Given a set of lines, line grouping considers the problem of deciding which lines are likely to belong to the same object or to a set of similar objects, before any recognition of objects has actually taken place. Vision scientists have suggested a number of factors that may be involved in the grouping process of lines, among which proximity, parallelism and collinearity are the easiest to quantify. These properties have often been measured by empirical estimates. Previous work, however, has shown that it is also possible to follow a more systematic approach based upon the uncertainty of pixel positions. Thus we can give precise definitions regarding the parallelism, collinearity or concurrency of lines whose parameters are only known to lie within given regions in the parameter space of lines. In this work we generalize this framework and show how it can be used during an entire line grouping process.