Bivariate density estimation using BV regularisation

The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the taut-string algorithm which provides adequate approximations with a small number of local extrema is generalised for analysing two- and higher dimensional data, using Delaunay triangulation and diffusion filtering. Results are based on equivalence relations in one dimension between the taut-string algorithm and the method of solving the discrete total variation flow equation. The generalisation and some modifications are developed and the performance for density estimation is shown.