compare-histograms-using-opencv-python/
Best Answer
You are comparing distributions over a two-dimensional grid. A very common way to do this is the Earth mover's distance, also known as the Wasserstein metric. (You may need to normalize your images first.)
In looking for an implementation, you need to make sure it works with two dimensional data - many are restricted to one dimensional histograms. However, there seem to be multiple Python implementations you could use.