Symmetry detection in images in Python

Question

I'm working with an algorithm to detect symmetries in an irregular object, I'm using only Python with nunmpy and matplotlib, no possibility to use OpenCv, after I rotate my object along the principal axes, I get something like that rotated image

Then I wrote an algorithm which evaluate horizontal and vertical symmetries and make an average of the two:

def symmetry(self, mat):

mat is the matrix of coordinates of the points of my binary image

    coords = np.around(mat) #coordinates are rounded 
    i, j = coords.shape
    x, y = coords

    horizontal = 0
    vertical = 0



    for k in range(j):    
        for m in range(k, j):
            if(x[k] == x[m] and y[k] == -y[m]):
                horizontal += 1            
            if((x[k] == -x[m] and y[k] == y[m]):
                vertical += 1

    symmetry = (horizontal + vertical)/ j


    print('The symmetry index is:')
    print(symmetry)

    return

Since I wanted to evaluate the symmetry counting if each pixels has a correspondent with respect to the horizontal and the vertical axis I rounded the coordinates to integers, the problem is that if I test my algorithm with a cirlce, from which I expect perfect symmetry, I get about 0.5, the maximum value should be 1. Can somebody suggest a better metrics for evaluating the symmeytry in this situation or improve my code, In your opininon my solution should work?