Random fields estimation theory

Estimation of Random Fields

Let u(x) = s(x) + n(x) , where s(x) and n(x) are random fields, s(x) is useful signal, n(x) is noise. Assume that s(x) = n(x) = 0 , where the bar stands for mean value. Suppose that the covariance functions R(x, y) := u * (x)u(y) and f (x, y) := u * (x)s(y) are known, where the asterisk stands for complex conjugate. Assume that u(x) is observed in a bounded domain D ⊂ R r of the Euclidean space...

Integral Operators Basic in Random Fields Estimation Theory

1 2 The paper deals with the basic integral equation of random field estimation theory by the criterion of minimum of variance of the error estimate. This integral equation is of the first kind. The corresponding integral operator over a bounded domain Ω in Rn is weakly singular. This operator is an isomorphism between appropriate Sobolev spaces. This is proved by a reduction of the integral eq...

Random Fields Theory

Efficient Parallel Estimation for Markov Random Fields

We present a new , deterministic, distributed MAPes­ timation algorithm for Markov Random Fields called Local Highest Confidence First (Local HCF). The al­ gorithm has been applied to segmentation problems in computer vision and its performance compared with stochastic algorithms. The experiments show that Local HCF finds better estimates than stochas­ tic algorithms with much less computation.

Consistent Change Estimation in 2D Random Fields