Topological Relations Between Objects Are Categorically Coded

How do individuals compare images-for example, two graphs or diagrams-to identify differences between them? We argue that categorical relations between objects play a critical role. These relations divide continuous space into discrete categories, such as "above" and "below," or "containing" and "overlapping," which are remembered and compared more easily than precise metric values. These relations should lead to categorical perception, such that viewers find it easier to notice a change that crosses a category boundary (one object is now above, rather than below, another, or now contains, rather than overlaps with, another) than a change of equal magnitude that does not cross a boundary. We tested the influence of a set of topological categorical relations from the cognitive-modeling literature. In a visual same/different comparison task, viewers more accurately noticed changes that crossed relational category boundaries, compared with changes that did not cross these boundaries. The results highlight the potential of systematic exploration of the boundaries of between-object relational categories.