The method for exploiting stochastic smoothing techniques to develop dynamical recursive algorithms for the deterministic problem of d interpolation (optimal curve fitting) is shown. A reproducing kernel Hilbert space approach is used to develop an explicit correspondence between spline interpolation and linear least-squares smoothing of a particular zero-mean random process. This random process is shown to be the output of a white-noise-driven dynamical system whose parameters and initial conditions are fixed by the functional form chosen for the spline. A recursive algorithm is then derived for this (nonstandard) smoothing problem, and thus also for the original spline interpolation problem.

It is shown how certain innovations decompositions can be used to obtain aa alternative derivation of some new estimating algorithms, based on Chandrasekhar-type equation. Such equations were originally obtained in radiative-transfer theory by using some invariance principles due to Ambartsumian and Chandrasekhar. Stationary processes have a natural shift invariance, but we show here how state-space descriptions can be used to bring out such invariances for nonstationary processes generated as the response to white noise of constant-parameter state-space models.

In this paper the problem of numerical encoding of pictures consisting of regions of differing contrast is discussed. For this purpose we define the containment code, a special case of the more general property code presented in [1]. The containment code leads in a natural way to procedures for following the boundaries of the regions of the picture. This permits a compression of data into a linear array that can be stored for later processing or for picture reconstruction. The boundary following algorithms presented lend themselves well to hardware implementation as can be seen from an explicit sequential machine description. Related codes such as the boundary index code and the directional code are obtained from the containment code. Procedures are described for extracting various topological features such as curve length, chord length, area, and moments.