# How to normalize by the covariance matrix? [duplicate]

I am trying to understand an image processing research paper [1] that calls for normalizing a distance between an object's center point and the center of a cluster of points by the covariance matrix of the cluster.

Given

$m^f_c$ - center of cluster $c$ at frame $f$ (2 dimensional $x,y$ point)

$m^f_t$ - center of cluster $t$ at frame $f$ (2 dimensional $x,y$ point)

$\Psi_c$ - covariance of cluster c

For each object $t$, the distance to each cluster $c$ is calculated $D_{ct}=\frac{1}{f}\sum_f(m^f_c-m^f_t)(\Psi^f_c)^{-1}(m^f_c-m^f_t)^T$

The paper says "It is important to normalize the cluster-to-[object] distance by the covariance matrix of the cluster to handle the scale variation of objects"

What is meant by "normalize by the covariance matrix"? I understand normalization by a scalar, but by a covariance matrix is confusing me.

[1] Anjulan, A., & Canagarajah, N. (2009). A Unified Framework for Object Retrieval and Mining. IEEE Transactions on Circuits and Systems for Video Technology, 19(1), 63–76. doi:10.1109/TCSVT.2008.2005801