We present a specification of the problem of combining evidence that arises in the approach to consistent object-labelling known as probabilistic relaxation. This specification differs from others in several important respects. Firstly, we ensure internal consistency by distinguishing between directly and indirectly interacting objects. Secondly, we avoid certain problems of interpretation and meaning by regarding the iterative updating of probabilities as a filtering process on the measurements for objects. Finally, we overcome the problem of the exponential complexity of the resulting evidence combining formula by deriving practical support functions of at most polynomial complexity. The computational realisation of the advocated approach to combining evidence is demonstrated for the application of edge labelling. This application includes details of how both the measurement generation process and the world-model may be expressed probabilistically and what the advantages are to be gained from using different forms of support-function.