Voronograms are a primitive form of nonparametric regression intended to explore edge detection methods. Given scattered data on the plane, the idea is to fit piecewise constant functions defined on the Voronoi tessellation. I was motivated to revive an 2004 R package for this by some recent conversations about total variation smoothing with Ryan Tibshirani and one of his students. The package is linked here. The idea was an off-shoot of work with Ivan Mizera on triograms which were intended to fit quantile surfaces using a roughness penalty that corresponded to total variation of the gradient of the fitted function on the Delone triangulation of a sample of scattered points. Triograms are piecewise linear with breaks in the gradient along the edges of the triangulation. In contrast Voronograms are piecewise constant with breaks in the function itself across edges of the Voronoi tessellation. Examples appear in the figure below which can be reproduced by the command demo(tseg) in the R package. As usual there is a lambda parameter that controls the strength of the penalization.
