Cool Fusion Statistical Modelling for Data Fusion

ABSTRACT The consequences of the use of probability in modelling under uncertainty are explored, and it is shown how data and parameter independence and likelihood modularity emerge as desirable properties for statistical models. They lead directly to multi-object models which themselves create the association problem. The expectation-maximisation (EM) technique is introduced and then applied to discriminative training of a Gaussian mixture model classi er. Generalised training is introduced which interpolates between the extremes of maximising discriminative and non-discriminative likelihoods. A generalisation of EM, the conditional expectation-maximisation process is presented, and applied to designing an algorithm for estimating the location and rotation parameters for transforming a 3D reference model to generate an observed x-ray image. The EM E-step is derived for the case in which the nuisance variables (\missing data") are divided into sets and integrated out separately. This compact result is the basis of the application of EM to hierarchical problems. The object pose algorithm, above, is extended to include uncertain association between image features and control points on the reference object. The key design problem in data fusion is identi ed as designing the structure of the underlying statistical models, and the present capability to infer multi-object models is brie y reviewed.