Probabilistic feature-labelling schemes: Modelling compatibility coefficient distributions

In previous work, we have developed a probabilistic method for labelling of 2D geometric features. One of the requirements of this method is the provision of a probability distribution for the measurement errors when generating the compatibility coefficients. This distribution has hitherto been specified heuristically, and a training stage was needed to establish the distribution covariances. In this paper, we develop an improved error model. Using as a basis the error distributions of the feature measurements, we find the distributions for the compatibility coefficients by propagating the covariances of the feature measurement errors through into the calculation of the coefficients. A means of explicitly modelling small scaling errors is also included. The most important consequence of this development is that the training stage is no longer required to generate the error distributions for the compatibility coefficients. In addition, the distributions that are generated by the process described in this paper are tailored to fit the individual sets of feature relations, instead of being a compromise over all the sets of relations. As a result, we obtained better results compared with those obtained using the heuristic distributions.