How to compute "EMD" for 2 numpy arrays i.e "histogram" using opencv?

Question

Since I'm new to opencv, I don't know how to use the cv.CalcEMD2 function with numpy arrays.
I have two arrays:

a=[1,2,3,4,5]  
b=[1,2,3,4]

How can I transfer numpy array to CVhistogram and from Cvhistogram to the function parameter signature?

I would like anyone who answers the question to explain any used opencv functions through the provided solution.

"EMD" == earth mover's distance.

Update:-
also ,It will be helpful if anyone can tell me how to set the cv.CalcEMD2 parameter i.e"signature" using numpy array!!

Note:-
* For those who may be interested in this question ,This answer needs more testing.

Answer 1

You have to define your arrays in terms of weights and coordinates. If you have two arrays a = [1,1,0,0,1] and b = [0,1,0,1] that represent one dimensional histograms, then the numpy arrays should look like this:

a = [[1 1]
     [1 2]
     [0 3]
     [0 4]
     [1 5]]

b = [[0 1]
     [1 2]
     [0 3]
     [1 4]]

Notice that the number of rows can be different. The number of columns should be the dimensions + 1. The first column contains the weights, and the second column contains the coordinates.

The next step is to convert your arrays to a CV_32FC1 Mat before you input the numpy array as a signature to the CalcEMD2 function. The code would look like this:

from cv2 import *
import numpy as np

# Initialize a and b numpy arrays with coordinates and weights
a = np.zeros((5,2))

for i in range(0,5):
    a[i][1] = i+1

a[0][0] = 1
a[1][0] = 1
a[2][0] = 0
a[3][0] = 0
a[4][0] = 1

b = np.zeros((4,2))

for i in range(0,4):
    b[i][1] = i+1

b[0][0] = 0
b[1][0] = 1
b[2][0] = 0
b[3][0] = 1    

# Convert from numpy array to CV_32FC1 Mat
a64 = cv.fromarray(a)
a32 = cv.CreateMat(a64.rows, a64.cols, cv.CV_32FC1)
cv.Convert(a64, a32)

b64 = cv.fromarray(b)
b32 = cv.CreateMat(b64.rows, b64.cols, cv.CV_32FC1)
cv.Convert(b64, b32)

# Calculate Earth Mover's
print cv.CalcEMD2(a32,b32,cv.CV_DIST_L2)

# Wait for key
cv.WaitKey(0)

Notice that the third parameter of CalcEMD2 is the Euclidean Distance CV_DIST_L2. Another option for the third parameter is the Manhattan Distance CV_DIST_L1.

I would also like to mention that I wrote the code to calculate the Earth Mover's distance of two 2D histograms in Python. You can find this code here.