The changing structure of a city: temporal changes in cubic spline urban density patterns

"Using the basic summary of urban structure given by the population density function, this paper estimates changes which have occurred in the structure of the Detroit [Michigan] metropolitan area during the past two decades. Both overall density changes and direction-specific changes are estimated using census data and the method of cubic spline regression. The results give more revealing insight into the structural changes which have occurred in the city than has been possible with traditional models of urban population density."