and 
are
two points from the same distribution which has covariance matrix 
, then
the Mahalanobis distance is given by
The Mahalanobis distance is the same as the Euclidean distance if the covariance matrix is the identity matrix.
Bob Fisher
The distance between two N dimensional points scaled by the statistical
variation in each component of the point. For example, if and are
two points from the same distribution which has covariance matrix , then
the Mahalanobis distance is given by
The Mahalanobis distance is the same as the Euclidean distance if the covariance matrix
is the identity matrix.
A common usage in computer vision systems is for comparing feature vectors whose elements are quantities having different ranges and amounts of variation, such as a 2-vector recording the properties of area and perimeter.