Can a Training Image Be a Substitute for a Random Field Model?

International audienceIn most multiple-point simulation algorithms, all statistical features areprovided by one or several training images (TI) that serve as a substitute for a ran-dom field model. However, because in practice the TI is always of finite size, thestochastic nature of multiple-point simulation is questionable. This issue is addressedby considering the case of a sequential simulation algorithm applied to a binary TIthat is a genuine realization of an underlying random field. At each step, the algo-rithm uses templates containing the current target point as well as all previously sim-ulated points. The simulation is validated by checking that all statistical features ofthe random field (supported by the simulation domain) are retrieved as an averageover a large number of outcomes. The results are as follows. It is demonstrated thatmultiple-point simulation performs well whenever the TI is a complete (infinitelylarge) realization of a stationary, ergodic random field. As soon as the TI is restrictedto a limited domain, the statistical features cannot be obtained exactly, but integralrange techniques make it possible to predict how much the TI should be extendedto approximate them up to a prespecified precision. Moreover, one can take advan-tage of extending the TI to reduce the number of disruptions in the execution of thealgorithm, which arise when no conditioning template can be found in the TI