In the frame of image matching, I try to compare two distributions in relying on Earth Mover Distance (EMD). What happens if I consider an image Img1, then I add a constant value to this Img1 to obtain an Image Img2 (just a little bit brighter). Then I compute the two distributions Distr1 and Distr2 of respectively img1 and Img2 (Dist2 is just shifted w.r. to Dist1). Then I compute EMD distance between Dist1 and Dist2.
Which output can we expect from EMD(Dist1; Dist2)? Is it reasonable to expect EMD=0? because the shape of the two distributions are rigorously similar?
Thank you for any feedback
Hi, if the distribution you are referring to is that of brightness, then the EMD will not be nil. The EMD is a metaphor for the work of moving dirt from a pile to fill a hole. So the distance between the pile and the hole is important.
You can refer to the original article by Rubner:
A Metric for Distributions with Applications to Image Databases, ICC '98
EMD will increase linearly with increments in the constant value you add to img1 to produce img2 (it is actually better than the behaviour you would obtain if you were comparing the distributions using histogram intersection. ).
Actually, EMD is 'robust' to changes in the shape of the distribution. For example if img2 is a partly occluded version of img1, the EMD between their respective distributions should not change drastically.
Hope this helps.
Thank you really much Cyril. Your confirmation is of great help. What is the alternative so? How to make EMD working in such situations? From your knowledge, is there any other distance metrics insensitive to that kind of constant shift? I am more particularly interested in comparing joint distributions.
I think mutual information between distributions is a good candidate. But unfortunately I don't have references handy for this.
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