In the hereafter mentioned chapter, section 4, there are 5 distance measures used in comparing vectors associated with pixel values along with a method to test its suitability for your application. I hope this will be valuable for you.
you can download the chapter from In-tech website. The chapter's title is:
I think that if you have data (measurements) with related variables, or you want to compare the similarity between your data, you could perform a clustering analysis.
The question is very general as depending on the type of application and the variability between images to be compared, the techniques could be totally different. I suggest you take a look at this article first and see different applications.
E. Chalom, E. Asa, and E. Biton, “Measuring image similarity: an overview of some useful applications,” IEEE Instrumentation Measurement Magazine, vol. 16, no. 1, pp. 24–28, Feb. 2013.