What I built
Adapt edge-detection logic to measure a boundary between two populations.
Computer-vision edge detection finds places where values change sharply across an image. I adapted that gradient logic to smoothed maps of Census population density, then added two sociological requirements: both racial populations must be locally present, and one must become more common as the other becomes less common nearby.
- 01Enough local population
A pair needs enough local population density to make the interface interpretable.
- 02Both groups present
The score is strongest when both groups are locally present, not when one is nearly absent.
- 03Opposing change
The two smoothed population-density maps must change in opposite directions rather than move together at a general population edge.
Formula and variables
P = (dA + dB) / (dA + dB + τ)M = 4p(1 − p)A = max(0, −∇log dA · ∇log dB)dA and dB are the two groups’ local population densities; p is group A’s share of the pair; τ is the low-density support constant. A gradient describes the direction and rate at which local population density changes.
Compared with segregation
A boundary measure answers a different question than a segregation index.
A segregation index summarizes how unevenly groups are distributed across a city or region. The Sharp Boundary Index maps where two specific racial populations meet sharply.
One summary for a larger area such as a city or commuting zone.
A local, pairwise score that can be mapped across small Census areas.
White, Black, Hispanic, and Asian population-density maps produce six racial pairs. The racial pair with the highest valid score is assigned to each Census block group, allowing different racial interfaces to characterize different parts of the city.
Chicago map
Map Chicago’s strongest local racial interfaces.
Color ranks each block group’s highest pairwise score within Chicago; black outlines mark travel communities.