STOverlaps

STOverlaps is a measure used in spatio-temporal analysis to quantify the amount of overlap between two or more objects whose extents change over time. It captures how much space and time two phenomena share on a common timeline and is used in fields such as geographic information systems, ecology, and traffic analytics.

Formally, let A and B be spatio-temporal objects with time intervals [t0_A, t1_A] and [t0_B, t1_B], and spatial footprints S_A(t) and S_B(t) for each time t in the overlap of their lifespans. The unnormalized spatio-temporal overlap is O(A,B) = ∫_{t = max(t0_A,t0_B)}^{min(t1_A,t1_B)} area( S_A(t) ∩ S_B(t) ) dt. If time is discretized into steps Δt, this becomes a sum over t of area( S_A(t) ∩ S_B(t) ) Δt. The overlap can be normalized by dividing by the area of the union, O_norm(A,B) = O(A,B) / ∫ area( S_A(t) ∪ S_B(t) ) dt, or by alternative normalizations such as O(A,B) divided by the total activity of one object.

Variants include IoU-like measures in spacetime or existence predicates that indicate only whether a nonzero overlap occurs. In practice, STOverlaps can be computed on rasterized grids, polygonal footprints, or via bounding volumes, and may be evaluated exactly or approximately depending on data resolution and performance constraints.

Applications include monitoring motion co-occurrence, detecting interacting events, clustering moving objects, and supporting spatio-temporal querying. Related concepts include the Jaccard index and Intersection over Union generalized to the spacetime domain.