Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Computational Statistics & Data Analysis
Density estimation under qualitative assumptions in higher dimensions
Journal of Multivariate Analysis
Tube Methods for BV Regularization
Journal of Mathematical Imaging and Vision
SIAM Journal on Numerical Analysis
Taut-String Algorithm and Regularization Programs with G-Norm Data Fit
Journal of Mathematical Imaging and Vision
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
Nonparametric Functional Data Analysis: Theory and Practice (Springer Series in Statistics)
The Equivalence of the Taut String Algorithm and BV-Regularization
Journal of Mathematical Imaging and Vision
Smooth functions and local extreme values
Computational Statistics & Data Analysis
Nonparametric density estimation and clustering in astronomical sky surveys
Computational Statistics & Data Analysis
Computational Statistics & Data Analysis
A Variational Framework for Region-Based Segmentation Incorporating Physical Noise Models
Journal of Mathematical Imaging and Vision
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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.