Adaptation of multiscale function extension to inexact matching. Application to the mapping of individuals to a learnt manifold

International audience; This paper targets the specific issue of out-of-sample interpolation when mapping individuals to a learnt manifold. This process involves two successive interpolations, which we formulate by means of kernel functions: from the ambient space to the coordinates space parametrizing the manifold and reciprocally. We combine two existing interpolation schemes: (i) inexact matching, to take into account the data dispersion around the manifold, and (ii) a multiscale strategy, to overcome single kernel scale limitations. Experiments involve synthetic data, and real data from 108 subjects, representing myocardial motion patterns used for the comparison of individuals to both normality and to a given abnormal pattern, whose manifold representation has been learnt previously.