Visual Search Task Reveals Categorical Representation of Topological Spatial Relations Between Objects

Geometry provides a rigorous mathematical framework for understanding the spatial relations between objects. Topological properties are regarded as among the most fundamental invariants in geometry. To investigate how the visual system represents topological structures (e.g., inside/outside relations, connectivity), the current study employed the visual search task and visual stimulus sets designed by varying the distance between two objects equally. Results showed that task performance improved when the difference in object relations crossed category boundaries defined by topological properties. The study excluded the influence of potential confounding factors, such as the perceived depth caused by occlusion (experiments 1a and 1b). Furthermore, when the relevant inside/outside topological category boundary was removed, performance varied systematically with metric distance (experiment 1c). The categorical advantage was further observed across different modes of connectivity (experiments 2a, 2b, and 2c). These findings provided evidence for the categorical representation of topological spatial relations in visual perception.