  Smoothing is often used to improve the readability and interpretability of
noisy areal data. However there are many instances where the underlying
quantity is discontinuous. In this case, specific methods are needed to
estimate the piecewise constant spatial process. A well-known approach in this
setting is to perform segmentation of the signal using the adjacency graph, as
does the graph-based fused lasso. But this method does not scale well to large
graphs. This article introduces a new method for piecewise-constant spatial
estimation that (i) is fast to compute on large graphs and (ii) yields sparser
models than the fused lasso (for the same amount of regularization), giving
estimates that are easier to interpret. We illustrate our method on simulated
data and apply it to real data on overweight prevalence in the Netherlands.
Healthy and unhealthy zones are identified which cannot be explained by
demographic of socio-economic characteristics. We find that our method is
capable of identifying such zones and can assist policy makers with their
health-improving strategies. The implementation of our method in R is publicly
available at github.com/goepp/graphseg.
