Hi, It's a great paper and I'm inspired a lot. But I am confused that why the bijection is unique when the sum of point displayment reaches the minimum value. I don't kown why the correspondence between input and targrt point clouds is unique, and I find it is not unique. Like the following picture, a cube, x1 x2 move to x1' x2' , there are midpoint of one line， a) x1 to x1' and x2 to x2' b) x1 to x2' and x2 to x1' are both the minimum. Maybe I do not understand the EMD, Thank you very much.
Hi, It's a great paper and I'm inspired a lot. But I am confused that why the bijection is unique when the sum of point displayment reaches the minimum value. I don't kown why the correspondence between input and targrt point clouds is unique, and I find it is not unique. Like the following picture, a cube, x1 x2 move to x1' x2' , there are midpoint of one line， a) x1 to x1' and x2 to x2' b) x1 to x2' and x2 to x1' are both the minimum. Maybe I do not understand the EMD, Thank you very much.