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normalized euclidean Distance between 2 points in an image

Hello forum,

When attempting to find the distance stated above, would it be better to use the bhattacharrya distance or the mahalanobis distance ?

The mahalanobis function requires an input of the covariance matrix. Based on wikipedia it says the matrix should be diagonal for the function to be equal to the normalized euclidean distance. I am not sure how to get that diagonal covariance matrix from 2 points in an image.