Measuring global and local spatial correspondence using information theory

The evaluation of spatial correspondence between binary objects resulting from a segmentation step performed by two different observers or methods is a critical part of the validation of a segmentation criterion or technique. Several global measures of correspondence have been previously proposed, but all of them assume a one-to-one correspondence between objects, thus failing to address local problems such as the splitting of an object by one of the observers. Moreover, such global measures do not distinguish between the reference and the observed objects and most of them lack a solid theoretical foundation. In this paper, we introduce a set of spatial correspondence indices that can evaluate global (many-to-many), local (many-to-one) and individual (one-to-one) spatial correspondence between observed and reference objects and vice versa. The proposed measures, derived from applying information theory concepts to the problem of spatial correspondence, are shown to be well-behaved and suitable to be used in medical imaging applications.