Similarity between two raster maps

Question

Having two raster maps as the examples below:

We are interested in evaluating their similarities. As shown, they are not fully overlapping. We guess one way is to clip small one area from the bigger one, therefore there will be two same size raster maps, e.g., arrays. So we may use pixel-wise correlation to find out how similar they are.

The existing issues/difficulties are:
1) The resolution of the two raster maps are not the same. So even for the above idea there is a problem of point-wise proceeding.

We wonder to know:

1) a better way to find their similarities as human-eye (+brain) does, that is, there is absolutely high similarity in the trend of spatial variation in the two maps.
2) if pixel-wise correlation is OK for our purpose?

EDIT
Think this way: image one as a matrix of size mxn and image two as a matrix of size pxq. A bounding box for matrix one is {x1,y1,x2,y2} which mean regardless to image one resolution its dual matrix (one) must fit the bounding box perfectly. The same scenario for image two and so matrix two. Note that their bounding boxes are also different. Thus this first stage is to stretch matrices to fit their dual bounding boxes. How to do this job while not using any image manipulation software? We prefer to do it using Python + Numpy (Scipy). The second stage is to resample each stretched matrix to a unique dimensions. This makes it possible to do element-wise operations on both matrices. How to do this? We are mostly concerned in the algorithms. You may notice that since the final comparison will be element-wise thus both the above stages must be properly chosen to avoid any distortion (change in the data). We are looking for some algorithms to handle all the above to result something that visually we see in terms of relationships in the two images (matrices).

Answer 1

You can solve this using R. The below code produces a scatter plot with linear regression and a Pearson correlation value. Because you're solving in R you have access to a massive range of statistical tools.

install.packages(raster)
library(raster)

# read rasters
r1 = raster("/dir/dir/file1.tif")
r2 = raster("/dir/dir/file2.tif")
# Resample r2 to r1
r2.samp = round(resample(r2, r1, "bilinear"))

# plot results
# Points
plot(getValues(r2.samp) ~ getValues(r1))
# Linear regression
abline(lm(getValues(r2.samp) ~ getValues(r1)))
# (Pearson) Correlation
legend("topleft", legend=paste("Correlation =", round(cor(getValues(r1),
getValues(r2.samp), use="complete.obs"), 2)))

Answer 2

This is a fairly common problem so probably of great interest to many people. I can tell you how I would go about solving it using Whitebox GAT (http://code.google.com/p/whitebox-geospatial-analysis-tools/downloads/list) although I'm sure that there would be an equivalent workflow in either QGIS or Arc*.

1. Use the 'New Raster From Base' tool to create a new blank raster the same dimensions (rows and columns) and extent as the smaller of the two grids.

2. Use the 'Resample' tool to resample the data from the larger of the two grids into your newly created grid. You can use nearest neighbour, bilinear interpolation or cubic convolution as the resampling method. I'd probably recommend bilinear interp for your grid.

3. Use either the 'Image Correlation' or perhaps the 'Image Regression' tool to discern the relation (and strength of association) between the two grids. This is fairly commonly used in the field of remote sensing to determine the amount of redundancy among various bands of multispectral imagery. There is also a tool in Whitebox called 'Compare Images for Significant Differences' which performs a paired sample t-test on the two grids. It can also be set up to take a random sample from the images in order to get around the problem that statistically significant differences can often be found even when there is no meaningful or substantive difference when the sample size is very large (as is often the case when you're dealing with images).

Answer 3

I would suggest clipping the same AOI and use ImageMagick which is opensource using maybe a fuzz tolerance.