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Matching of images and analysis of shape differences is traditionally pursuedby energy minimization of paths of deformations acting to match the shapeobjects. In the Large Deformation Diffeomorphic Metric Mapping (LDDMM)framework, iterative gradient descents on the matching functional lead tomatching algorithms informally known as Beg algorithms. When stochasticity isintroduced to model stochastic variability of shapes and to provide morerealistic models of observed shape data, the corresponding matching problem canbe solved with a stochastic Beg algorithm, similar to the finite temperaturestring method used in rare event sampling. In this paper, we apply a stochasticmodel compatible with the geometry of the LDDMM framework to obtain astochastic model of images and we derive the stochastic version of the Begalgorithm which we compare with the string method and anexpectation-maximization optimization of posterior likelihoods. The algorithmand its use for statistical inference is tested on stochastic LDDMM landmarksand images.

String Methods for Stochastic Image and Shape Matching