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- W1680923786 abstract "Now the Gibbs estimators are used to solve many problems in computer vision, optimal control, Bayesian statistics etc. Their determination is equivalent to minimization of corresponding energy functions. Therefore, the real use of the estimators is restricted by opportunity to compute or evaluate satisfactory values of the energy functions. New combinatorial techniques that have been developed for the last years allowed efficient employment of high dimensional Ising models with Boolean and rational valued variables. In addition, graph cut methods were proposed to minimize energy functions U = P gµ(xµ)+ P gµ,�(xµ, x�)+ P gµ,�,�(xµ, x�, x�) of Boolean variables xµ and U = P µ h(iµ)+ P µ,� g(|iµ −j�|) of integer variables iµ with submodular functions g. In the paper energy functions that often occur in applications (for instance, in estimating of images) are considered. They are suppose to be depended on variables taking values in totally ordered finite sets (finite sets of arbitrary numbers are among them). The representation of functions by Boolean polynomials are described. Fast methods of minimization of submodular Boolean polynomials that correspond to the energy functions are developed. For that the Modified algorithm of minimization of submodular functions (MSFM) is proposed. Also the minimum graph cut technique is presented for submodular Boolean polynomials that satisfy some additional condition. Among such polynomials are, for instance, those with all coefficients before nonlinear monomials negative as well as submodular Boolean polynomials, which have all coefficients before monomials of order more than two positive. Mathematics Subject Classification 2000: 90C27, 62N, 62H, 68W" @default.
- W1680923786 created "2016-06-24" @default.
- W1680923786 creator A5062069620 @default.
- W1680923786 date "2003-04-03" @default.
- W1680923786 modified "2023-09-27" @default.
- W1680923786 title "Efficient Determination of Gibbs Estimators with Submodular Energy Functions" @default.
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