  We present \emph{telescoping} recursive representations for both continuous
and discrete indexed noncausal Gauss-Markov random fields. Our recursions start
at the boundary (a hypersurface in $\R^d$, $d \ge 1$) and telescope inwards.
For example, for images, the telescoping representation reduce recursions from
$d = 2$ to $d = 1$, i.e., to recursions on a single dimension. Under
appropriate conditions, the recursions for the random field are linear
stochastic differential/difference equations driven by white noise, for which
we derive recursive estimation algorithms, that extend standard algorithms,
like the Kalman-Bucy filter and the Rauch-Tung-Striebel smoother, to noncausal
Markov random fields.
