  We develop the information geometry of scaled Gaussian distributions for
which the covariance matrix exhibits a Kronecker product structure. This model
and its geometry are then used to propose an online change detection (CD)
algorithm for multivariate image times series (MITS). The proposed approach
relies mainly on the online estimation of the structured covariance matrix
under the null hypothesis, which is performed through a recursive (natural)
Riemannian gradient descent. This approach exhibits a practical interest
compared to the corresponding offline version, as its computational cost
remains constant for each new image added in the time series. Simulations show
that the proposed recursive estimators reach the Intrinsic Cram\'er-Rao bound.
The interest of the proposed online CD approach is demonstrated on both
simulated and real data.
